Today we are looking at quarter-end funding pressure, and at whether it shows up in the rate everyone uses to measure it. Across the twenty-five ordinary quarter-ends in the SOFR record, the median spread between SOFR and the policy floor on the turn date is exactly zero basis points. Against ordinary month-ends the difference is 3.01 basis points with a p-value of 0.217. On the number that gets quoted, quarter-end is not a thing.

The same days, measured in the upper tail of the same distribution, look completely different. A quarter-end roughly doubles the dislocation there, and unlike the level result, it survives dropping September 2019. It scales with reserve scarcity: each percentage point lower on reserves as a share of bank assets raises it about 39%. The largest reading in the sample is not September 2019 either. It is June 2019, when the quoted rate ranked it sixth of twenty-five, unremarkable.

Let’s dive right in.

Introduction

The standard account of quarter-end in funding markets is that balance sheet constraints bind on reporting dates, dealers pull back from intermediating repo, and the overnight rate spikes. September 2019 is the canonical illustration. The mechanism is right. The question is where you can see it.

SOFR is a volume-weighted median. The New York Fed publishes it alongside the first, twenty-fifth, seventy-fifth, and ninety-ninth percentiles of the same day’s transactions, and the median is the only one of those numbers that gets quoted. On a normal day the choice does not matter much. On a turn date it matters enormously, because the marginal borrower who cannot find balance sheet is not transacting at the median. They are transacting in the tail, and the tail is a different series with different behavior.

I want to be careful about what follows. This is not a trading strategy, and there is no instrument at the end of it. It is a measurement argument: a widely discussed phenomenon has been evaluated with the wrong statistic, and the right statistic tells a cleaner story about reserve scarcity than the wrong one does.

Data and Methodology

Everything here comes from two sources. The New York Fed’s markets API publishes SOFR, the tri-party and broad general collateral rates, and the effective fed funds rate, each with the full percentile distribution and daily volume, from 3 April 2018. FRED supplies interest on reserves, overnight reverse repo balances, reserve balances, the Treasury General Account, and total commercial bank assets. No API key is required for either.

Two construction choices drive most of what follows, and both are worth stating plainly.

Turn dates come from the observed rate calendar, not a calendar offset. Roughly a third of quarter-ends fall on a weekend and settle on the prior business day. Using MonthEnd or QuarterEnd offsets misaligns those, and since the effect is concentrated in a two or three day window, misalignment destroys it. I label every trading day by its position in the published SOFR series and define the turn window as one business day either side of the last observed trading day of the period.

The premium is measured relative to the ambient level, not to the policy floor. This one changed the whole analysis. When reserves are scarce, SOFR trades above the floor every day of the month, not only at turns. A model that regresses the raw turn-date spread on reserve scarcity will score well by predicting the ambient level while explaining nothing at all about the turn. So for each turn I compute the median spread over a reference window spanning twenty to five business days before and five to twenty business days after, and subtract it. What remains is the part specific to the turn date.

The correlation between the raw turn-date spread and the ambient level is 0.778. Most of what looks like quarter-end pressure in the unadjusted series is simply the funding regime you happened to be in that quarter.

The sample runs from April 2018 to August 2026 and contains twenty-five ordinary quarter-ends, sixty-seven ordinary month-ends, and eight year-ends. Year-ends are held out of every model and reported separately, because G-SIB scoring is a point-in-time measurement on 31 December and pooling them contaminates both groups. Twenty-five observations is a small sample, and I will come back to what that rules out.

Predictors are read five business days before each turn, using only vintages published by then. Reserve balances and bank assets are weekly for the week ending Wednesday and appear in the H.4.1 the following Thursday, so the code enforces that Wednesday W is not available until W+1 rather than merging on nearest date. The reserve ratio is reserve balances as a percentage of total commercial bank assets, which ranges from 7.99% at the September 2019 blowup to 19.26% at the peak of the abundant-reserve period, and sits at 11.48% today (the most recent reading).

Results

Here is the level measure, and it is a null result.

The turn-specific excess averages 7.58 basis points at quarter-ends and 4.57 at ordinary month-ends. The difference is 3.01 basis points with a Welch p-value of 0.217 and a Mann-Whitney p-value of 0.177. Neither test comes close to conventional significance. On the raw unadjusted spread the picture is worse: the quarter-end mean is 2.16 basis points, the median is exactly zero, and twelve of the twenty-five quarter-ends printed a negative spread, with SOFR below the floor.

Pooling quarter-ends and month-ends into a single regression with a quarter-end dummy, controlling for the reserve ratio and overnight reverse repo balances, gives a dummy of +3.33 basis points at p=0.034. That looks like a result until you remove September 2019, at which point it falls to +1.86 and p=0.163.

Fitting the excess on reserve scarcity gives an in-sample R-squared of 0.346 and a leave-one-out R-squared of 0.091. Removing September 2019 takes the reserve coefficient from −2.02 to −0.91 and its p-value from 0.014 to 0.136. Restricting to 2020 onward, which is the regime anyone would actually care about, the leave-one-out R-squared goes negative, at −0.195. Worse than predicting the sample average.

September 2019 has a Cook’s distance of 1.011 and a studentized residual of 4.76. Those are not the numbers of an influential observation. They are the numbers of a different data-generating process that happens to be sitting in the sample.

The level measure says quarter-ends are not special, the relationship with reserves is one repo crisis, and nothing here supports a forecast. But the percentile columns say otherwise.

Read more

Let’s get into it.

Fifteen Minutes Before the Close

The 4:00 PM close, the timestamp the entire derivatives industry marks its books against, has quietly become the worst fifteen minutes of the day to measure volatility.

Two identical measurements, fifteen minutes apart. The researchers built the same at-the-money, shortest-maturity implied volatility measure twice a day, once at 3:45 and once at the bell, using identical filters. The 3:45 version produces a usable number on 99.8% of trading days. The closing version works on 36.5%.

Figure 1: Correlation between each implied volatility signal and the next day's realized variance, by year. Same options, same selection rules, fifteen minutes apart.

Blame 0DTE options, which now account for much of the near-the-money volume and carry essentially zero remaining time value by market close, leaving the conversion from option price to implied volatility unstable or outright impossible. A wide gap in usefulness follows. Next-day realized volatility barely responds to the raw closing series, while the 3:45 series moves with it. On days when the close does return a real figure, that figure predicts perfectly well, which points to a broken thermometer rather than a market with nothing to say. Running the whole surface through a convolutional network adds accuracy, though a plain EGARCH stays annoyingly hard to beat. In the authors' words, “a later timestamp is not necessarily a better volatility signal.” Risk systems and valuation models fed by closing marks absorb that noise daily.

Clark, Brian J. and Palepu, Sai and Potì, Valerio and Siddique, Akhtar R., Last Fifteen Minutes: Equity Options Volatility at the Close (August 13, 2026). Available at SSRN: https://ssrn.com/abstract=7279624 or http://dx.doi.org/10.2139/ssrn.7279624

Borrowed Elasticity

Hedge funds hardly react to what it costs them to borrow a bond, because the size of the position was settled somewhere else entirely.

Insurers and pension funds routinely want more government bonds than actually exists. The gap gets filled by hedge funds, who sell the bond short and borrow it in the repo market so they can deliver it. Working from regulatory data on every repo backed by German government debt, the authors show that these borrowers barely respond to the price of borrowing. Push the borrowing cost up 10% and their borrowing falls roughly 1%.

Figure 2: Same investors, opposite behavior. Each dot is one type of institution, plotted by how much its bond buying responds to price against how much its bond borrowing responds to price. Hedge funds, the bulk of the “foreign” dot, sit in the bottom right corner.

Strange, given that the same funds are among the twitchiest buyers in the cash bond market. What explains it is that the repo leg was never a decision in the first place. It is machinery supporting a short whose size somebody else's appetite for the physical bond had already determined. The adjusting happens on the lending side instead, largely at the German debt office and the ECB. Investors can take two things from this. Repo specialness (what you pay to borrow one particular bond) doubles as a real time pressure gauge on the cash market, and whoever sets the marginal price in Europe's safe asset funding market is sitting offshore, well past the reach of any European supervisor.

Poinelli, Andrea and Pelizzon, Loriana and Tomio, Davide and Nguyen, Benoît and Linzert, Tobias, Elastic in Cash, Inelastic in Repo: Hedge Funds in the Treasury and Repo Markets (August 07, 2026). SAFE Working Paper No. 492, Available at SSRN: https://ssrn.com/abstract=7258361 or http://dx.doi.org/10.2139/ssrn.7258361

Funding-Technology Feedback in the AI Buildout

The AI financing loop is close to the point where a shock stops fading and starts feeding itself, and the weak link is the leveraged miners, not NVIDIA.

Cao and Huang model the 2026 compute buildout (NVIDIA funding OpenAI, OpenAI committing to Oracle capacity, bitcoin miners pivoting into GPU colocation) as a circuit where a funding freeze blocks the next hardware refresh, obsolescence craters the collateral behind the debt, and the freeze deepens.

It reduces to one number: how much distress returns to a borrower after one lap around the loop. Below one it dies out, above one it compounds. Their reference scenario lands at 0.98, and two defensible corrections (refusing to count intra-loop revenue as a real buffer, adding idle capacity from weak demand) push it past 1.4.

The useful part is where the fragility sits. Cutting NVIDIA out of the graph barely moves the index, removing the capital-constrained miner cohort moves it a lot, and netting every bilateral exposure does almost nothing, because the binding loop lives inside one balance sheet rather than between two.

Figure 3: Removing NVIDIA from the network barely changes the system's fragility score. Removing the leveraged miner cohort does.

The authors call these “scenario-conditioned structural diagnostics,” not measurements. Still, the watch list they imply is utilization and the weakest GPU-backed borrowers, not the vendor everyone already monitors.

Cao, Zeyu and Huang, Shaosai, Stability of Compute-Capital Networks: Funding-Technology Feedback and Scenario Diagnostics (July 25, 2026). Available at SSRN: https://ssrn.com/abstract=7295260 or http://dx.doi.org/10.2139/ssrn.7295260

ESG Ratings vs. Portfolio Decarbonization

ESG ratings tell you almost nothing about which companies in a sector actually emit less per dollar of revenue.

Hwang and Patatoukas rank S&P 500 firms against their own sector peers on both ESG scores and carbon intensity (emissions per dollar of revenue), and find the two rankings barely relate. The environmental pillar, which you would expect to be the exception, tracks the composite score so closely that it is effectively the same measure. What drives that pillar explains why: two process indicators, one covering the quality of environmental disclosure and one covering how climate risk is framed in strategy, account for most of the variation. Firms are scored on how well they report and position, not on what they emit.

Figure 4: Average annual financed emissions per $1M invested, 2017 to 2024. Recreated from Table 10 (Panel A) of Hwang and Patatoukas (2026). Both tilted indices hold the same sectors in the same proportions as the S&P 500; only the within-sector weights change.

The part that should worry investors is what this does to a portfolio. An index tilted toward carbon-efficient firms cut financed emissions by 43% and matched the market's return. An index tilted toward high ESG scores raised emissions by 10% instead, because the highest scorers tend to be the biggest companies in each sector, and bigger companies emit more in absolute terms regardless of efficiency. As the authors put it, “sustainability ratings and sustainability performance are not the same thing.” If you hold an ESG fund for climate reasons, the label and the outcome are separate purchases.

