Despite the growth of exotic-type options, some of the most basic hedging strategies are still popular as they fulfill basic hedging needs in a simple and effective way. A closer look at hedging performance using empirical tests reveals important statistics.
DEFINITION
A risk-reversal is the price difference between two out-of-the-money options. For hedging needs, strikes are often struck to create a zero-cost strategy, making what is often called a zero cost collar. Although a 25-delta risk-reversal is a benchmark quote in the interbank market, setting the strikes (deltas) is very flexible and depends on customer needs. As the delta on each strike is increased towards 50 the characteristics will converge to a forward hedge. Low-delta strikes tend toward an open position and are used to hedge against extreme events. Using just one side of the strategy, for example, buying a protective put or selling a covered call, significantly changes the risk-return pattern and the performance will be much more dependent on the volatility level.
EMPIRICAL TEST OF OPTION STRATEGIES
The following data is based on an empirical test in U.S. dollar/Deutschmark from 1992-1998, assuming one-month hedging periods and hedge rollover at the end of each period. The forward rate is used as a benchmark for comparison and all calculations are based on mid-market prices.
For a Deutschmark-based company with U.S. dollar revenues, leaving the position open provides a small average profit of 0.1 percent per month. The best month was up 8.18 percent and the worst down 6.37 percent compared to a forward hedge. The risk, defined as the standard deviation (SD), was 2.89 percent or 10 percent annualized. The profit would turn into a similar average loss were it for U.S. dollar liabilities.
RISK-REVERSAL HEDGE
Putting on a 25 delta risk-reversal reduces SD to 1.70 percent (-41.10 percent). Basically the strategy cuts off both sides of the tail, reducing both profit and loss. The skews of the distribution are not really changed and are close to zero.
The cost of doing risk-reversals depends very much on market preferences. In the above example the average profit for the hedge is +0.01 percent assuming a flat volatility, but will be reduced by approximately 0.012 percent per 0.10 percent volatility spread. As the risk-reversal tends to favor U.S. dollar puts on average, extra cost can be expected, if long U.S. dollar positions are hedged. Hedging against market preferences might give additional return. As an example, risk-reversals including a short position in Japanese yen calls, tend to include a significant volatility pick-up.
HEDGING USING PROTECTIVE PUTS OR COVERED CALLS
Probably the most simple hedge is buying the protective option. In the example of the German company, that would be buying a U.S. dollar put. Another simple strategy would be selling a covered option (call) only. Removing one leg from the 25-delta risk-reversal increases risk, but the SD is still reduced by more than 20 percent compared to an unhedged position.
When buying or selling options, the volatility level will affect the profit or loss (P/L) on the hedge. In terms of risk reduction, at-the-money options provide similar numbers to a 25-delta risk reversal. For the tested period, buying 50 delta puts or selling 50 delta calls reduces SD by 40.5 percent on average. The covered call strategy performs well giving an average profit of 0.18 percent per month. For the protective put the average is a loss of 0.07 percent compared to the forward hedge. A major difference in risk is that doing just one side change the skewness significantly. For the put strategy skewness is + 1.69. A positive reading is a statistical indication of small losses but few large gains. The skewness for the covered call strategy is 1.55. The best month here is a profit of 2.16 percent and the worst a loss of 5.03 percent. On average the covered call strategy outperforms in two-thirds of all hedging periods, and the put strategy in approximately one-third of the periods. As gains/losses are not symmetrical the average P/L is really not that different.
The probability distribution for protective puts and the 25-delta risk-reversal is illustrated in the graph.
The reason for this difference in performance is quite simple. Over the test period implied volatility overshot actual volatility by 1.06 percent, leading to better performance for short option positions. In terms of risk the numbers also tell a different story. Using just standard deviation as a measure of risk is misleading when options are included. Using traditional measures for performance such as Sharpe ratios (Return divided by standard deviation) provides little help in performance evaluation. Positive skewness provides flexibility, but the real value is not well described in financial literature.
The summary statistics for risk and return (see graphic, previous page) are similar if other currency pairs are included, although the relative profit-loss performance between short volatility and long volatility strategies is very small. It is worth noting that many financial market prices might include a small risk premium (peso-effect) to include rare but extreme events. That could be high nominal interest rates, volatility levels or risk-reversals. The financial markets are both competitive and efficient and focusing on the best suitable hedging structure is by far the most important issue.
This week's Learning Curve was written by Erik Hulvej, a v.p. in currency options trading at Den Danske Bankin New York.
