Variance Swap Carry (Harvesting the Variance Risk Premium)

Overview

A variance swap is about as clean as volatility trading gets. You agree on a level of variance today, the strike. At expiry, you settle against the variance that the underlying actually realized over the life of the contract. If you sold the swap, you make money when realized variance comes in below the strike and lose when it comes in above.

No delta hedging. No strike selection. No path dependence in the payoff. Just a direct bet on realized volatility versus the level the market priced.

And the market prices it high. Consistently. This gap, implied variance minus subsequently realized variance, is the variance risk premium, and it is one of the most thoroughly documented effects in the whole of empirical finance. Selling variance and holding to expiry has been profitable across decades, across markets and across asset classes.

There is a very good reason for this, and it is the same reason it is dangerous.

Strategy logic

• The trade: Sell variance at the prevailing strike. Hold to expiry. Settle against realized.
• The edge: Implied variance has historically exceeded realized variance most of the time, often by a meaningful margin. You collect that difference.
• Why it is paid: Realized variance spikes precisely when portfolios are in trouble. An asset that pays off in a crash is worth more than its statistical expectation, so investors overpay for it. The seller collects that overpayment as compensation for taking on crash exposure.
• The catch: Variance is the square of returns. That single fact is the entire risk story.

The convexity problem

This is the part that separates variance swaps from every other short-volatility trade, and it deserves its own section.

Because you settle on squared returns, the loss on a short variance position does not scale linearly with the size of the market move. It scales quadratically. A market that moves twice as much as you expected does not cost you twice as much. It costs you roughly four times as much.

Put a number on it. If you sold variance at a level corresponding to 15 percent volatility and realized volatility comes in at 60 percent, your loss is proportional to 60 squared minus 15 squared, against a premium proportional to a much smaller number. The loss is not a bad month. It is a multiple of the entire notional.

A short variance position that is not capped has, in principle, an unbounded loss. This is why almost every variance swap actually traded in size is a capped variance swap, where the payoff is limited to some multiple of the strike, typically 2.5 times. Even capped, the loss can be enormous relative to the premium.

Parameters (knobs)

• Cap level: Lower caps cost you some premium and buy you survival. Take the survival.
• Tenor: One month is the standard. Longer tenors have a bigger premium in absolute terms and much more mark to market volatility along the way.
• Entry filter: The premium is not constant. It is far richer after a volatility spike, when everyone is frightened, than it is in a quiet market. Selling variance only when the premium is in the upper part of its historical range materially improves the risk-adjusted outcome. It also means sitting out a lot.
• Notional: Set by worst case, always. If the cap is 2.5 times the strike, your maximum loss is knowable. Size so that maximum loss is survivable, then work backwards to the notional.

Where it works and where it hurts

It works in the long quiet stretches, which is most of the time. Realized volatility is lower than implied, the swaps settle in your favour, and you bank the premium month after month.

It hurts in the fat left tail, and because of the squaring it hurts more than any other short-vol structure. In the worst months of 2008 and in March 2020, short variance positions lost multiples of their annual carry in weeks. Funds closed.

There is one nuance worth knowing: the premium is usually largest immediately after a crash, when implied variance is enormous and fear is at its peak. That is exactly when selling variance is most attractive and most psychologically impossible. Systematic rules exist to force you to do the thing you will not do on your own.

Backtest design checklist

• Compute realized variance the way the contract does. Close to close, no overnight adjustment, no smoothing. Small definitional differences change the results.
• Backtest the capped payoff, not the uncapped one. An uncapped backtest will either look impossible or produce a loss so large it distorts every summary statistic.
• Model the mark to market path. You may intend to hold to expiry, but your clearer marks you daily. If those marks trigger a margin call you cannot meet, holding to expiry was never available to you.
• If you are replicating with options, model the replication error. The theoretical replication needs options at every strike. Real chains do not have that, and the missing wings are exactly where the crash lives.
• Do not report a Sharpe ratio as the headline. For a payoff this skewed it is close to meaningless. Report the worst outcome and the recovery.

Common failure modes

• Thinking linearly about a quadratic payoff. People size short variance as if a bad month costs a bit more than a normal month. It costs many multiples more.
• Selling variance when the premium is thin. In calm markets the implied to realized spread compresses, but the tail risk does not compress at all. You are taking the same crash exposure for less pay.
• Replicating badly. A homemade variance swap built from a few liquid strikes is not a variance swap. It is a short option position with a gap where the disaster scenario should be.
• Ignoring the daily mark. The trade can be right at expiry and still liquidate you in week two.

Our notes and suggestions

The variance risk premium is real. It is one of the few effects in finance we would call genuinely robust. But it is compensation for bearing a specific, terrible risk, and the compensation exists because the risk is real, not because the market is stupid.

Anyone selling you a "variance carry" product with a beautiful backtest and no discussion of the convexity is either not being straight with you or does not understand the product. Insist on the cap. Size on the cap. Only sell when the premium is genuinely elevated, and accept that this means sitting on your hands for long stretches.

What would change our mind: a sustained period where realized variance exceeds implied, which would mean the premium has flipped and you are being paid nothing to hold the tail.