Patatoukas, Panos N. and Hwang, Jinsung, ESG Ratings Undermine Portfolio Decarbonization. Available at SSRN: https://ssrn.com/abstract=7301860 or http://dx.doi.org/10.2139/ssrn.7301860

This week for paid subscribers

This week for paid subscribers: Paid subscribers are replicating the 2024 Polymarket lead-lag, rebuilding the 34-asset Trump-trade portfolio and testing whether prediction market moves predicted next-day returns in banks, rates, and FX. This post covers turning a noisy directional signal into a percentile-ranked position, a placebo panel that rules out broad equity beta, and where the replication diverges from the paper. Python backtest code included.

Alpha in Academia

The Odds Lead the Tape

Read more

8 days ago · 7 likes · Alpha in Academia

Disclaimer: The content provided in this newsletter, "Alpha in Academia," is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Today, we are taking inspiration and guidance from a new paper by Goldstein, Li, and Wang. This explores the 2024 U.S. presidential election, where changes in Polymarket’s Trump probability predicted next-day returns on Trump-sensitive assets by roughly 13 basis points per percentage point of movement, with a simple long-short strategy earning a Sharpe of nearly 2. We tested it. The lead-lag is real, the placebo is clean, and the story it tells about prediction markets is more interesting than the trading signal it produces.

Let’s dive right in.

The Setup

Prediction markets are supposed to be information aggregators. People bet real money on future outcomes, and the resulting prices, in theory, distill dispersed information into a single number. That number is useful only to the extent that other people look at it and act on it. This paper asks a specific version of the question about whether people look at it. During the 2024 U.S. presidential election, did traders in traditional financial markets watch Polymarket, and did they trade on what they saw?

The authors examine daily changes in the Polymarket Trump-YES probability and test whether those changes predict next-day returns on a portfolio of assets that market commentary flagged as sensitive to Trump’s electoral prospects. Their answer is yes. A one percentage point increase in Trump’s implied probability was associated with about 13 basis points of next-day return on the Trump-trade basket, statistically significant and economically meaningful.

The identification challenge is the usual one. Both markets might be reacting to the same underlying news, with Polymarket happening to move first. To distinguish real cross-market learning from sequential news arrival, the authors exploit on-chain wallet-level data to classify individual Polymarket traders as informed or uninformed based on their post-trade profitability. They then show that price impact from uninformed trades also propagates to traditional markets before partially reversing. Since noise cannot reflect fundamental information, its transmission establishes that traders in equities and currencies are genuinely extracting signals from Polymarket prices, not just responding to the same news feed at a lag.

For our test we focus on the price-level analysis in the paper’s Section 3. Wallet-level classification requires pulling and processing the full universe of on-chain Polymarket transactions, which is a separate exercise. What follows uses public price data from the Polymarket CLOB API and daily returns from yfinance for the 34 signed Trump-trade assets.

Figure 1. Polymarket-implied probability of a Trump win, January through November 2024. Key events annotated.

The Trump Trade Portfolio

The paper’s Trump-trade portfolio is not a factor model. It is a narrative-based classification. The authors reviewed contemporaneous financial media, primarily Bloomberg, the Wall Street Journal, and the Financial Times throughout 2024, and cataloged the assets that analysts and commentators repeatedly identified as exposed to Trump’s electoral prospects. The result is a portfolio of 34 assets across five categories: broad equity ETFs, bond ETFs, six large bank stocks, currencies and commodities, and a small “Connected” set consisting of Trump Media, Phunware, and Tesla.

Each asset gets a directional sign based on whether it would benefit or suffer from a Trump victory. Bank stocks and equity ETFs go long on the expectation of tax cuts and financial deregulation. Treasury bonds go short on the expectation of fiscal expansion and inflation. The dollar goes long against foreign currencies, reflecting tariff policy. Bitcoin, Ethereum, and gold go long. The three Connected names go long as direct campaign-linked equities.

Once we sign each asset’s return in the expected direction, the paper’s construction implies that if the market genuinely tracks Trump’s odds, all five categories should trend up together as those odds rise, and down together as they fall. This is exactly what we see in the data.

Figure 2. Cumulative signed returns by asset category. Each category is equal-weighted across its constituents.

The Connected category is extraordinary, mostly driven by DJT’s post-merger volatility, but the more instructive pattern is the broad co-movement of the other four categories through the second half of the year. Bank stocks, equities, and the dollar basket climb together as Trump’s implied probability rises from roughly 45 percent in April to over 60 percent by early July, then move sideways after the Biden withdrawal, then accelerate together into the election. Bonds are the mirror image, drifting slightly negative on the signed basis. This is a real portfolio-level exposure to a single political factor, and it makes the lead-lag test meaningful.

Read more

Let’s get into it.

Private Equity's "Free Lunch" Was Just a Pricing Illusion

When you value buyout funds at real market prices instead of sponsor-reported estimates, their famous risk-adjusted outperformance disappears entirely.

Private equity has long sold itself as the rare asset that beats stocks while smoothing out the ride, low volatility, low correlation, better returns. This paper tests that claim using a clever workaround: a set of buyout funds that trade on European stock exchanges, giving researchers both the official NAV (the fund’s own periodic self-appraisal) and the actual price investors are willing to pay for the same assets, every day. The gap is striking. Priced at NAV, these funds look tame, with volatility close to public stocks. Priced at market, volatility jumps to 29%, correlation with stocks climbs to 0.94, and beta lands around 1.5, meaning these funds are about 50% more volatile than the market, not less. Once that real risk is accounted for, the outperformance vanishes, with alpha statistically indistinguishable from zero.

The authors frame it plainly: NAV-based accounting lets buyouts “appear to generate significant alpha” that isn’t really there. For investors leaning on private equity as a smoother, higher-returning complement to stocks, this is a reason to check whether that cushion is real or just an artifact of how infrequently the assets get marked to market.

Ennis, Richard and Rasmussen, Daniel, Buyout Performance with Assets Valued at Market (July 01, 2026). Available at SSRN: https://ssrn.com/abstract=7157298 or http://dx.doi.org/10.2139/ssrn.7157298

Is Volatility Really "Rough"?

A new model suggests the popular “rough volatility” framework may be forcing two separate questions, how choppy volatility looks up close and how long its memory lasts, into a single number, and separating them changes the picture.

For the past decade, quants have modeled market volatility as “rough,” meaning it looks jagged and unpredictable at short timescales, using a single parameter (the Hurst index) borrowed from fractal math. This paper argues that parameter is secretly doing two jobs at once, setting both how volatility scales over time and how much it remembers its own past, when those are logically different properties. Borrowing a tool from physics (originally used to model particles bouncing around in fluids), the author builds a more flexible framework that lets memory and scaling move independently. Testing it on real order book and stock data, two of the model’s predictions hold up clearly: volatility’s memory decays slowly rather than instantly, and there’s a measurable asymmetry where past price moves predict future volatility more than the reverse.

The short-term “roughness” question, though, turns out to be essentially unmeasurable with current data, neither confirmed nor ruled out. For traders and risk modelers, this matters because it suggests some volatility models may be more constrained than the data actually requires, and that memory in markets is a real, testable phenomenon rather than just a curve-fitting trick.

Itkin, Andrey, Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation (July 29, 2026). Available at SSRN: https://ssrn.com/abstract=7202798 or http://dx.doi.org/10.2139/ssrn.7202798

When the Spread Doesn't Come Back: The Math of Knowing When to Stop

Capping your position size in a pairs trade doesn’t just limit your losses, it actually changes the optimal trade itself, because a smart investor starts hedging against future limits before they ever get hit.

Pairs trading lives and dies on one assumption: that two related stocks, after drifting apart, eventually snap back together. This paper asks the uncomfortable question that assumption usually skips over, what happens when they don’t. The author builds a formal model where a trader sets hard position limits on both legs of the trade, then solves for the mathematically optimal strategy under those limits. The twist is that this constrained strategy isn’t just the unconstrained strategy clipped at the edges. Anticipating that limits might bind later, the optimal trader adjusts positions earlier than you’d expect, even while still comfortably within bounds.

Tested on Ford and GM stock from 2022 to 2024, a period where their prices diverged and stayed diverged, the constrained strategy lost about 70 dollars per unit of capital versus roughly 280 for the unconstrained version. The takeaway for anyone running a spread trade: sizing discipline isn’t just risk management bolted on afterward, it should shape the trade from day one.

Chen, Ziyi, Optimal Pairs Trading with Position Constraints (July 30, 2026). Available at SSRN: https://ssrn.com/abstract=7205360 or http://dx.doi.org/10.2139/ssrn.7205360

Can the Shape of a Probability Curve Predict a Crash Before Volatility Does?

A new early-warning model that reads the geometry of market volatility, not just its size, flagged the COVID crash and the 2022 rate-hike selloff an average of 18 days before a standard volatility filter did.

Most volatility models, including the classic Markov regime-switching approach used across the industry, work by waiting for enough big price swings to pile up before declaring that markets have shifted into a stressed state. That’s inherently reactive. This paper tries something different, borrowing a tool from topology (the math of shapes and connectivity) to track how the pattern of a volatility signal reorganizes itself in the days before a real shift, not just how big it gets. Applied to JPMorgan stock and the S&P 500 from 2020 through 2024, this topological layer detected the two biggest volatility events of that period nearly three weeks earlier than the standard model, and the signal was statistically unrelated to VIX or realized volatility, meaning it’s genuinely picking up something different rather than just repackaging existing data.

The catch is that this early-warning system throws a lot of false alarms, roughly seven flagged windows out of ten turn out to be nothing, so it’s built to work as a tripwire that prompts a closer look, not a system that trades on its own. For risk managers and active investors, that tradeoff, faster warning bought with more noise, is worth understanding before leaning on any signal that claims to see trouble coming early.

Faris, Mahrus, Early-warning Volatility Regime Detection in Equity Markets: A Combined Markov Switching and Persistent Homology Approach (July 20, 2026). Available at SSRN: https://ssrn.com/abstract=7206123 or http://dx.doi.org/10.2139/ssrn.7206123

This week for paid subscribers

Paid subscribers are watching the G10 currency carry trade erase two decades of calm-regime gains across high-volatility selloffs, then testing whether an implied equity volatility filter can predict those crash regimes in advance. It isolates the funding-driven unwinds that destroy the trade and is blind to the basket’s own realized volatility, with a simple 80th-percentile threshold turning a zero-Sharpe basket into a 0.32 net Sharpe. Python backtest code included.

Disclaimer: The content provided in this newsletter, “Alpha in Academia,” is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Today we are looking at the G10 currency carry trade, and at the ETF that existed to sell it to retail investors between 2006 and 2023. Rebuilt from free data, the basket returned 0.74% annualized over nineteen and a half years on 9.8% volatility, which is a Sharpe ratio of 0.07. Taking realistic costs into consideration, it returned nothing at all.

That number is an average of two regimes that happen to cancel. In the calmest fifth of the sample, the basket earned 4.8% annualized, whereas in the most stressed fifth, it lost 15.6%. The stressed regime can be identified in advance, but only with implied equity volatility. The basket’s own realized volatility tells you nothing useful, and realized equity volatility gets you about half way. There is also a construction quirk in the original index that turns out to have been hedging the crash risk by accident.

Let’s dive right in.

