# Volatility Risk Premium Effect

The implied volatility from stock options is usually bigger than the actual historical volatility. Research therefore suggests the possibility to earn a systematic risk premium by selling at-the-money options short-term. Numerous papers show that this premium is quite substantial - selling put options gives average returns ranging from 0.5% to 1.5% per day. However, strong caution is needed in implementing these short volatility strategies (strategies which exploit the volatility premium by selling volatility - usually selling put options or straddles) as the return distribution is very abnormal (put sellers historically could incur losses up to -800%). There is also a strong serial correlation in large negative days (from the put seller's point of view); therefore, substantial margin reserves are needed when implementing these strategies and returns are then much lower. We present a simple option strategy exploiting the option premium, with a backtested period which includes the 1987 crash.

## Fundamental reason

Most researchers speculate that the volatility premium is caused by investors who strongly dislike negative returns and the high volatility on equity indexes and are therefore willing to pay a premium for portfolio insurance offered by puts. Other researchers explain the volatility premium with the Peso problem (Black Swan event) - a situation when a rare but influential event could have reasonably happened (and removed the premium) but did not happen in the sample; this explanation is, however, highly unlikely as other researchers show that huge market crashes would have to occur every few years to completely remove the volatility premium.

### Keywords:

## volatility effect, volatility premium

## Simple trading strategy

Each month, at-the-money straddle, with one month until maturity, is sold at the bid price with a 5% option premium, and an offsetting 15% out-of-the-money puts are bought (at the ask price) as insurance against a market crash. The remaining cash and received option premium is invested in the index. The strategy is rebalanced monthly.

## Source Paper

Coval, Shumway: Expected Option Returns

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=189840

Abstract:

This paper examines expected option returns in the context of mainstream asset pricing theory. Under mild assumptions, call options have expected returns which exceed those of their underlying security and which are increasing in their strike prices. Likewise, put options have expected returns which are below the risk-free rate and which are also increasing in their strike prices. Across a variety of time periods and return frequencies, S&P 500 and 100 index option returns strongly exhibit these characteristics. Under stronger assumptions, expected option returns are a linear function of option betas. Fama-MacBeth-style option return regressions produce risk premia close to the expected market return. However, the regression intercepts are significantly below zero. As a result, zero-beta, at-the-money straddle positions produce average losses of approximately three percent per week. Zero-beta straddles in other markets also lose money consistently. These findings suggest that some additional factor, such as systematic stochastic volatility, is priced in option returns.

## Other Papers

Carr, Wu: Variance Risk Premia

http://finance.eller.arizona.edu/documents/seminars/2004-5/PCarr.VarianceSwap03-05.pdf

Abstract:

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.

Bondarenko: Why are Put Options So Expensive?

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=375784

Abstract:

This paper studies the "overpriced puts puzzle" - the finding that historical prices of the S&P 500 put options have been too high and incompatible with the canonical asset-pricing models, such as CAPM and Rubinstein (1976) model. Simple trading strategies that involve selling at-the-money and out-of-the-money puts would have earned extraordinary profits. To investigate whether put returns could be rationalized by another, possibly nonstandard equilibrium model, we implement a new methodology. The methodology is "model-free" in the sense that it requires no parametric assumptions on investors' preferences. Furthermore, the methodology can be applied even when the sample is affected by certain selection biases (such as the Peso problem) and when investors' beliefs are incorrect.

Doran, Fodor: Is there Money to be Made Investing in Options? A Historical Perspective

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=873639

Abstract:

This paper examines the historical performance of 12 portfolios that include S&P 100/500 index options. Each option portfolio is formed using options with different maturities and moneyness, while incorporating bid-ask spreads, transaction costs, and margin requirements. Raw and risk-adjusted returns of option portfolios are compared to a benchmark portfolio that is only long the underlying asset. This allows the marginal impact of including options in the portfolio to be examined. The analysis reveals that including options in the portfolio most often results in underperformance relative to the benchmark portfolio. However, a portfolio that incorporates written options can outperform the benchmark on a raw and risk-adjusted basis. This result is dependent on restricting option investment relative to the maximum allowable margin. While positive and significant risk-adjusted performance is observed for some option portfolios, greater risk tolerance relative to the long index benchmark portfolio is required.

Duarte, Jones: The Price of Market Volatility Risk

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106960

Abstract:

We analyze the volatility risk premium by applying a modified two-pass Fama-MacBeth procedure to the returns of a large cross section of the returns of options on individual equities. Our results provide strong evidence of a volatility risk premium that is increasing in the level of overall market volatility. This risk premium provides compensation for risk stemming both from the characteristics of the option contract and the riskiness of the underlying equity. We also show with a large scale Monte Carlo simulation that measurement error in option prices and violations of arbitrage bounds induce highly economically significant biases in the mean returns of options. In fact, our simulation results demonstrate that biases can be up to several percentage points per day. These large biases can lead researchers to faulty conclusions with respect to both the magnitude of the volatility risk premium and the sign of expected option returns.

