Assignment 1

Dynamic Option Trading Strategies

(DOTS)

Sunday, February 28, 1999

Qi (Tom) Chen

Ray Franzi

Yves Geniaux

Gustavo Vello

Zade Zalatimo

Our approach was to identify pricing errors in the S&P 100 Index options, as initially identified by Harvey and Whaley (1991). The S&P index option contract (OEX) is traded on the Chicago Board Options Exchange (CBOE). It is the most actively traded index option contract in the world, and its implied volatility is an accurate reflection of market volatility.

One measure of the level of implied volatility in index options is the CBOE's Volatility Index (VIX). The VIX, introduced by the exchange in 1993, measures the volatility of the U.S. equity market. It provides investors with up-to-the-minute market estimates of expected volatility by using real-time OEX index option bid/ask quotes. This index is calculated by taking a weighted average of the implied volatility of eight OEX calls and puts. The chosen options have an average time to maturity of 30 days. Consequently, the VIX is intended to indicate the implied volatility of 30-day index options. Implied volatility levels in index options change frequently and substantially. Consequently, when trading short-term index options, traders should forecast the index level, the time period, and the volatility level. Traders of long-term index options should also include a forecast of interest rates. (CBOE website).

We gathered monthly returns for the S&P 100 over a twelve-year period and built a model to forecast the index return. We forecasted the volatility of the S&P 100 index with an ARCH model, and identified differences between VIX predictions and our forecast of volatility. As a result, we built a model that would allow us to take advantage of this discrepancy.

We compare our strategies to the return of the S&P 100. The model is designed to recommend the optimal strategy on a monthly basis depending on the observed scenario.

The forecasted volatility is lower than the VIX or lower than the VIX by a determined hurdle rate. Three different strategies could be applied:

• Strategy 1: we sell one-month at-the-money S&P 100 calls recognizing that they are overvalued.
• Strategy 2: we sell one-month at-the-money S&P 100 puts recognizing that they are also overvalued.
• Strategy 3: we sell one-month at-the-money S&P puts and one-month at-the-money calls recognizing that they are both overvalued.

The forecasted volatility is higher than the VIX or higher than the VIX by a determined hurdle rate. The strategies developed previously would be altered as follows:

Strategy 1: we invest in S&P 100 (another approach could have been to buy one-month at-the-money S&P 100 calls recognizing that they are undervalued).

• Strategy 2: we invest in S&P 100 (another approach would have been to buy one-month at-the-money S&P 100 puts recognizing that they are also undervalued).
• Strategy 3: we invest in S&P 100 (another approach would have been to buy one-month at-the-money S&P 100 puts and one-month at-the-money calls recognizing that they are both undervalued).

Furthermore, we can refine our strategy by including the forecasted S&P 100 return movement in our first scenario. Due to the current market conditions and the improved economic fundamentals, we were able to predict the market returns with a regression model based on the information available. The hit rate of our prediction model is about 77% in the past four years, and the adjusted R-squared is 13%. Based on the reasonable predictability, we designed an improved strategy which will take both returns and volatility forecasting into account:

• Strategy 4 (base case with only returns forecasting): if the forecasted return on the S&P 100 index is positive and above a predetermined hurdle rate, we buy calls because of the bullish expectation on the index. If the forecasted return is negative and below a hurdle rate, we buy puts because of the bearish expectation on the index.
• Strategy 5 (DOTS): This stratgey seeks to set two hurdles, the original volatility hurdle as prescribed in the previous strategies and an additional hurdle for forecasted returns on the underlying index. If the forecasted return on the S&P 100 index is positive and above a predetermined hurdle rate, and our forecasted volatility exceeds the predetermined VIX hurdle, we buy calls recognizing that they are undervalued because of the higher forecasted volatility and because of the bullish expectation on the index. If the forecasted return is negative and below a predetermined hurdle rate and our forecasted volatility exceeds the predetermined VIX hurdle, we buy puts because of their mispricing and because of the bearish expectation on the S&P index. If the forecasted return failed to reach the hurdle rate and the forecasted volatility is low, we would invest in the S&P; if the forecasted return is flat, and the forecasted volatility is high, we will swap out of the S&P 100 with the combination of calls and puts.

We create a fund benchmarked on the S&P 100 return. Every month, if we see an opportunity to apply our concept (our forecasted volatility is greater or less than the VIX by more than the hurdle rate), we would invest 1 million dollars of the fund or a percentage of the fund in one of our trading strategies.

We benchmarked our model on the S&P 100 over a period of 12 years. The results are quite self-explanatory and seem to reveal that our strategies are very successful. We compared our model’s returns, standard deviations and Sharpe ratios to determine their effectiveness against the S&P 100 index (The hurdle rate used for VIX was 10%):

Strategies 1, 2 and 3 have a better Sharpe ratio than the S&P 100. That is, they offer a better tradeoff between their return and standard deviation. These strategies were only taking advantage of our volatility forecast against the VIX and did not include any S&P 100 return monthly forecast.

On the contrary Strategy 4 and Strategy 5 which are using return forecast on the S&P 100 show a higher volatility than the S&P 100 due to the nature of this strategy. The interesting feature of this approach is that the volatility arises when there are frequent trades. In fact, the volatility is in out favor. Strategy 5 (DOTS) which uses both return and volatility forecast outperforms the S&P 100 index for last to years (including out-of-sample test).

Indeed, it was considering the forecasted monthly return on the S&P 100 index as an input in the strategy layout. When the forecasted volatility was lower than the VIX and the forecasted return was positive, the strategy was to buy calls and sell puts. The investment in calls, suggested by the forecasted return direction, is contrary to our primary idea since it results in buying overvalued calls (forecasted volatility being lower than the VIX). Similarly, when the forecasted volatility was lower than the VIX and that the forecasted return was negative, the strategy was to buy puts and sell calls. The investment in puts, suggested by the forecasted return direction, is again consistent with our primary impression since it results in buying overvalued puts (forecasted volatility being lower than the VIX).