Introduction

Carry is the oldest trade in currency markets. Borrow where rates are low, lend where they are high, keep the spread. Uncovered interest parity says the high-yielding currency should depreciate by exactly the interest differential and leave you flat, and it does not, which is why the trade has a forty-year academic literature behind it.

The Deutsche Bank G10 Currency Future Harvest Index formalized it about as plainly as possible. Rank the G10 currencies by yield, go long the top three at a third of NAV each, short the bottom three the same way. Gross notional of 200%, rebalanced quarterly. The index was calculated back to March 1993 at a base of 100, and by July 25, 2007, it stood at 315.27.

In September 2006, an ETF launched to track it: DBV, the Invesco DB G10 Currency Harvest Fund. It ran for a little over sixteen years and was liquidated on March 10, 2023.

So the index tripled, then the product arrived, then nothing happened for sixteen years. That sequence is what this post is about. The question is not whether the carry premium exists in the data, because it does. The question is what it did during the only window in which an ordinary investor could have bought it.

Data and Methodology

Daily spot rates for the nine non-USD G10 currencies from Yahoo Finance, normalized to USD per unit of foreign currency so a rise always means the foreign currency strengthened. Three-month interbank rates from FRED’s OECD series. DBV, VIX and S&P 500 history are from Yahoo.

The sample runs from June 2006, where AUD spot history begins, to December 2025, where every currency still has published rate coverage.

Three construction choices, all taken from the fund’s final 10-K:

1. Ranking uses the previous month’s rate observation, lagged so that nothing in a given month depends on data published during it. The index actually ranked on a currency carry ratio (front-month futures over the three-month futures) rather than cash rates, and rebalanced quarterly rather than monthly. Interbank rates are observable live, so my lag is stricter than it needs to be.

2. The dollar is ranked but never traded. When USD lands in the top or bottom three, that leg is simply not established and gross exposure falls to about 1.67:1. This happened in 65.4% of months in the sample, which is more often than I expected, and it matters later.

3. Returns are excess returns: the spot move plus the interest differential against USD. DBV shareholders received excess return plus collateral income minus 0.78% in fees, so the comparison against the fund adds those back.

The Reconstruction Tracks the Fund

Before trusting any of this it needs to match the thing it claims to replicate.

Figure 1: The reconstruction net of fees against DBV’s actual returns over the fund’s listed life. Daily correlation is 0.29, which looks alarming until you notice it is a clock problem rather than a disagreement.

Over the fund’s life, the reconstruction returned −0.25% annualized against DBV’s −0.34%, on volatility of 10.5% against 12.1%, with daily skew of −0.64 against −0.86.

The daily correlation of 0.29 is a measurement artifact. Yahoo’s spot quotes are a 24-hour snapshot taken at an arbitrary time; DBV was a 4pm Arca close on futures that settled at 2pm. Different clocks. Aggregate the returns and the gap closes: 0.61 weekly, 0.88 monthly, 0.90 quarterly.

Twenty Years of Nothing

Here is the full sample.

Read the columns from left to right. The first is fourteen months, and it sits on the terminal blow-off of the largest carry run in modern history, so I am not going to use it for anything. The middle column is the fund's entire listed life. The one to its right is what happened after it closed: 1.4% annualized at a Sharpe of 0.26, and 2.3% at 0.40 once the accidental dollar position comes out.

Carry did not stop paying. It paid on either side of the window in which you could buy it. This shows that it is not underperformance against a benchmark. Over nineteen and a half years, the trade produced nothing, while taking a 37% drawdown and carrying negative skew the whole way. You held a left tail and were paid zero for it.

DBV tracked that faithfully. The fund was not the problem, and the fees were not the problem either. The strategy did this.

Figure 2: The reconstructed basket over the full sample. The shaded band is DBV’s entire life on the exchange, and the dotted line is the index’s all-time high in July 2007.

Zero is an Average

A twenty-year Sharpe of 0.07 invites the conclusion that carry stopped working, but I do not think that is what happened. Sort every day by where the VIX closed, cut it into quintiles, and the average falls apart immediately.

The premium is not missing. It is large, and then it is violently negative, and the two cancel. Four fifths of the sample pays, with the top fifth taking it all back. Volatility triples from Q1 to Q5, so the losses arrive levered as well as late.

The relationship is not monotonic, which is worth flagging rather than smoothing over. Q2 sits below Q1 in both the version I am showing and in the balanced version. The reliable statement is that the top two quintiles are where carry dies.

This is what “carry is short volatility” means in practice, and the claim deserves a proper test rather than an assertion. Regressing monthly returns on the monthly change in VIX gives a slope of −0.0017 with a t-statistic of −7.0. Adding a quadratic term, which tests whether the payoff bends the way a short option position does, gives a curvature coefficient with a t of −2.8 and adds 2.7 percentage points of R². Significant, and modest. The strong version of the short-volatility claim survives the test without running away with it.

Figure 3: Each point is one month. The slope says carry dislikes rising volatility, which nobody disputes. Only the curvature says the payoff is option-like, and that is the weaker of the two results.

So, can the destructive fifth of the sample be spotted in advance?

Read more

Let’s get into it.

Alpha from Mandelbrotian Prices

The most accurate option pricing model turned out not to be the most profitable one.

The authors ran five pricing models against S&P 500 option chains, then turned each into a simple trading rule: buy when the model says the market price is too low, sell when it says the market price is too high. On raw accuracy, classical Black-Scholes held up remarkably well, landing closest to actual prices across most medium and long dated contracts, which is a little annoying given how many of its assumptions are known to be false. But when those same models became strategies, Black-Scholes finished fifth out of nine. The winner was Mandelbrot's multifractal model, which treats prices as rough and self-similar rather than smoothly random, and which more than tripled starting capital in the backtest.

Figure 1: Every model-based strategy roughly tripled its starting capital. Buy-and-hold, momentum, and mean reversion finished essentially flat. Note that Black-Scholes, the most accurate pricer in most categories, sits mid-pack here.

The paper says it plainly, noting that “accuracy in option price calculation does not always translate” into trading results. The catch is that data limits confined the backtest to a single date in 2023, so read this as proof of concept, not verified edge. The broader lesson still holds, that the model that best explains yesterday's prices is not automatically the one that finds tomorrow's mispricings.

Bhattacharyya, Ritabrata and Goh, Zhi Hwee and Korovedzai, Rudairo Orpah and Chen, Jun-Han, Alpha Generation using Option Trading Strategies based on Modeling Options Prices considering Mandelbrotian Movement of Prices (July 21, 2026). Available at SSRN: https://ssrn.com/abstract=7154800 or http://dx.doi.org/10.2139/ssrn.7154800

ETF (Mis)pricing: Blame the Inventory

ETF prices drift from the value of their underlying holdings largely because the firms responsible for keeping the two aligned run into inventory limits, not because the underlying assets are broken.

Authorized Participants (the large trading firms permitted to create and redeem ETF shares) are supposed to arbitrage away any gap between an ETF's market price and the value of its basket. Using FCA regulatory data covering 128 UK listed ETFs from 2018 to 2022, the authors observe each firm's daily inventory directly for the first time, and the pattern is consistent. When an AP holds more ETF shares than it wants, it quotes cheaper prices to offload them, and the fund slips to a discount. The adjustment shows up almost entirely in the ETF price, while NAV barely responds.

Figure 2: Corporate bond ETFs, February to May 2020. Median price to NAV gap (black), spread across funds (bands), Fed and BoE interventions (vertical lines). The gap closes as policy eases dealer funding pressure.

The effect also splits by asset class, with equity ETFs more sensitive to inventory and bond ETFs more sensitive to unexpected order flow. APs sometimes take directional positions instead of correcting gaps immediately, which undercuts the assumption that arbitrage is instantaneous. For investors, this reframes premiums and discounts (bond ETFs moved over 5% from NAV in March 2020) as a read on dealer capacity rather than fund quality, since inventory practices “can exacerbate mispricing, particularly during periods of stress.”

Kraus, Wladimir and Kirilenko, Andrei A. and Linton, Oliver B. and Xiao, Mingmei, ETF (Mis)Pricing (May 25, 2025). Available at SSRN: https://ssrn.com/abstract=7143458 or http://dx.doi.org/10.2139/ssrn.7143458

Climate Attention and the Bond Market

Public curiosity about global warming, measured by Google searches, predicts higher returns on U.S. Treasury bonds over the following year.

The authors built a monthly index of worldwide searches for “global warming” and test whether it forecasts the excess return Treasuries earn over cash. It does, and not marginally. Higher search interest reliably precedes higher bond returns across maturities from two years all the way out to twenty four, and the relationship survives controls for the yield curve, the standard bond forecasting factors, and five separate uncertainty measures.

More impressively, the signal holds up out of sample, where most predictors quietly die, cutting forecast errors by roughly 15% against the historical average benchmark. The mechanism is less exotic than it sounds. Rising climate attention travels with expectations of a softer economy (weaker production, higher unemployment) and a tilt toward safer assets, so investors mark down the expected path of policy rates. The effect sits almost entirely in expected short rates rather than term premia, and it barely existed before the Paris Agreement. For investors, that suggests attention data can proxy for shifts in macro expectations before conventional indicators register them.

Yu, Deshui and Tang, Jiachen and Li, Luyang and Zhou, Mingtao, Climate Attention and Treasury Bond Risk Premia. Available at SSRN: https://ssrn.com/abstract=7203448 or http://dx.doi.org/10.2139/ssrn.7203448

Trading on Language Models Under Market Frictions

Large language models beat word-counting sentiment on financial news, but their edge lives almost entirely in the sentences where meaning depends on structure rather than vocabulary.

The authors push nearly a million firm specific news stories through six sentiment engines, from the classic Loughran McDonald word list to an 8 billion parameter LLaMA-3, then force every signal through the frictions an actual desk faces (trades happen only after the news was genuinely observable, positions pay spreads and costs, and no trade can exceed a tenth of a stock's daily volume). The word list barely beats a coin flip and loses money once turnover is paid for. The decoder models survive, with LLaMA-3 posting the strongest net long short performance in a test window chosen to sit after its own training cutoff.

On plainly worded news, a 1980s word list trails an 8 billion parameter model by 17 points. On contrastive clauses (revenue beat, guidance cut) the gap more than doubles to 37, and the word list lands below a coin flip. Sample of 1,200 test articles, coded by two annotators. Chart: Alpha in Academia. Data: Table 13, MFAST working paper (SSRN 7213792).

The more useful result is where that edge comes from. LLaMA-3's advantage over the dictionary is smallest on plainly worded headlines and roughly doubles on negation, contrastive clauses, and forward looking guidance, exactly the sentences where a revenue beat sits next to a guidance cut. It also widens in less liquid names. The lesson for investors is that reading comprehension, not model size, is the thing being sold, and that a signal only counts once costs and capacity are in the room.

Kirtac, Kemal, Financial Language Models as Applied Artificial Intelligence Systems for News-Based Trading under Market Frictions. Available at SSRN: https://ssrn.com/abstract=7213792 or http://dx.doi.org/10.2139/ssrn.7213792

This week for paid subscribers

Paid subscribers are watching the equity correlation matrix collapse onto a single factor across the 2008 and 2020 crashes, then testing whether that same fragility measure warns of a crash in advance. It forecasts the crisis that built up endogenously and is blind to the exogenous one, with the first sustained signal crossing fifteen months before Lehman. Python backtest code included.