Eraker: The Volatility Premium

http://www.marginalq.com/eraker/volPremiumPaperJune08.pdf

Abstract:

Implied option volatility averages about 19% per year, while the unconditional return volatility is only about 16%. The di®erence, coined the volatility premium, is substantial and translates into large returns for sellers of index options. This paper studies a general equilibrium model based on long-run risk which in an e®ort to explain the premium. In estimating the model on past data of stock returns and volatility (VIX), the model is successful in capturing the premium, as well as the large negative correlation between shocks to volatility and stock prices. Numerical simulations verify that writers of index options earn high rates of return in equilibrium.

Hodges, Tompkins, Ziemba: The Favorite/Long-Shot Bias in S&P 500 and Ftse 100 Index Futures Options: The Return to Bets and the Cost of Insurance

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=424421

Abstract:

This paper examines whether the favorite/long-shot bias that has been found in gambling markets (particularly horse racing) applies to options markets. We investigate this for the S&P 500 futures, the FTSE 100 futures and the British Pound/US Dollar futures for the seventeen plus years from March 1985 to September 2002. Calls on the FTSE 100 with three months to expiration display a relationship between probabilities and average returns that are very similar to the favorite/long-shot bias in horse racing markets pointed out by Ali (1979), Snyder (1978) and Ziemba & Hausch (1986). There are slight profits from deep in-the-money calls on the S&P 500 futures and increasingly greater losses as the call options are out-of-the-money. For 3 month calls on the FTSE 100 futures, the favorite bias is not found, but a significant long-shot bias has existed for the deepest out of the money options. For call options in both markets, for the one month horizon, only a longshot bias is found. For the put options on both markets, and for both 3 month and 1 month horizons, we find evidence consistent with the hypothesis that investors tend to overpay for all put options as an expected cost of insurance. The patterns of average returns is analogous to the favorite/longshot bias in racing markets. For options on the British Pound/US Dollar, there does not appear to be any systematic favorite/long-shot bias for either calls or puts.

Israelov, Nielsen: Still Not Cheap: Portfolio Protection in Calm Markets

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2579232

Abstract:

Recent equity volatility is near all-time lows. Option prices are also low. Many analysts suggest this represents a good opportunity to purchase put options for portfolio insurance. It is well-known that portfolio insurance is expensive on average, but what about in calm markets? History suggests it still is. We investigate the relationship between option richness and volatility across ten global equity indices. Option prices may be low, but their expected values tend to be even lower.

Ilmanen: Do Financial Markets Reward Buying or Selling Insurance and Lottery Tickets?

https://www.aqr.com/~/media/files/papers/faj-do-financial-markets-reward-buying-or-selling-insurance-and-lottery-tickets.pdf

Abstract:

Selling financial investments with insurance or lottery characteristics should earn positive longrun premiums if investors like positive skewness enough to overpay for these characteristics. The empirical evidence is unambiguous: Selling insurance and selling lottery tickets have delivered positive long-run rewards in a wide range of investment contexts. Conversely, buying financial catastrophe insurance and holding speculative lottery-like investments have delivered poor longrun rewards. Thus, bearing small risks is often well rewarded, bearing large risks not.

Li, Wang: Option-Implied Downside Risk Premiums

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2603857

Abstract:

This article examines downside risk premiums using S&P 500 index (SPX) options. Portfolios are constructed using the index options to replicate the downside risk factors and their average excess returns provide estimates of downside risk premiums. We show that all the market risk premium comes from the downside. The mimicking portfolio returns also show that most of the downside risk premium is associated with large market-level losses that are rarely observed. In contrast, investors seem to require little excess return for bearing moderate market-level losses. Therefore, the downside risk premium is largely a tail risk premium. We compare the downside risk premiums measured from stocks and the options to examine whether the risk is priced consistently across the two markets. Our evidence raises several concerns about the downside risk premium measures from the stock market. Overall, we find no robust evidence that downside risks are priced in the stock market in the same way as in the options market.

Donninger: Hedging Adaptive Put Writing with VIX Futures : The Affenpinscher Strategy

http://www.godotfinance.com/pdf/AffenPinscherStrategy_Rev1.pdf

Abstract:

In a previous working paper I analyzed the Austrian and Doberman Pinscher strategy. The Austrian is an adaptive Put Writing strategy. One hedges the short position with a long Put with a lower strike. The Doberman is more aggressive. The long hedge is omitted. The risk is in both cases reduced by entry and exit conditions. The Affenpinscher uses the same general framework. But the hedging is done with long VIX Futures. There are several VIX Futures available. One selects the VIX Future with the lowest roll-value. The overall performance of the Affenpinscher is between the Austrian and Doberman Pinscher. The Pinscher strategies have generally an attractive performance. The best choice within the family is a matter of risk appetite. Revision 1 extends the historic simulation for the SPX Options till 2014-06-13. As the original parameters are not changed we perform an out of sample test. The attractive properties of the strategy are confirmed. Revision 1 is added before the Conclusion of the original paper. A similar update has been done for the other Pinscher strategies.

