Variance swaps are sick, and thanks to Goldman Sachs, Derman, Carr, Madan, and others, we have an elegant and intuitive understanding of the price under risk-neutral dynamics for a standard diffusion.  In fact, the modern VIX is quite literally just the Goldman Sachs / Carr-Madan variance swap model printed on a ticker.

However, in the context of a trade, these variance swaps aren't a pure volatility play.

The biggest gotcha in the variance swap world is that you aren't trading σ (volatility); you’re trading σ^2 (variance). While that sounds like a minor pedantic distinction for a math quiz, in a live book, it changes the entire risk profile.  

Mechanically, this comes down to additivity.  Under standard diffusion dynamics, variance is linearly additive over time.  By applying Itô's Lemma to a log contract, we can isolate the variance by continuously delta-hedging away the directional spot movements (the cross-terms).  With volatility, however, this additivity completely breaks down; the cross-terms persist, making it impossible to cleanly isolate and statically hedge.

Effectively, calling a variance swap a pure vol play is like calling a Ferrari a commuter car. It’ll get you there, but the way it handles the corners (and the crashes) is fundamentally different.  

Curious to learn more?  I'll have a video out soon deriving the risk-neutral pricing formula for variance swaps in the context of volatility trading, and the history of the model.  Stay tuned!

With that I will leave you to the Weekly Guild Letter.  I hope you enjoy, and I hope you learn something!

- Roman

By the mid 1990s, the Fama–French three-factor model had already reshaped how academics and practitioners thought about returns. Market, size, and value explained far more than CAPM ever could. But one anomaly kept surviving every robustness check. Momentum.

In 1997, Mark Carhart extended the Fama–French framework by adding a fourth factor based on prior returns. Stocks that had outperformed over the past year tended to continue outperforming, while recent losers continued to lag. The effect was too persistent to ignore and too systematic to dismiss as noise.

The Carhart Four-Factor Model keeps the original three factors and adds momentum as an additional source of priced risk. It acknowledges that markets reward not only exposure to economic characteristics like size and value, but also exposure to persistent price trends driven by behavior, flows, and structural frictions.

Here is what the four-factor model looks like:

After the original three factors explained market exposure, size, and value, one effect still stood out. Stocks that had recently gone up tended to keep going up. Stocks that had recently fallen often kept falling. That persistence became the momentum factor.

Momentum simply captures exposure to trends. If your portfolio loads positively on it, you benefit when winners continue winning and losers continue lagging. It is not about fundamentals like size or value. It is about behavior, flow, and the tendency of prices to move in streaks.

Once momentum is added, a lot of what used to look like skill starts to look like systematic exposure to trend. The Carhart model therefore expands the question from “Are you beating the market?” to “Which persistent risks are you actually taking?”

📈 Model applications

In practice, the Carhart four-factor model is used less as a forecasting tool and more as a lens for understanding and engineering returns. It allows you to decompose performance into exposures to market, size, value, and momentum. If a portfolio is making money, you can ask whether that P/L is coming from true stock selection or simply from loading on trending names.

On the generation side, the model naturally leads to factor portfolios. You can construct long–short momentum portfolios, tilt toward value while neutralizing market beta, or blend exposures to create diversified sources of return. Smart beta strategies are essentially structured implementations of these ideas, targeting compensated risk premia rather than relying purely on discretionary views.

For portfolio managers and traders, the model also serves as a risk management tool. By measuring factor loadings, you can avoid unintended exposures, hedge specific risks, or deliberately allocate capital to factors you believe are in favor. In that sense, P and L becomes less about guessing direction and more about consciously selecting which systematic risks you want to be paid for.

🎓 A little story

Some of the first serious work I did with factor models was in the context of what people call “factor zoos.” If you have not heard that term before, it is exactly what it sounds like. Hundreds of published factors. Value variations, quality definitions, momentum flavors, profitability tweaks, investment intensity measures, accrual anomalies, liquidity premia. Every paper seemed to introduce a new animal.

At first, it was pure information overload. I was trying to understand which factors were real, which were redundant, which were just repackaged versions of something else. It felt like the answer to performance was hiding somewhere inside a spreadsheet with far too many columns. More factors had to mean more edge, right?

What I eventually realized, mostly by watching how senior quants approached the problem, was that they were doing the opposite. They were collapsing complexity back into structure. Instead of chasing every new anomaly, they were asking simpler questions. What risk is this actually capturing? Is it just value in disguise? Is it momentum with a different lookback? Is it a microstructure artifact? They were mapping the zoo back to a small set of underlying drivers.

That was a turning point for me. The edge was not in memorizing every animal in the zoo. It was in understanding the ecosystem. Once you see that most factors cluster around a few fundamental sources of risk or behavior, you stop drowning in features and start building portfolios intentionally. Simplicity, not accumulation, is what lets you actually deploy capital with conviction.

💡 Takeaway

The key insight is that returns don’t show up evenly through time. Factor premia wax and wane, sometimes disappearing for years before reasserting themselves. That means success isn’t about betting everything on one factor forever, it’s about understanding where you’re exposed, why you’re exposed, and how those exposures interact across regimes. Diversification, in this world, isn’t just about owning more assets; it’s about diversifying across types of risk.

This is where trading, alpha, and factor investing meet. Some strategies are about harvesting known premia, smart beta in its purest form, systematically tilting toward risks that have historically been compensated. Others are about discovering new structure, inefficiencies, or behaviors before they become common knowledge. Both live inside the same framework. Factor models don’t eliminate alpha, they help you identify it, contextualize it, and decide whether it’s something structural, cyclical, or fleeting.

In the end, factor models don’t tell you what to trade. They tell you what you’re being paid for. And once you understand that, you can choose, deliberately, which risks to hold, which to avoid, and when to shift exposure as the cycle turns.

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