Alpha in Academia

When correlations concentrate

Read more

22 days ago · 10 likes · Alpha in Academia

Disclaimer: The content provided in this newsletter, "Alpha in Academia," is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Today we will take a look at how when markets crash, the correlation matrix of the equity cross section collapses. The market factor absorbs a rising share of total variance and the effective number of independent factors falls sharply. This spectral concentration replicates cleanly across both the 2007-08 financial crisis and the 2020 Covid crash. But the same signal, run as a causal early-warning indicator, only forecasts the crisis that built up endogenously, and the exogenous shock is invisible to it in advance.

Let’s dive right in.

Introduction

Igor Halperin’s July 2026 paper introduces an approach called Observable Matrix Dynamics that tracks the equity cross section through the trajectory of a fixed-size distance matrix and its spectrum. We run two fixed-size matrix observables across the crisis decades using the current S&P 500 universe with daily adjusted closes, and the central empirical finding is that the correlation spectrum collapses onto the market factor at the 2008 and 2020 onsets.

A separate section tests whether these fragility signals actually forecast the crash they concentrate on, and finds that only the endogenously building 2008 crisis is predictable in advance.

“An endogenous fragility measure can forecast a crisis that grows out of the correlation structure itself, and cannot forecast an exogenous shock such as a pandemic, or a dispersed decorrelated unwind.”

Data & Methodology

The setup is a rolling Pearson correlation matrix on the S&P 500 cross section over a 504-day window, from which we extract the eigenvalues and read two summary statistics. The first is the market-factor share, the largest eigenvalue divided by the sum of all eigenvalues, which measures how much of total return variance is absorbed by the single largest common factor. The second is the participation ratio, defined as the square of the sum of eigenvalues divided by the sum of squared eigenvalues, which counts the effective number of independent factors. Both are standard diagnostics from the random matrix theory of correlation matrices, and both are known to move sharply at crisis onsets.

We compute these statistics across two crisis periods and average them over the calm year before onset and the first two months of the crash. The universe is current S&P 500 constituents with full history back to each period’s two-year pre-roll, filtered to 349 names for the 2007-08 window and 353 names for the Covid window. This universe is survivorship-biased by construction, which means 2008-era failures like Lehman, Bear Stearns, and Washington Mutual are absent from our sample. If anything this should understate the correlation stress at the 2008 onset, since the survivors are disproportionately the firms that made it through the crisis intact.

Read more

If you have been reading Alpha in Academia for a while, you will know that the Thursday posts tend to go a little further than the weekly paper summaries. Sometimes I implement a strategy. Sometimes I replicate a result, work through a model, or find that an interesting idea does not quite survive contact with the data.

This page is where all of that work lives. I have also included the research companions I have available. Depending on the investigation, that may mean code, a notebook, data, tests, or reference results. They are there if you want to rerun the work, change an assumption, or take the analysis in another direction.

If you find something I missed, get a different result, or have an idea you would like me to look at next, please let me know.

Read more

Let’s get into it.

The Stock Market Never Learns

Halperin borrows a tool from AI research to watch how the entire stock market’s correlation structure moves over time, and finds that unlike a neural network, the market never settles into a stable pattern, even decades after a crisis passes.

The core idea here is clever: treat the whole S&P 500 like a machine learning model in training, and watch whether its “internal representation” (the correlation structure between all 500 stocks) ever stabilizes the way a trained neural network’s does. It never does. Across three crises (the 2001 dot-com bust, 2008, and 2020), the market’s correlation geometry collapses in dimension during a crash, as everyone starts moving together, then partially unwinds afterward, but never settles into the kind of clean, learned structure you’d see in a model that’s finished training. Separately, Halperin ranks stocks by relative performance and volatility each day and tracks those rankings as their own systems. Performance rankings shuffle fast (a week), while volatility rankings are sticky (a month or more), and only the volatility ranking shows a real “arrow of time,” meaning it behaves differently forwards than backwards, flaring hardest at the 2002 and 2008 lows. For investors, the practical takeaway is: the correlation-based fragility signals only gave advance warning for 2008, the slow-building crisis. They were blind to Covid.

As Halperin puts it, the market is best read as an object that a crisis “drives further from equilibrium rather than toward a new one.”

Halperin, Igor, Observable Matrix Dynamics of Stocks (July 20, 2026). Available at SSRN: https://ssrn.com/abstract=7149898 or http://dx.doi.org/10.2139/ssrn.7149898

Why a Yen Funding Rate Half a World Away Moves the Price of U.S. Corporate Debt

Japanese banks fund roughly a quarter of America’s CLO market through yen-dollar swaps, and the cost of that swap, not U.S. credit conditions, is what actually drives pricing at the top of the capital structure.

Here’s the setup that makes this paper fun: Japanese banks, led by the agricultural cooperative bank Norinchukin (nicknamed “the CLO whale”), hold about a quarter of all AAA-rated U.S. collateralized loan obligations. But they don’t fund those purchases with dollars, they fund them by swapping yen into dollars through FX derivatives. That swap has a price, called the cross-currency basis, and it turns out to explain over 60% of the quarterly variation in CLO issuance, more than VIX, credit spreads, or any domestic macro variable the authors threw at it.

The real hook, though, is that this sensitivity isn’t stable. After Japan tightened bank capital rules in 2019, the pass-through from funding costs to AAA spreads roughly tripled, because the shock pushed the price-insensitive whale out and let more rate-sensitive buyers set the margin. That’s a good reminder that “foreign ownership share” is a lazy proxy for exposure. What matters is who’s marginal, and how easily they can walk away.

Huber, Amy and Kundu, Shohini, When Funding Markets Move Credit Markets: Foreign Investors and U.S. CLOs (May 15, 2026). Available at SSRN: https://ssrn.com/abstract=7086758 or http://dx.doi.org/10.2139/ssrn.7086758

Deep Hedging Finds Free Money

A neural network trained to hedge derivatives will, if left alone, quietly convert itself into a leveraged bet on the market’s historical drift rather than an actual hedge.

Deep hedging replaces the classic quant approach of assuming a price model (Black-Scholes, Heston, etc) and deriving a formula, with a network that just learns the best trading policy directly from simulated or historical paths, optimizing for a risk-adjusted objective rather than a textbook Greek. The elegant idea, borrowed from Buehler and coauthors, is that “the price of a derivative is the cost of its hedge,” so if you can learn the optimal hedge, you’ve also learned the fair price. The catch shows up fast: when the author trained this framework on S&P 500 data from 2015 to 2025, the network didn’t learn to hedge options responsibly, it learned to go long the index, sell puts, and mostly ignore the derivative it was supposed to be hedging, because that combination was simply the highest-Sharpe trade over that specific decade.

Figure 2: shows the distribution of trading gains “Under P” (raw historical drift) versus “Under Q” (drift-adjusted, risk-neutral measure), which visually demonstrates how removing the statistical arbitrage collapses the fat right tail into a distribution centered near zero.

The fix involves reweighting the training paths into a new probability measure that strips out the drift, forcing the model to actually hedge instead of quietly rediscovering “stocks go up.” It’s a clean reminder that any backtested strategy, human or machine, can mistake a decade’s tailwind for genuine skill.

Buehler, Hans, (Deep) Learning to Trade II - Deep Hedging, Model Uncertainty, Deep Bellman Hedging (March 18, 2026). Available at SSRN: https://ssrn.com/abstract=7086438

A Machine That Draws Arbitrage-Free Options Markets, and Then Learns to Simulate Them

A weighted sum of Black-Scholes prices, fit with plain linear programming, can capture an entire options market’s shape without ever creating a mathematical arbitrage, and once encoded into just twenty numbers, that shape can be simulated forward in time under a risk-neutral measure.

Building a model of the options market has always meant a tradeoff. Flexible models fit reality poorly, while accurate ones (like local volatility) are painfully hard to compute and calibrate without human babysitting. This paper’s answer, called SANOS, sidesteps the mess entirely by expressing every option price as a weighted mix of simple Black-Scholes prices across a grid of strikes. Because that structure is mathematically guaranteed to avoid static arbitrage, fitting it becomes a fast, off-the-shelf optimization problem rather than an art project, and in testing it priced 91.4% of real SPX options within the bid-ask spread, in well under a second.

Note: Fitted 1000 options within 2 ATM implied volatility standard deviations which had a Vega/sqrtT of at least 0.1% on 2025-05-06 across all 48 expiries from 1D to 657 business days. Options were chosen by closeness to ATM. The model fitted 91.4% of all options within bid/ask. Of those options not fitted the median error is just 21% of half spread.

The authors then compress five years of these fitted surfaces into a 20-number daily state, run PCA to find just five real drivers of surface dynamics, and use that to simulate future markets. As they put it, once set up, “it is fast.” For traders, this means a genuinely tractable way to stress-test strategies against markets that behave like the real thing, without hand-tuning a volatility surface every morning.

Buehler, Hans and Horvath, Blanka and Kratsios, Anastasis, DYSANOS - Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces (Presentation) (July 01, 2026). Available at SSRN: https://ssrn.com/abstract=7047878 or http://dx.doi.org/10.2139/ssrn.7047878

This week for paid subscribers

This week, paid subscribers get full access to a special two-part deep dive on pricing spread options and forecasting correlation when traditional models fail. Part 1 covers the pricing machinery and where standard approximations break down, while Part 2 tackles the hidden risk of correlation instability and how to actually select your parameters. Both posts include complete Python backtest code and historical datasets so you can run the entire pipeline yourself.

Part 1:

Part 2:

Disclaimer: The content provided in this newsletter, “Alpha in Academia,” is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Yesterday we built three ways to price a spread option and found that the pricing machinery is not the problem. Kirk’s approximation is accurate to a few basis points in the region where it actually gets used.

We ended on the thing that is the problem. A spread option’s price depends on the correlation between its two legs about as much as it depends on either leg’s volatility. But unlike volatility, correlation has no market, no implied surface, and no vocabulary for expressing how unsure you are. It’s a number someone types into a box.

Today: which number, and what the choice costs.

Let’s dive right in.

How Much Does It Actually Move?

The case for treating correlation as a fixed parameter is that it does not wander much. Volatility clusters and spikes, but two things that are economically linked (crude oil and the fuels made from crude oil) ought to stay linked.

Over our sample, the sixty-day rolling correlation between crude and the 2:1 product basket has a full-sample value of 0.677. That single number is the one most likely to end up in the box.

Here is what the rolling estimate actually did.

Figure 1: Sixty-day and 250-day rolling correlation between crude and the product basket, 1986–2026. The dashed line is the full-sample value a model would typically use.

The sixty-day estimate ranges from 0.22 to 0.98, nearly the entire theoretical span. And the departures are not brief excursions around an otherwise stable mean. The rolling correlation sits more than 0.15 away from the full-sample value on 33.7% of all trading days.

Put differently, for a third of the past forty years, the number in the box was wrong by an amount we are about to put a price on.

What That Range Is Worth

A parameter wandering between 0.22 and 0.98 only matters if the price cares. So take our three-month at-the-money crack spread option, hold both volatilities fixed at their forty-year values, and change nothing at all except the correlation.

A 5.6x range. Same strike, same expiry, same volatilities, same underlying. The entire difference is an assumption.

And that is not a point made with implausible extremes. Restricting to the middle of the distribution (5th to 95th percentile of what correlation has actually done), the same option still spans $3.30 to $7.78, a factor of 2.4.