Shulte, Stamos: The Performance of Equity Index Option Strategy Returns During the Financial Crisis

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2669999

Abstract:

Equity index option writing strategies delivered abnormally high returns in the past. This empirical fact is often attributed to the so-called Path Peso argument, which states that put option prices reflect risk premiums for extreme jumps in prices and volatility, which are underrepresented in empirical data. This paper uses option price data collected during the financial crisis as a natural experiment to to examine whether the empirical evidence of abnormally high index option returns persists in periods with adverse outcomes of jump and volatility risk. To this end, this paper uses S&P 500, DAX, and EURO STOXX 50 option price data to analyze returns of a wide array of index option strategies.

Israelov, Nielsen: Covered Calls Uncovered

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2444999

Abstract:

Equity index covered calls have historically provided attractive risk-adjusted returns largely because they collect equity and volatility risk premia from their long equity and short volatility exposures. However, they also embed exposure to an uncompensated risk, a naïve equity market reversal strategy. This paper presents a novel performance attribution methodology, which deconstructs the strategy into these three identified exposures, in order to measure each’s contribution to the covered call’s return. The covered call’s equity exposure is responsible for most of the strategy’s risk and return. The strategy’s short volatility exposure has had a realized Sharpe ratio close to 1.0, but its contribution to risk has been less than 10 percent. The equity reversal exposure is responsible for about one-quarter of the covered call’s risk, but provides little reward. Finally, we propose a risk-managed covered call strategy that hedges the equity reversal exposure in an attempt to eliminate this uncompensated risk. Our proposed strategy improved the covered call’s Sharpe ratio, and reduced its volatility and downside equity beta.

Bondarenko: An Analysis of Index Option Writing with Monthly and Weekly Rollover

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2750188

Abstract:

This paper analyzes the performance of the two CBOE PutWrite Indexes through the end of 2015. The two PutWrite indexes are found to have had strong performance in several areas: 1) Annual premium income: From 2006 to 2015, the average annual gross premium collected was 24.1 percent for the PUT Index and 39.3 percent for the WPUT Index. While a one-time premium collected by the weekly WPUT Index usually was smaller than a one-time premium collected by the monthly PUT Index, the WPUT Index had higher aggregate annual premiums because premiums were collected 52 times, rather than 12 times, per year. 2) Lower risk: Over the last 10 years, since the launch of Weeklys options, the WPUT Index had a lower standard deviation than the PUT and S&P 500 Indexes. The maximum drawdowns were 24.2 percent for the WPUT Index, 32.7 percent for the PUT Index and 50.9 percent for the S&P 500 Index. 3) Higher long-term returns with lower volatility: Looking longer-term with the PUT Index, since mid-1986, the annual compound return of the PUT Index was 10.13 percent, compared with 9.85 percent for the S&P 500 Index. The standard deviation of the PUT Index was substantially lower as well, 10.16 percent versus the S&P 500 Index’s 15.26 percent.

Dapena, Siri: Index Options Realized Returns Distributions from Passive Investment Strategies

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2733774

Abstract:

Few papers provide research about options returns, and the few available are focused in the analysis from the perspective of the long side of the option contract, i.e. the buyer that pays the price and her expected and realized option return. The main point of our research work is to provide a simple metric to analyze option returns from the perspective of the short side of the contract, the seller, where at the time of the sale of naked options, capital is committed in the form of a guarantee or margin (similar to net worth). We estimate realized returns from passive investment strategies, by assuming puts and calls are kept until the expiration of the maturity. To that purpose we develop an appropriate algorithm which is applied on real historic data. Our result is a distribution of realized option returns (ex-ante prices and ex-post cash flows whether the options end up in or out-of-the-money with respect to margin requirements) for the seller point of view, as if the seller was an insurer seeking to calculate how profitable the insurance activity is. From the results we can see that selling puts is more profitable than selling calls, without adjusting for the return of the underlying asset and for the risk free rate of return, something in line with what was expected, but we also find that the risk is approximately the same. We also find that time tends to increase the realized returns, measured everything on annual basis.

Dotsis: Option Pricing Methods in the Late 19th Century

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2831362

Abstract:

This paper examines option pricing methods used by investors in the late 19th century. Based on the book called “PUT-AND-CALL” written by Leonard R. Higgins in 1896 and published in 1906 it is shown that investors in that period used routinely the put-call parity for option conversion and static replication of option positions, and had developed no-arbitrage pricing formulas for determining the prices of at-the-money and slightly out-of-the-money and in-the-money short-term calls and puts. Option traders in the late 19th century understood that the expected return of the underlying does not affect the price of an option and viewed options mainly as instruments to trade volatility.

Israelov, Tummala: Which Index Options Should You Sell?

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2990542

Abstract:

This paper explores historical return and risk properties of equity-hedged options across the S&P 500 option surface. We evaluate returns by estimating alpha to the S&P 500 index, and we quantify risk using three metrics: return volatility, losses under stress tests, and conditional value at risk. We show that analyzing option risk-adjusted alphas using different risk metrics leads to significantly different conclusions. We find that the most compensated options to sell on the S&P 500 surface per unit of stress-test loss are front-month options with strikes near-the-money and moderately below the index level. We apply these results to evaluate return expectations for short volatility strategies, potential added return from option selection, and implications for variance swaps.

## Hypothetical future performance

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