Duration volatility risk premia

May 28, 2022

Jupyter Notebook

The analysis of this post has been updated on June 22, 2023

Duration volatility risk premium means compensation for bearing return volatility risk of an interest rate swap (IRS) contract. It is the scaled difference between swaption-implied and realized volatility of swap rates’ changes. Historically, these premia have been stationary around positive long-term averages, with episodes of negative values. Unlike in equity, simple duration volatility risk premia have not been significant predictors of subsequent IRS returns. However, they have helped predict idiosyncratic IRS returns in non-USD markets.
Moreover, two derived concepts of volatility risk premia hold promise for trading strategies. [1] Term spreads are the differences between volatility risk premia for longer-maturity and shorter-maturity IRS contracts and are related to the credibility of a monetary policy regime. Historically, term spreads have been significant predictors of returns on curve positions. [2] Maturity spreads are the differences between volatility risk premia of longer- and shorter-maturity options and should be indicative of a fear of risk escalation, which affects mainly fixed receivers. Indeed, maturity spreads have been positively and significantly related to subsequent fixed-rate receiver returns. These premia are best combined with fundamental indicators of the related risks to give valid signals for fixed-income positions.

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Variance risk premia for patient investors

January 8, 2022

The variance risk premium manifests as a long-term difference between option-implied and expected realized asset price volatility. It compensates investors for taking short volatility risk, which typically comes with a positive correlation with the equity market and occasional outsized drawdowns.
A recent paper investigates a range of options-related strategies for earning the variance risk premium in the long run, including at-the-money straddle shorts, strangle shorts, butterfly spread shorts, delta-hedged shorts in call or put options, and variance swaps. Evidence since the mid-1990s suggests that variance is an attractive factor for the long run, particularly when positions take steady equal convexity exposure. Unlike other factor strategies, variance exposure has earned premia fairly consistently and typically recovered well from its intermittent large drawdowns.

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The risk-reversal premium

December 10, 2021

The risk reversal premium manifests as an overpricing of out-of-the-money put options relative to out-of-the-money call options with equal expiration dates. The premium apparently arises from equity investors’ demand for downside protection, while most market participants are prohibited from selling put options. A typical risk reversal strategy is a delta-hedged long position in out-of-the-money calls and an equivalent short position in out-of-the-money puts. Historically, the returns on such a strategy have been positive and displayed little correlation with the returns of the underlying stocks. The strategy does incur gap risk with a large downside, however. The long-term profit of risk-reversal strategies reflects implicit market subsidies related to “loss aversion”.

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Measures of market risk and uncertainty

August 8, 2020

In financial markets, risk refers to the probability distribution of future returns. Uncertainty is a broader concept that encompasses ambiguity about the parameters of this probability distribution. There are various types of measures seeking to estimate risk and uncertainty: [1] realized and derivatives-implied distributions of returns across assets, [2] news-based measures of policy and political uncertainty, [3] survey-based indicators, [4] econometric measures, and [5] ambiguity indices. The benefits for macro trading are threefold. First, uncertainty measures provide a basis for comparing the market’s assessment of risk with private information and research. Second, changes in uncertainty indicators often predict near-term flows in and out of risky asset classes. Third, the level of public and market uncertainty is indicative of risk premia offered across asset classes.

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Realistic volatility risk premia

November 17, 2018

The volatility risk premium compensates investors for taking volatility risk. Conceptually it is based on the difference between options-implied and expected realized volatility. In equity markets this premium should be positive in the long run and fluctuate overtime depending on the market’s willingness to pay for protection against future changes in price volatility. In practice, measuring the premium overtime is challenging, particularly because expected realized volatility is not known. Using recent realized volatility as a proxy can be highly misleading. However, a realistic estimate can be constructed by considering the trade-off between timeliness and noise ratio of recent price changes and the long-term mean reversion of volatility. This “realistic” volatility risk premium has been positively correlated with subsequent daily volatility index future returns.

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Variance term premia

October 27, 2018

Variance term premia are surcharges on traded volatility that compensate for bearing volatility risk in respect to underlying asset prices over different forward horizons. The premia tend to increase in financial market distress and decrease in market expansions. Variance term premia have historically helped predicting returns on various equity volatility derivatives. The premia themselves can be estimated based on variance swap forward rates and their decomposition into expected underlying price variance and risk premia. In particular, the variance term premia are obtained as the difference between forward swap rates and realized volatility forecasts, whereby the latter are related to a “volatility state vector”.

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What variance swaps tell us about risk premia

August 4, 2018

Variance swaps are over-the-counter derivatives that exchange payments related to future realized price variance against fixed rates. Variance swaps help estimating term structures for variance risk premia, i.e. market premia for hedging against volatility risk based in the difference between market-priced variance and predicted variance. The swap rates conceptually produce more accurate estimates of variance risk premia than implied volatilities from the option markets. An empirical analysis suggests that swap-based variance risk premia are positive and increasing in maturity. A drop in equity prices or rise in credit spreads pushes variance risk premia higher. The effect is strongest for short maturities up to 6 months, but more persistent for long maturities.

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The dangerous disregard for fat tails in quantitative finance

July 28, 2018

The statistical term ‘fat tails’ refers to probability distributions with relatively high probability of extreme outcomes. Fat tails also imply strong influence of extreme observations on expected future risk. Alas, they are a plausible and common feature of financial markets. A summary article by Nassim Taleb reminds practitioners that fat tails typically invalidate methods and conventions applied in quantitative finance. Standard in-sample estimates of means, variance and typical outliers of financial returns are erroneous, as are estimates of relations based on linear regression. The inconsistency between the evidence of fat tails and the ongoing dominant usage of conventional statistics in markets is plausibly a major source of inefficiency and trading opportunities.

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The importance of volatility of volatility

July 21, 2018

Options-implied volatility of U.S. equity prices is measured by the volatility index, VIX. Options-implied volatility of volatility is measured by the volatility-of-volatility index, VVIX. Importantly, these two are conceptually and empirically different sources of risk. Hence, there should also be two types of risk premia: one for the uncertainty of volatility and for the uncertainty of variation in volatility. The latter is often neglected and may reflect deep uncertainty about the structural robustness of markets to economic change. A new paper shows the importance of both risk factors for investment strategies, both theoretically and empirically. For example, implied volatility and “vol of vol” typically exceed the respective realized variations, indicating that a risk premium is being paid. Also, high measured risk premia for volatility and “vol-of-vol” lead to high returns in investment strategies that are “long” these factors.

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Finding implicit subsidies in financial markets

May 26, 2018

Implicit subsidies in financial markets can be defined as expected returns over and above the risk free rate and conventional risk premia. While conventional risk premia arise from portfolio optimization of rational risk-averse financial investors, implicit subsidies arise from special interests of market participants, including political, strategic and personal motives. Examples are exchange rate targets of governments, price targets of commodity producers, investor relations of institutions, and the preference for stable and contained portfolio volatility of many households. Implicit subsidies are more like fees for services than compensation for standard financial risk. Detecting and receiving such subsidies creates risk-adjusted value. Implicit subsidies are paid in all major markets. Receiving them often comes with risks of crowded positioning and recurrent setbacks.

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