So, which number do you type in? Before answering that, it is worth understanding one property of this correlation, because it turns out to explain more than it looks like it should.

Does Correlation Really Spike in a Crisis?

There is a well-documented result in equity markets that correlations rise in a downturn. Diversification thins out precisely when it is wanted, because in a sell-off individual names stop trading on their own news and start trading on the market’s.

The question is whether that transfers here. A crack spread is not a portfolio of equities. It is one commodity against the fuels refined out of it, and the link between them is a physical production process rather than a shared risk appetite. So it is genuinely unclear, before looking, whether the same pattern should hold.

We can check directly. Split every day in the sample into five buckets by the prevailing crude volatility, from calmest to most stressed, and see what correlation was doing in each.

Correlation rises from calm into the middle of the distribution, which is the equity pattern working as advertised. And then, in the most stressed quintile, where crude volatility averages 61% annualized, three times the calm regime, it falls back to 0.696, below the mid-regime level. The dispersion widens too: the standard deviation of ρ is at its highest, 0.148, exactly where you would want it lowest.

So the shape is a hump, not a ramp. The equity intuition holds through ordinary stress and then inverts in genuine crisis.

The mechanism is not mysterious once you look at the individual events. In a real dislocation crude stops trading on the same information as the products. April 2020 is the cleanest illustration in the sample: crude collapsed on a storage constraint, a mechanical problem about where to physically put barrels, while gasoline and diesel kept tracking actual fuel demand. On the day WTI printed −$36.98, gasoline was still trading comfortably above zero. The legs had decoupled entirely.

Hold onto this finding. It looks like a piece of trivia about crisis behavior, and it turns out to be the reason the standard way of estimating correlation is biased.

Read more

On 20 April 2020, West Texas Intermediate settled at minus $36.98 a barrel as storage at Cushing filled to the brim and long contract holders paid buyers to take physical oil off their hands.

It was reported as a curiosity of storage economics, and it was. But it also quietly broke something. If you were pricing an option on a refining margin that week using the standard toolkit, the model did not give you a bad number. It gave you no number at all.

Today we will look at what you use instead. There are three approaches: one that is exact but narrow, one that is approximate and lives on every commodities desk in the world, and one brute-force method that makes no assumptions at all. Along the way we will find something sharper than any of them.

Let’s dive right in.

The Spread That Runs a Refinery

A refinery is, financially speaking, a machine that converts one commodity into two others. It buys crude oil and sells gasoline and distillate. What it earns is not the price of any of those three things, but the gap between what it sells and what it buys.

The industry has a shorthand for this: the 3:2:1 crack spread. For every three barrels of crude a typical US refinery processes, it yields roughly two barrels of gasoline and one of distillate. So the margin per barrel of crude run is

with one bookkeeping detail. Crude is quoted in dollars per barrel; refined products are quoted in dollars per gallon. Nothing means anything until the products are multiplied by 42.

That number is what a refiner actually earns, and therefore what a refiner actually wants to hedge. Which is why options on it exist, and why we need something to price them with.

All three legs are published daily by the EIA and are free to pull back to 1986: WTI at Cushing for crude, New York Harbor gasoline and heating oil for the products. Requiring all three to print on the same day gives us 10,080 trading days spanning forty years.

Figure 1: The legs and the margin, 1986–2026. Crude and the product basket track each other closely. The gap between them is what the option is written on.

Over the full sample the margin averages $12.11 per barrel, with a median of $7.86, ranging from −$3.72 to $71.74. It has been negative on 5 days out of 10,080, about 0.05% of the time. Which makes sense, since refiners shut down when processing crude loses money.

But notice that it can go negative, and the entire reason why there is a problem with standard pricing methods.

Why Black-Scholes Cannot Price This

The instinct is to treat the crack spread as an asset like any other: Feed it into Black-Scholes, and get on with your day.

However, Black-Scholes assumes the underlying asset is lognormal, which makes the mathematics tractable, but rests on the assumption that prices compound multiplicatively and cannot fall below zero.

A spread is the difference of two lognormals. And the difference of two lognormals is sadly not lognormal. There is no change of variables that makes it so. Thus, no lognormal variable can go below zero. But history shows that our spread has been negative before. Because you can’t take the logarithm of a negative number, Black-Scholes would actually return nothing.

So we need machinery built for two assets from the beginning.

Method One: Margrabe (1978)

William Margrabe solved a specific version of this problem in 1978, and the trick is worth understanding even if you never use the formula, because it explains why these options behave the way they do.

Consider an option to exchange one asset for another: the right to give up asset 2 and receive asset 1. Its payoff is max⁡(S1−S2, 0), a spread option with a strike of exactly zero.

Margrabe’s move is to stop pricing in dollars and price the option in units of S2 instead. The payoff becomes:

which is an ordinary call option on the ratio struck at 1.

And here is the point. The difference of two lognormals is not lognormal, but the ratio of two lognormals is. Black-Scholes applies exactly, with an effective volatility of

The correlation between the two legs enters the price directly, and it enters with a negative sign. Higher correlation means lower effective volatility, which means a cheaper option.

Two assets that move together produce a spread that barely moves, and an option on something that barely moves is not worth much. Push correlation toward 1 and the spread flatlines. Push it toward −1 and the spread whips around violently. The option price follows.

Which raises an uncomfortable question we will return to at the end: if correlation is baked this deeply into the price, how confident are you in the number you are using for it?

But first, there is a catch, and it is a serious one. Margrabe’s trick works only at a strike of exactly zero. Put a real strike K on the option and the payoff in units of S2 becomes

and K/S2 is random. The strike stops being a constant, the ratio is no longer a clean call option, and the closed form collapses.

Margrabe is exact. It is also, for most real options, unusable.

Read more

Let’s get into it.

Flexible Forwards in Time-Dependent Models

A widely used shortcut in pricing currency hedges, assuming the optimal exercise trigger moves in a straight line with volatility, turns out to be wrong, and fixing it is now fast enough to do on a trading desk.

Flexible forwards let a company lock in an exchange rate but choose when to actually settle inside a window, which quietly makes them American style options on timing rather than plain forwards. Andersen, Itkin and Kazbek price them under a Heston model whose parameters drift with time, letting the skew stay steep at longer maturities instead of flattening out. The interesting result is not the speed (though pricing a contract in roughly a second, about ten times faster than a fine grid solver, is nice), it is the shape of the exercise surface. Earlier work assumed the trigger price rises linearly with variance. It does not. The curve bends, sometimes sharply, and the bend changes through time.

Figure 1: The early exercise surface for an American put: the full surface (left) and slices at fixed dates (right). The curves bend with variance rather than running straight.

Their localized basis method (DSINC) stays accurate where the standard cosine expansion wobbles, roughly twelve times better on median error. In one test the timing option was worth 271 pips versus a typical 50 to 100 pips quoted, which is the kind of gap that eats a sales margin whole.

Andersen, Leif B.G. and Itkin, Andrey and Kazbek, Rakhymzhan, Valuing American options and Flexible Forwards contracts in time-dependent models (June 24, 2026). Available at SSRN: https://ssrn.com/abstract=6991498 or http://dx.doi.org/10.2139/ssrn.6991498

Corporate Bond Dealers Aren't Just Plumbing

Corporate bond dealers quietly telegraph where prices are heading, and almost nobody outside the market is watching.

Dealers in corporate bonds broadcast “axes,” non-binding signals telling clients which bonds they would like to buy or sell. The conventional story says these are housekeeping, dealers nudging inventory back toward comfortable levels, nothing more. This paper, using a huge dataset of axes from the Neptune platform (over eight billion of them, covering most of the US investment grade and high yield indices), finds something more interesting. Bonds dealers signal interest in buying go on to outperform those they want to sell, by roughly 25 basis points over the following month. The telling detail is the shape of the move. Inventory-driven price pressure reverses, because temporary imbalances clear. Dealer interest does not reverse, it keeps drifting in the same direction, which is what information looks like as it seeps into prices.

Figure 2: Top and bottom quintiles, tracked 60 days either side of portfolio formation. Sorting on dealer inventory (left) produces the familiar snap back. Sorting on dealer interest (right) produces a drift that keeps going.

The effect is strongest in high yield, where fewer analysts look and information travels slowly, and axes even foreshadow rating upgrades and downgrades. The author concludes that “pre-trade dealer quoting activity may contribute to price discovery.” For investors, that reframes dealers as participants, not plumbing, and suggests the quotes arriving in your inbox carry a signal worth reading.

Geilen, Max, Corporate Bond Dealers and Price Discovery (June 24, 2026). Available at SSRN: https://ssrn.com/abstract=6990060 or http://dx.doi.org/10.2139/ssrn.6990060

Steadier Factors: Anchoring Rolling PCA With Prior Exposures

Nudging a rolling factor model toward an economically sensible starting point makes it far more stable, at little cost to accuracy.

When analysts break multi-asset returns into a few underlying factors, they usually re-run the model each month on a moving window of data. The trouble is that these factors keep drifting: the “growth” factor this month may quietly turn into something else next month, forcing constant rebalancing and muddying any story about what is actually driving returns. The authors add a gentle pull toward a prior set of exposures grounded in economic intuition, then let the data decide how hard to pull. At a moderate setting, year-ahead factor drift shrinks by roughly a quarter and the turnover of factor-mimicking portfolios falls noticeably, while the model's ability to reconstruct next month's returns barely moves.

Figure 2: Each point is a regularization strength. Left means steadier factors, down means better fit. The moderate setting (λ = 0.3) wins on both.

Push too hard and the model just parrots the prior, so the sweet spot is deliberately mild. Tested on nearly a century of US stock portfolios and dropped into a minimum-variance strategy, the stabilized version preserved risk performance while trimming both trading and drawdown. For investors, that means lower turnover costs and factor attributions you can trust from one month to the next.

Nakagawa, Kei and Kato, Masahiro and Imamura, Mitsuyoshi, Subspace Regularized Principal Component Analysis Using Prior Exposure Information (June 25, 2026). Available at SSRN: https://ssrn.com/abstract=6993538

Risky Oil: Betting on the Tails

A machine learning model built to bend around extreme events forecasts oil price tails better than the linear workhorses most analysts still rely on.

Forecasting the average future oil price is one thing; forecasting the ugly surprises at either end of the distribution is what actually keeps producers, airlines, and central bankers awake. This paper pits three approaches against each other and finds that a flexible machine learning model (which lets relationships between oil and its drivers stay linear when that suffices, but bends into nonlinear shapes when markets go haywire) consistently produces the sharpest tail forecasts.

A stochastic-volatility Bayesian VAR comes a close second, while the popular quantile regression approach barely beats a naive no-change forecast. The edge widens as the forecast horizon lengthens, and it holds even against a benchmark that already accounts for shifting volatility, so the gains come from capturing genuine nonlinearity rather than just noisier noise.

Demand factors drive the downside, supply factors drive the upside, and the authors show these tail signals even help predict Fed rate moves. For anyone hedging oil exposure or pricing energy risk, the takeaway is that allowing for nonlinearities when forecasting oil prices matters most precisely when it is hardest, during the turbulent episodes that break simpler models.

