Traditionally, short volatility trading is regarded as a risky investment approach. Even during quiet periods, strategies based on selling naked options can lead to considerable losses. It is no wonder that a financial crisis, accompanied by a sharp rise in historical and implied volatilities, is commonly considered a factor that dramatically raises the risk of substantial losses, right up to the near-bankruptcy level. Scrutinizing the data of the current crisis allows us to judge whether such views are correct.
Three basic issues will be examined: how does the crisis influence the profitability of short option positions, does the crisis change the structure of trading opportunities existing at the option market and is the effectiveness of the criterion used in selection of the most promising trading opportunities affected by the crisis?
Because the timing of trade entry plays a key role in volatility selling strategies, all of these questions will be studied in the context of different time intervals between trade entry and option expiration.
The success of almost any strategy based on selling naked options depends on the selection procedure. This procedure can be based on one or several criteria that may be informal, or have strict mathematical guidelines. A popular metric is profit expectations based on various probability distributions. Here, we’ll examine how the current financial crisis affects the mathematical expectation of profit estimated using lognormal distribution. This is calculated as the integral of the payoff function with respect to the lognormal probability density function.
Two databases were used in this study. The first one, corresponding to the crisis period, covers the time interval from Aug. 1, 2007, to March 30, 2009. The second database corresponds to the period before the crisis (Jan. 2, 2003, to July 31, 2007). Both data arrays contain prices of options corresponding to the shares that make up the S&P 500 index.
Within each database, a series of 60 portfolios was created for each expiration date. These portfolios differed from each other in terms of time to expiration. The most “distant” portfolio was 60 trading days away from the expiration, the next one was 59 days, and so on.
Each portfolio consisted of 500 short straddles related to the stocks forming the S&P 500 index. Each straddle used the strike closest to the current stock price. The quantity of options corresponding to each stock was determined as $1,000,000/x, where x is the price of the stock underlying the straddle.
For all combinations, criterion values were calculated at portfolio creation. Profits were calculated at the expiration date. The sum of mathematical expectations of all straddles in the portfolio gives the criterion value, while the profit is calculated by summing up profits and losses of these combinations.
During calm periods, profit does not depend on the number of days left to expiration, while at the time of crisis, the profitability of short option portfolios falls as the time left to expiration increases (see “Comparing profits” ). Besides, a decrease of average profit is accompanied by a sharp increase in its variability (vertical bars on chart), which can be explained by high market volatility during the crisis. Close to expiration date profits during both crisis and quiet periods are virtually the same, which may be the most important conclusion of this study.
TAKING A TRADE
A trading opportunity arises when the market price of the option deviates from its fair value — that is, the value that implies zero profit for both buyers and sellers. We assume that trading opportunities are inherent to combinations for which the absolute difference between market and fair values exceeds 1%. The relative frequency of such combinations reflects the abundance of potential trading opportunities existing in the market at a specific time moment.
“Trading opportunities” (above) shows that in crisis, potential trading opportunities exceed those in a calm market. As expiration approaches, the number of trading opportunities falls sharply. However, during the crisis, the rate of this decrease is not as high as during the calm period. Close to expiration, the number of opportunities existing during the crisis is greater than those in the calm period. Also, far from the expiration, the difference between trading potentials is negligible.
Thus, when expiration approaches, more unfairly priced combinations arise during the crisis. Does it mean that the criterion used to reveal potentially profitable combinations would allow identifying these additional trading opportunities, which could raise the number of profitable combinations. Analyzing the criterion effectiveness will answer this.
CRITERION EFFECTIVENESS
Several valuation methods should be applied to investigate the impact of the crisis on criterion effectiveness. We begin with ranking analysis developed on the basis of the set theory. This method is based on calculation of the coefficient of the criterion effectiveness k:
k=KP X B/K X P
In the above, B is the total number of combinations (500 in this study, which is the number of straddles in every portfolio), K is the number of combinations with expected profit higher than 1% of the current underlying asset price, P is the number of combinations with profit realized at expiration that is higher than 1% of the current underlying asset price, KP is the number of combinations included in both K and P sets (those of the profitable combinations which were correctly identified by the criterion at the stage of portfolio creation).
The criterion is considered to possess a forecasting capacity when k value exceeds 1. The higher the value of this coefficient, the more effective is the criterion.
“Ranking analysis” shows that the criterion used in this study does not allow benefiting from the sharp rise in the number of trading opportunities occurring during the crisis. While near expiration, the number of trading opportunities is much higher during the crisis than during the calm period, the criterion based on mathematical expectation and on lognormal distribution is more effective in a quiet market. However, when this criterion is applied far from expiration, it shows the same effectiveness regardless of the market phase. In both market environments, the criterion effectiveness is highest close to expiration and decreases sharply as the time to expiration increases.
Ranking analysis of criterion effectiveness estimates the relationship between different combination sets. This method is based on relative frequencies and omits absolute profits of separate combinations. This drawback can be compensated for by considering deviations of actual profits from their expected values and by using correlations between criterion and profit values.
The difference between expected and realized profits increases as the interval between portfolio creation and expiration widens. Such direct relationship is evident both during calm and crisis periods. However, during the crisis, the divergence of two profits increases at a higher rate (see “Deviations from reality,” above). Positive difference means that potential profitability of a combination was overestimated. Negative difference implies that the criterion underestimated the potential profit.
When the expiration is distant, average profit is slightly overestimated in calm periods and highly overestimated during the crisis. Near expiration, deviations between actual and estimated profits are small for both market phases. This means that the crisis does not decrease the effectiveness of criteria applied shortly before expiration date. However, if the investor estimates the potential profitability of option combinations far from expiration, criterion values should be adjusted by introducing a correcting coefficient (the slope of the regression line shown in the figure can be used). At the same time, during the crisis, the variability of deviations of actual profit from estimated values is high, especially far from expiration. Therefore, adjusting coefficients will produce no more than a limited effect.
The correlation between criterion values and calm-period profits grows as time to expiration increases (see “Correlations”). The inverse relationship is observed during crisis: the farther away expiration, the lower the correlation coefficient. Nevertheless, close to expiration, correlation coefficients corresponding to both market phases are almost equivalent. The crisis does not affect the effectiveness of the criterion when its application is limited to a short time interval between portfolio creation and expiration.
The dawning of the crisis period generated additional trading opportunities for option traders (see “Trading opportunities”). This owes to the sharp price fluctuations (historical volatility) and to growing option premiums (implied volatility) that lead traders to make more mistakes in estimating fair option values. However, exploiting these additional trading opportunities is difficult because their discovery using traditional criteria (developed and optimized during calm periods) is impossible.
Despite the adverse effect of crises on high-risk strategies, such as short volatility trading, it does not mean that the whole class of strategies based on selling naked options should be excluded from the investment plans. Although the majority of short portfolios might indeed generate considerable losses during crisis periods, these losses can be reduced and even turned into profits by shortening investment horizons (see “Comparing profits”).
During the crisis period, the criterion fails only when there are more than 10-15 working days until expiration. Close to expiration, the crisis does not affect the quality of the criterion. Although the frequency of false estimates may increase even in this situation, it does not affect the valuation of average profitability of short option portfolios.
Because markets can go several years without extreme crises, traders need a risk management plan that goes beyond simple modeling. The next crisis is usually different from the last and often more extreme than what is
modeled for.
Sergey Izraylevich has a Ph.D. from Hebrew University of Jerusalem. He is the chief investment officer of Hortan SARL and chairman of High Technology Invest Inc. Vadim Tsudikman is a director at Hortan and develops trading systems based on genetic optimization algorithms. Contact the authors at izraylevich@htinvest.ru