Baumeister, Christiane and Huber, Florian and Marcellino, Massimiliano, Risky Oil: It's All in the Tails. Available at SSRN: https://ssrn.com/abstract=7118662 or http://dx.doi.org/10.2139/ssrn.7118662

This week for paid subscribers

Paid subscribers are getting a from-scratch DCC-GARCH check on whether gold, silver, wheat, and corn actually hedged four US equity sectors around COVID, going beyond theoretical hedge ratios to measure realized volatility reduction. We find gold's hedge against financials didn't just weaken but briefly flipped to increasing portfolio risk, silver grew more entangled with materials, and corn quietly outperformed its weak-safe-haven billing as the most consistent volatility reducer in the study. Python backtest code and data included.

Alpha in Academia

Did Commodities Actually Hedge Sector Risk During COVID?

Read more

a month ago · 9 likes · Alpha in Academia

Disclaimer: The content provided in this newsletter, "Alpha in Academia," is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Today we will take a look at how Gold’s reputation as a universal hedge doesn’t hold up (and briefly inverted), while corn quietly outperformed its “weak safe haven” reputation as a consistent volatility reducer.

Let’s dive right in.

Introduction

A 2025 working paper by Grant, Moodliar, Rissik and Huang raised the question whether hard commodities (gold, silver, platinum) and soft commodities (corn, soybeans, wheat, livestock) behaved as hedges or safe havens for US equity sectors between 2014 and 2024. Using wavelet coherence and DCC-GARCH models across eleven GICS-classified sectors, we find that gold’s traditional role as a strong hedge deteriorated after the COVID-19 pandemic, that silver and platinum grew more positively correlated with cyclical sectors, and that soft commodities such as corn and wheat became weak but improving safe havens, with corn and wheat increasingly favored in optimal portfolio construction during the pandemic period.

We isolate four commodities (gold, silver, wheat, corn) against four sectors (Financials, Energy, Utilities, Materials), rebuild the DCC-GARCH pipeline from scratch using daily ETF proxy data, and ask a narrower and more falsifiable question: did the correlation structure between these assets actually shift around COVID, and if an investor had mechanically applied the resulting hedge ratios, would their portfolio have actually been less volatile as a result? The second half of that question, real realized volatility reduction rather than a theoretical hedge ratio, is not something the original paper focuses on, and is the main addition here.

Data and Methodology

Daily adjusted closing prices were pulled from Tiingo for 1 January 2014 through 31 December 2024 (2,768 trading days after return calculation). Four sector SPDR ETFs stand in for the Bloomberg GICS sector indices: XLF (Financials), XLE (Energy), XLU (Utilities), and XLB (Materials). Four commodity ETFs stand in for continuous futures: GLD (gold), SLV (silver), WEAT (wheat), and CORN (corn). This substitution is a real limitation worth flagging up front: ETFs carry expense ratios and can drift from spot or front-month futures pricing, and standard EOD data providers such as Tiingo do not carry continuous futures series. The substitution is reasonable for a correlation and hedging study, since ETF returns track the underlying commodity closely at daily frequency.

Read more

Let’s get into it.

Gold's Hedge Is Cracking

Gold’s decades-old reputation as the market’s default safe haven quietly broke down after COVID, while unglamorous soft commodities like corn and wheat became meaningfully better portfolio diversifiers.

Researchers at the University of Cape Town and Stellenbosch tracked how seven commodities, three “hard” (gold, silver, platinum) and four “soft” (corn, soybeans, wheat, livestock), moved alongside eleven US equity sectors from 2014 to 2024, using wavelet coherence and DCC-GARCH models to capture how correlations shift across both time and investment horizon. The headline result: gold, long treated as the default flight-to-safety trade, went from negatively correlated with sectors like financials and industrials before the pandemic to increasingly positively correlated after it, stripping away the protection investors assumed was there.

Silver and platinum told a similar story, drifting toward stronger positive co-movement with cyclical sectors like materials and energy. Soft commodities never became strong safe havens either, but corn and wheat held up better, with optimal portfolio weights rising across every sector during COVID. As the authors put it, gold’s “traditional role as a strong safe haven and hedge asset deteriorated after the COVID-19 pandemic.” Anyone still parking risk in gold out of habit might want to check whether that hedge is actually still there.

Grant, Mark and Moodliar, Bhavaniya and Rissik, Luke and Huang, Chun-Sung, On the Hedge and Safe Haven Properties of Soft and Hard Commodities: Evidence from the United States GICS-Sectors (March 01, 2025). Available at SSRN: https://ssrn.com/abstract=7046078 or http://dx.doi.org/10.2139/ssrn.7046078

Bond Futures Spreads That Trade Like Their Own Market

European government bond futures calendar spreads aren’t just a synthetic byproduct of two expiring contracts, they behave like an independent liquidity venue precisely when rollover pressure peaks.

Using 127 million order book updates from nine EUREX bond futures (Bund, Bobl, Schatz, BTP, OAT, and others), this paper tracks what happens in the ten days before contract expiry across three linked markets: the expiring contract, the new contract, and the calendar spread connecting them. The expected story plays out late, trading activity and tighter quotes migrate from the old contract to the new one mostly in the final two or three days. But the spread book gets interesting earlier. It builds up meaningful resting depth well before that late migration, and for eight of nine products, buying the spread directly is consistently cheaper than manually legging into both contracts separately, sometimes dramatically so in less liquid names like the Spanish BONO future.

The authors put it plainly: calendar spreads play an active and economically meaningful role within the rollover process. For anyone rolling futures positions near expiry, that’s a real, quantifiable execution cost sitting on the table if you’re not checking the spread book first.

Uzun, Illia and Stenfors, Alexis, Calendar Spreads as Autonomous Liquidity Pools: Evidence from Triangular Rollover Dynamics in Bond Futures Markets. Available at SSRN: https://ssrn.com/abstract=6999365 or http://dx.doi.org/10.2139/ssrn.6999365

A Number Theory Trick Just Flagged Something Weird About This Bull Market

Since 2018, S&P 500 stock prices have started obeying Benford’s Law (the odd rule that natural datasets favor digit 1 over digit 9) more strongly than at any point in 64 years, and historically that pattern only ever showed up during a crisis.

Here’s the setup. Benford compliance in stock prices, it turns out, isn’t some mysterious market-efficiency signal, it’s almost entirely explained by how spread out prices are across the S&P 500 (one variable alone explains 82% of it). For 60 years, the only thing that stretched prices out enough to trigger strong compliance was a recession, and specifically a recession that crushed cheap stocks while expensive ones barely moved. Every time that happened (1970s oil crisis, 2008 crash), the pattern reverted within months once the economy recovered. But since 2018, the same statistical fingerprint has shown up for seven straight years with no recession attached, and it’s happening for the opposite reason: expensive stocks are rising fast while cheap stocks barely budge, not falling.

The paper ties this directly to M2 growth, and the authors frame it plainly, calling it the statistical configuration of crisis without its macroeconomic expression. If the plumbing that normally corrects stretched valuations (bankruptcies, recessions, deleveraging) has been sitting dormant this whole time, that’s worth knowing before you assume “no recession” means “no fragility.”

Mateos Sanchez, Carlos and Alcaraz Carrillo de Albornoz, Vicente and Farkas, Walter, The Signal beneath the Calm: Benford's Law and the Latent Fragility of Liquidity-Driven Financial Markets (June 17, 2026). Available at SSRN: https://ssrn.com/abstract=6962319

Sanctions Didn't Kill the Gold Arbitrage, They Just Slowed It Down (And Flipped Brent Entirely)

After Russia’s 2022 clearing and settlement infrastructure was severed from the West, gold and silver prices on the Moscow Exchange kept tracking their Chicago counterparts almost perfectly in the long run, but the market lost its ability to correct short-term price gaps quickly, while Brent crude oddly became more important to price discovery, not less.

Researchers compared Moscow Exchange futures on gold, silver, and Brent crude to their Chicago and ICE equivalents from 2019 through early 2026, using the kind of statistical toolkit normally applied to cross-listed stocks or ETFs tracking the same asset. The long-run one-to-one price relationship never broke, even after sanctions cut off Russian banks and brokers from global clearing. What changed was speed: it used to take one or two trading days for a price gap between Moscow and Chicago gold to close, and now it takes up to five.

Gold’s informational role on the Moscow exchange nearly vanished, but Brent’s grew, likely because the contract increasingly reflects discounted Russian crude rather than the global benchmark. As the authors put it, “the relation survives, but the mechanism that enforces it is impaired.” For anyone modeling cross-border arbitrage or basis risk, that’s a useful, quantifiable lesson in how sanctions actually degrade a market.

Belanov, Aleksandr and Mischhenko, Viatcheslav, Price Discovery and Arbitrage Efficiency under Infrastructure Severance: Evidence from MOEX-CME Derivative Pairs, 2019-2026 (June 07, 2026). Available at SSRN: https://ssrn.com/abstract=6915859

Disclaimer: The content provided in this newsletter, “Alpha in Academia,” is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Let’s get into it.

Finding a Private Company's Public Twin

Private credit has exploded into a multi-trillion dollar asset class, but there is a basic problem, many private borrowers do not publish the kind of financial statements analysts need to estimate default risk, or the numbers arrive stale, months out of date. Researchers at BlackRock built a workaround using machine learning. They trained a random forest model (an algorithm that grows hundreds of decision trees) on thousands of publicly traded corporate bonds, using visible market signals like yield, spread, and bond structure to predict credit ratings. Then, instead of only using the model to make predictions, they mined its internal structure to measure “similarity” and find each private issuer’s closest public lookalikes, a small handful of public bonds trading like true peers. The private company’s implied rating becomes a weighted average of its public twins’ actual agency ratings.

Tested across a ten-year period that includes the 2020 crash, the model landed on the exact rating band or within one notch of it, achieving “more than 95% accuracy for both NA and EMEA regions,” and consistently beat a simpler sector-average benchmark. For investors underwriting private credit deals with limited disclosure, this offers a transparent, data-driven second opinion on where a borrower’s true credit quality sits.

Yadav, Ravi and Saha, Anubhab and Singh, Saurabh and Turmuhambetov, Gauhar Akylbekovna and Mehta, Dhagash, A Machine Learning-based Public Market Equivalent Framework for Estimating Default Risk in Private Credit (April 15, 2026). Available at SSRN: https://ssrn.com/abstract=6916138 or http://dx.doi.org/10.2139/ssrn.6916138

Why Long-Term Rates Overreact

Uncertainty about how persistent a shock will be is, by itself, enough to make even a perfectly rational forecaster overreact to distant news and under react to recent news, at the same time.

Ask any forecaster how long a shock to inflation or interest rates will actually last, and they will admit they are not fully sure. This paper shows that this honest uncertainty, once you write it into the math, forces long-horizon forecasts to become steadily more persistent and to eventually overreact the further out you look, no matter what the true underlying process is or how carefully the forecaster reasons.

The authors trace this one mechanism through six long-standing puzzles in finance: why 15-year Treasury forward rates move almost in lockstep with short-term rates, why the long end of the yield curve gets explained away by a vague “term premium” instead of actual rate expectations, why bond returns look predictable after the fact, and why long-horizon asset prices are excessively volatile. Fitting the model to the real Treasury curve, modest uncertainty (nothing exotic, just not being sure whether short rate persistence is 0.85 or 0.95) reproduces these patterns closely. As the authors put it, forecasts are “necessarily as persistent as is believable and over-react.” For investors, this means the long end of the curve may be less about bias or mispricing than about honest uncertainty doing exactly what the math says it must.

Greg Kaplan and Ken Miyahara, “How Does Monetary and Fiscal Policy Affect the Economy in the Face of Large Shocks?,” NBER Working Paper 35400 (2026), https://doi.org/10.3386/w35400.

What the VIX Doesn’t Tell You

The VIX, the “fear gauge” quoted everywhere from CNBC to options desks, is built from a formula that implicitly assumes you can observe option prices at every possible strike, from zero to infinity. In practice, exchanges only trade a limited band of strikes, and nobody prices the extreme tails. This paper shows that gap is not a minor technicality. For the standard VIX formula, and for nearly every popular measure of skewness and kurtosis used in academic finance, the missing tail information means there is no upper limit on what the true value could be. The number everyone reports is just one arbitrary point plucked from an unbounded range of values, all equally consistent with the option prices actually observed.

Predictive regressions and cyclicality studies built on these measures can be engineered to show almost anything, “rendering their empirical conclusions largely uninformative.” The authors also propose a fix, a family of alternative variance and skew measures that stay tightly bounded using the same visible data. For investors leaning on the VIX or similar option-implied signals, the point is blunt: the number is standing in for a far wider range of possibilities than it lets on.

Bondarenko, Oleg and Dillschneider, Yannick and Schneider, Paul Georg and Trojani, Fabio, What can you Really Tell from Option Prices? (June 24, 2026). Swiss Finance Institute Research Paper No. 26-49, Available at SSRN: https://ssrn.com/abstract=7017219

The Billion-Dollar Minimum for Bond Indexing

A bond portfolio can be too small to track its own benchmark, no matter how skilled the optimizer, because minimum trade sizes set a hard floor on how close it can get.

Bond portfolio optimization has always felt like equity optimization’s neglected cousin, and a new paper from an Amundi research team explains why, then builds the missing framework from scratch. The real payoff isn’t the math, it’s what happens when you try to actually trade the thing.

Using real ICE BofA corporate bond indices with anywhere from 4,663 to over 20,000 securities, the authors show that minimum trade sizes and lot constraints impose a hard floor on how closely a portfolio can hug its benchmark. At 50 million dollars, the best achievable active share (a measure of how much a portfolio diverges from its index) sits around 80% for the euro index and 85% for the global one, and these numbers only fall into reasonable territory once a portfolio crosses roughly a billion dollars. The paper notes this problem is “particularly acute for smaller portfolio sizes.” For anyone comparing bond ETFs or sizing up a smaller fixed income mandate, this is a reminder that tracking error isn’t just a skill problem, it’s a scale problem, and size alone can decide whether a strategy is even implementable.

Ben Slimane, Mohamed and Cherief, Amina and Roncalli, Thierry and Xu, Jiali, Bond Portfolio Optimization (July 03, 2026). Available at SSRN: https://ssrn.com/abstract=7064358

This week for paid subscribers

Paid subscribers are getting a look at whether crowded hedge fund positioning can actually be traded against. The post digs into why fading the crowd produces a clean, out-of-sample-stable edge in silver, why that same edge in gold is quietly decaying as the trade becomes more widely known, and why copper inverts the relationship entirely, exposing the fact that positioning was never the real signal, mean reversion was. Python backtest code included.

Disclaimer: The content provided in this newsletter, “Alpha in Academia,” is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Reviewed and updated 28 July 2026

Hello and welcome back to another paid post!

Today we are going to take one of the most repeated headlines in all of commodity markets and ask whether there is any money in doing the exact opposite. The idea is old and intuitively appealing: The fast money crowds into a trade, the trade gets stretched, and the crowd, as crowds tend to, eventually gets carried out. If that story is true, then the crowd’s own positioning should tell you when to fade it.

Let’s dive right in.

The Cheat Sheet the Government Publishes Every Friday

Every week, the Commodity Futures Trading Commission (CFTC) releases something called the Commitments of Traders (COT) report, and it is one of the closest things retail traders have to seeing the other side of their own hand. The report takes every major futures market and sorts the people holding positions into buckets, based on who they actually are and why they are there. Two of those buckets matter for us, and the whole strategy lives in the tension between them.

The first is Managed Money. In the CFTC’s disaggregated report, this category includes registered commodity trading advisers and commodity pool operators, along with unregistered funds identified by the Commission. It is a reporting category, not proof that every position follows the same trend strategy. Here I test its aggregate net position without assigning a motive to each trader.

The second bucket is Producer/Merchant/Processor/User. These are entities predominantly engaged in producing, processing, packing, or handling the physical commodity and using futures to manage commercial risk. Their aggregate position often sits across from speculative demand, but the report does not identify the motive for each trade.

The distinction still gives us a useful empirical question. Managed Money is a reportable speculative category; Producer/Merchant/Processor/User is tied to commercial activity. Their aggregate net positions can lean against each other, but the labels do not tell us which side is informed, patient, early, or late. The test below asks only whether an extreme Managed Money position was followed by a profitable contrarian portfolio in these three metals.

The hypothesis in one line: an extreme speculative position might coincide with an exhausted trend. That is the proposition under test, not something the category labels establish.

That gives us a clean question. When Managed Money’s net position is unusually high, fade it short; when it is unusually low, fade it long. Then ask whether the resulting portfolio was positive after the report could conservatively have become actionable. The outcome can support or reject the rule in this sample, but it cannot by itself identify why prices moved.

Read more

Let’s get into it.

Adverse Selection Eats the Spread

On a diverse basket of CME futures, the spread a market maker earns is almost perfectly cancelled out by the losses it pays to better-informed traders, leaving profit indistinguishable from zero.

When a market maker posts a passive quote, it collects a small spread but pays a hidden cost every time a smarter trader picks off that quote just before the price moves. Using rare data that carries the true buyer-or-seller sign on every trade across 13 CME futures (from crude oil to the S&P 500), Gatto measures both sides of that trade fill by fill and finds they essentially offset: the maker captures a sliver of spread and gives back almost exactly the same amount as prices drift against it, on every single contract.

Figure 1: Left: the half-spread a maker captures is consumed almost entirely by adverse selection, netting near zero. Right: the same near-cancellation holds on all 13 contracts.

In the author's words, “adverse selection consumes essentially the whole captured half-spread,” leaving profit statistically indistinguishable from zero. But under stress (the SVB scare, a hot FOMC week, the COVID crash) the losses actually exceed the spread, and the maker bleeds more as volatility rises. Standard clever quoting tricks and order-flow signals fail to fix it once real trading costs are charged. For investors, the takeaway is sobering, knowing that in these venues, passively supplying liquidity is structurally a break-even-at-best business, and the edge everyone chases mostly is not there.

Gatto, Daniel, Adverse Selection Consumes the Touch: A True-Aggressor-Signed Maker-P&L Decomposition Across 13 CME Futures (June 20, 2026). Available at SSRN: https://ssrn.com/abstract=7022599

What Investors Disagree About

When investors argue about a company's actual fundamentals, that disagreement predicts lower future returns, but the same fights over noise and chatter predict nothing.

Most research treats investor disagreement as a single number, a measure of how much people argue without asking what they argue about. This paper ran a large language model over 220 million posts on China's biggest stock forum and split the arguing into categories. The result is that content is everything. Disagreement about fundamentals (earnings, valuation, prospects) predicts lower returns of roughly 0.7% per month, the classic pattern where optimists dominate prices when shorting is hard and overvaluation later unwinds. Disagreement classified as noise predicts nothing, and the popular aggregate measure actually points the wrong way because it is really just tracking sentiment (the two move together at 0.81).

Figure 2: Risk-adjusted monthly returns by disagreement type. Recreated from Figure 1 of the original paper.

Tellingly, the effect shows up right when earnings get announced and the arguing gets resolved, and it survives once you account for whether earnings actually surprised. The authors put it plainly, that investor disagreement “is not one thing.” For anyone using crowd sentiment or forum buzz as a signal, the lesson is that the crude aggregate can quietly reverse the sign of what you think you're measuring.

Yi, Kefu and Wu, Feng, What Investors Disagree About: LLM-Decomposed Retail Disagreement and the Cross-Section of Stock Returns. Available at SSRN: https://ssrn.com/abstract=7027983 or http://dx.doi.org/10.2139/ssrn.7027983

Instant Liquidity, Latent Risk: When Bond ETFs Break

Bond ETFs break not because investors flee, but because the plumbing that keeps their prices honest quietly seizes up.

Melin and Rouxelin build a continuous-time model of two connected markets, a slow over-the-counter world where the actual bonds trade and a fast exchange where the ETF shares trade, linked by the authorized participants who shuttle assets between them.

The surprising result is that ETF fragility runs through prices, not redemptions. During March 2020, bond ETFs saw smaller outflows than mutual funds yet dislocated far more sharply from their net asset value, with the deepest discounts landing in the safer, more liquid segments rather than the riskiest ones. Their model explains this safety inversion, that when redemption baskets are costly for intermediaries to absorb, those middlemen demand a wider discount to play along, and once a single redemption looks doubtful, every share reprices as if none can be redeemed.

Figure 3: Premium or discount to NAV across four bond ETF categories, 2020 to 2024, with 90-day SOFR overlaid. Dislocations cluster in March 2020, deepest for municipals (near 8 percent), showing how stress hits some segments far harder than others.

For investors, the lesson is that a calm-looking ETF can mask a redemption mechanism that fails precisely when you need liquidity most, and those crisis discounts are structural signals, not free money.

Rouxelin, Florent and Melin, Lionel, Instant Liquidity, Latent Risk (July 01, 2026). Available at SSRN: https://ssrn.com/abstract=5304325 or http://dx.doi.org/10.2139/ssrn.5304325

The Enduring Influence of Openness on Risk-Taking

Cities forced open to foreign trade in 19th-century China still breed bolder investors today, 170 years later.

When the Qing dynasty was compelled to open a set of “Treaty Ports” to Western trade after 1842, those cities absorbed more than goods and factories. They picked up a taste for risk that never left. Lin and Tang trace this through three very different windows: commercial newspaper ads from 1850 to 1950 (Treaty Ports ran far more, especially in volatile industries like finance and real estate), state-controlled economic news from 1949 to 1988, and modern mutual fund accounts from Alipay.

The through-line is striking, because the formal institutions that created the advantage (foreign consulates, concessions, customs houses) were all dismantled after 1949, yet the behavior survived. Tellingly, the effect shows up only among long-rooted locals, not immigrants, pointing to culture passed down through families rather than current economics. For investors, it is a reminder that regional risk appetite is partly inherited, and that where money comes from can shape how boldly it gets deployed.

Lin, Tse-Chun and Tang, He, Enduring Influences of Openness on Risk-Taking Behaviors: Evidence from 170 Years of Ads, News, and Retail Investments. Available at SSRN: https://ssrn.com/abstract=7030024 or http://dx.doi.org/10.2139/ssrn.7030024

This week for paid subscribers

Paid subscribers are getting a look at whether tomorrow's stock direction is actually predictable, using a nonparametric sign-prediction rule that strips out the mechanical edge created by a stock's own upward drift before testing what real forecasting power remains. The post digs into why small-caps show a genuine 2.8 percentage point accuracy edge while large-caps mostly do not, why the drift adjustment quietly separates real signal from data artifact, and why mean-reverting names like a certain Arkansas community bank can turn a buy-and-hold loser into a tradable winner. Python backtest code included.

Disclaimer: The content provided in this newsletter, "Alpha in Academia," is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Reviewed and updated July 28, 2026

Hello and welcome back to another paid post!

Today I will take a look at a simple nonparametric sign-prediction rule and what it would take to test it reliably against a drift-adjusted random walk benchmark.

Let’s dive right in.

Introduction

Every retail trader has asked the same question at some point: if a stock just had a big day up, is tomorrow more likely to be up too, or is a reversal coming? The answer turns out to depend enormously on which stock you are asking about, what the broader drift of that stock looks like, and how you define a “big” day. Getting any one of those three things wrong produces results that look like forecasting ability when they are really just artifacts of the data construction.

The analysis is built around a nonparametric statistic called the Probability Difference (PD), designed to measure the sign predictability of daily equity returns after stripping out the mechanical component that comes from a positive expected return. The logic is elegant: if a stock earns 5 percent per year on average, then same-direction sequences will be slightly more common than reversals even if daily returns are purely random. The PD statistic accounts for this, then asks whether the residual predictability is statistically significant.

There are 3 questions at the center of the analysis. First, do smaller stocks show meaningful out-of-sample directional predictability? Second, do larger stocks show the same pattern? Third, does predictability differ after positive and negative extreme-return days? Those questions are worth asking, but the implementation has to identify company size correctly and control its statistical search before the answers can be trusted.

The Methodology: What the PD Statistic Actually Measures

Standard momentum and reversal research measures whether returns are correlated across time. The PD statistic takes a different approach: it only cares about the sign of the return, not its magnitude. Define Dt as plus one if today’s return is positive and minus one if it is negative. The PD statistic for a given estimation window of W trading days is:

Read more

Let’s get into it.

Decoding the Smart Money Trail

Institutional investors leave detectable footprints across options markets, dark pools, and the order book, and a systematic four-layer framework can help retail traders read them.

When a hedge fund takes a large directional position, it rarely announces the fact. Instead, it routes block trades through dark pools to avoid tipping its hand, sweeps call options across multiple exchanges to build leveraged exposure efficiently, and leaves a quiet but readable trail in the market’s plumbing. This paper by practitioner Vishal Chopra argues that four publicly accessible data streams, interpreted in sequence, can reconstruct much of that institutional intent: unusual options activity (particularly call or put sweeps that cross 50% of existing open interest), off-exchange volume spikes from FINRA’s weekly dark pool transparency data, large-lot patterns in the real-time tape, and price positioning relative to anchored VWAP (a volume-weighted average price calculated from a meaningful prior event rather than the daily open).

The author formalizes this into a weighted conviction score, where options flow carries the most predictive weight, followed by dark pool confirmation, tape patterns, and price structure. The framework stops well short of claiming to close the gap between retail and institutional participants entirely, but the evidence from market microstructure research it draws on is real: options order flow genuinely leads equity prices, and dark pool prints carry information about future returns. The practical question is whether the synthesis adds more than the sum of its parts.

Chopra, Vishal, Institutional Order Flow Analytics: Decoding Smart Money Signals in U.S. Equity and Options Markets: A Practitioner Framework for Identifying Informed Trading Activity Across Lit and Dark Market Venues. (June 06, 2026). Available at SSRN: https://ssrn.com/abstract=6889358

Catching Small Fish Before the Market Does

A simple, nonparametric measure of return sign dependence predicts next-day direction for the majority of small-cap stocks, while generating no edge at all in large caps.

The core intuition here is behavioral and almost disarmingly simple: if investors systematically under-react to news, positive returns should tend to follow positive returns, and negative should follow negative. The Probability Difference (PD) statistic formalizes this by measuring how often same-sign return sequences occur relative to reversals.

The clever part is what the author had to fix to make this work in equities specifically. Stocks have a positive long-run drift, which creates a false impression of momentum, and they suffer from microstructure noise (the random bounce between bid and ask prices) that obscures real patterns. The paper addresses these with a drift-adjusted null hypothesis and a threshold filter that only fires after a prior return is extreme enough to cut through the noise. Tested across 25 years of U.S. data, the adapted PD correctly predicted next-day direction for 84% of small-cap stocks, and PD-guided strategies delivered positive Sharpe ratios net of transaction costs.

Large caps showed essentially zero edge, which is exactly what you’d want to see: a model that goes quiet in efficient markets isn’t broken, it’s honest. The most striking finding is an asymmetry in where predictability lives: the signal after large positive returns is substantially stronger than after large negative ones, consistent with the disposition effect (investors hold losers too long and sell winners too soon), a pattern that notably disappears in large caps.

Semenov, Andrei, Nonparametric Directional Forecasting in Equity Markets: Size, Conditional Patterns, and Economic Payoffs. Available at SSRN: https://ssrn.com/abstract=6997954 or http://dx.doi.org/10.2139/ssrn.6997954

When Reddit Talks, Markets Move Together

Synchronized spikes in retail attention on WallStreetBets coincide with simultaneous price bubbles across NVIDIA, Bitcoin, and Ethereum, even though these assets share no fundamental economic linkage.

The GameStop saga of 2021 made it clear that retail investors coordinating on social media could move individual stocks. This paper asks a harder question: can that same coordination produce bubbles across entirely unrelated asset classes at the same time? Using hourly price and Reddit mention data from 2023 to 2024, the authors track explosive price episodes across AI stocks and cryptocurrencies using a statistical bubble-detection procedure (essentially a rolling test for whether prices are growing faster than any rational fundamental could justify). They find that NVIDIA alone registered twelve distinct bubble episodes over the sample period, with some lasting over 59 consecutive hours, and that its bubble windows overlap meaningfully with those of Bitcoin and Ethereum. The smoking gun is the attention data: during the March 2024 co-bubble episode, WallStreetBets mentions of NVIDIA ran more than four times their normal hourly rate, with Bitcoin and Ethereum mentions showing the same pattern simultaneously.

Critically, the paper distinguishes this from ordinary market connectedness: Tesla, which is economically linked to NVIDIA through AI exposure, shows return spillovers with it but no co-explosivity, suggesting that synchronized bubbles are a behavioral phenomenon driven by shared retail narratives, not just correlated fundamentals. For investors, the implication is interesting: Reddit is now a cross-asset contagion channel.

Aloosh, Arash and Choi, Hyung-Eun and Ouzan, Samuel and Shahzad, Syed Jawad Hussain, Social Media Co-Attention and Investment Co-Bubbles. Available at SSRN: https://ssrn.com/abstract=6985533 or http://dx.doi.org/10.2139/ssrn.6985533

The Hidden Third Market in Futures Rollovers

Calendar spread books in European bond futures don’t just reflect liquidity from their two underlying contracts: they generate their own, and often offer cheaper execution than trading the legs separately.

Every quarter, traders holding European government bond futures face a familiar chore: roll their position from the expiring contract to the next one. The conventional picture is a two-party handoff, with liquidity migrating from March to June. But a new paper using 127 million limit order book updates from EUREX argues there’s a third player worth watching: the calendar spread book itself. The rollover, it turns out, is better understood as a triangle than a baton pass.

As expiry approaches, the spread book quietly accumulates a large share of displayed (resting) liquidity even while raw order activity still dominates the outright contracts, and in eight of nine futures studied, executing the roll directly through the spread book was cheaper than legging into it through March and June separately. The execution advantage was especially striking in less liquid markets. For investors executing rollovers at scale, ignoring the spread book isn’t just leaving money on the table, it’s misreading the market’s actual structure.

Uzun, Illia and Stenfors, Alexis, Calendar Spreads as Autonomous Liquidity Pools: Evidence from Triangular Rollover Dynamics in Bond Futures Markets. Available at SSRN: https://ssrn.com/abstract=6999365 or http://dx.doi.org/10.2139/ssrn.6999365

This week for paid subscribers

Paid subscribers are getting a complete seasonal-trend decomposition of the legendary “glamour market” (pork bellies), derived from a 69-year-old USDA cold-storage dataset that reveals what price action alone never could: not just when a market dies, but the exact structural decay that killed it. Python decomposition code included.

Disclaimer: The content provided in this newsletter, “Alpha in Academia,” is for informational and educational purposes only. It should not be construed as financial advice, investment recommendations, or an offer or solicitation to buy or sell any securities or financial instruments. Past performance is not indicative of future results. The financial markets involve risks, and readers should conduct their own research and consult with qualified financial advisors before making any investment decisions.

The interpretations, opinions, and analyses presented herein are those of the author and do not necessarily reflect the views of the original researchers, their institutions, or the full implications of the cited academic papers. While every effort is made to accurately represent the research discussed, readers should be aware that the summaries and interpretations may not capture the full scope or nuances of the original studies. The information contained in this newsletter is believed to be accurate and reliable at the time of publication, but accuracy and completeness cannot be guaranteed. The author and publisher accept no liability for any loss or damage resulting from reliance on the information provided.

This newsletter may contain links to external websites or resources. The author is not responsible for the content, accuracy, or reliability of these external sources.

By subscribing to or reading this newsletter, you acknowledge that you have read and understood this disclaimer and agree to hold the author and publisher harmless from any liability that may arise from your use of the information contained herein.

Reviewed and updated 28 July 2026

Hello and welcome back to another paid post!

Today I will take a look at what a monthly USDA inventory series can—and cannot—tell us about one of America’s most famous agricultural futures contracts.

Let’s dive right in.

The Glamour Market

For about thirty years, if you wanted to gesture at the casino of commodity speculation without actually explaining anything, you reached for two words: pork bellies. It was the punchline. In Trading Places, pork bellies appear in the commodities monologue; frozen concentrated orange juice futures ruin the Duke brothers. Traders called it “the glamour market,” half in love with it and half embarrassed to be. Bellies were volatile, theatrical, and a little ridiculous, and everyone knew the name even if almost nobody could tell you what was actually in the contract.

And then, in 2011, it stopped. On 15 July, CME announced that frozen pork belly futures and options would be delisted after “a prolonged lack of trading volume” and “significant discussion with industry participants.” The infamous ticker went dark the following Monday.

The cold-storage record offers one clue. It can describe how frozen inventories changed, but it cannot establish what caused the market to disappear.

The Bet in the Freezer

Let’s start with the thing itself. A pork belly is the slab of layered fat and muscle that runs along the underside of the hog — the cut that, cured and sliced, becomes bacon. One hog, two bellies, and for most of the 20th century a very specific scheduling headache.

The historical rationale was a seasonal inventory problem: bellies could be stored for later sale, leaving packers and buyers exposed to the price at which that inventory would eventually change hands.

Freezing does not remove that price risk; it converts a perishable product into inventory whose future value is uncertain.

That is a textbook hedging problem, the kind that can summon a futures market into existence. CME’s own history dates the first frozen pork belly futures trade to 18 September 1961. The date is fixed; the exact mix of hedging motives is a separate historical question.

The storage hypothesis goes like this: buy a belly cheap in the off-season, pay to keep it frozen, sell it dear when demand peaks. On that account, the futures curve was, in effect, the market quoting you the price of that carry. The speculators who made bellies famous would have been renting exposure to a seasonal storage cycle, dressed up in enough volatility to make it thrilling.

This explanation depends on two historical questions: whether demand and storage were seasonal, and whether firms actually used the contract to hedge that risk.

The analysis below can examine the storage series. It cannot tell us, on its own, whether a change in that series caused traders to leave the contract.

Read more