Our analysis will classify the stock market as being in an up- or downtrend depending on whether the index spot trades above or below its 100-day simple moving average (SMA). The use of the 100-day SMA leads to an analysis of medium-term trends. If positions are traded whenever the spot crosses the moving average, taking a shorter-term SMA (such as 30 days) leads to more trading and higher turnover of the positions. A 200-day average, on the other hand, will lead to less trading.
Daily data of short-term implied volatilities of one-month at-the-money options and subsequently realized volatility between July 1998 and the end of August 2011 for different indexes generates an implied-to-realized spread for each day. The whole sample forms a distribution of the implied-to-realized spread with the spread on the x-axis and the frequency on the y-axis. "Implied-to-realized" (last page) shows results for the S&P 500 stock index in the United States as well the Eurostoxx 50 in Europe.
The charts illustrate the implied-to-realized spread when markets are trading above (blue line) or below (red line) the 100-day SMA. For the S&P 500 as well as the Eurostoxx 50, the distributions are more skewed to the left for the days when the market is in a downtrend, indicating that there are more days when the realized volatility exceeds the implied volatility.
From a pure volatility standpoint it would have been better to buy options instead of writing them in downtrending markets. Furthermore, there are many more days when the implied-to-realized spread was positive when the market was above its moving average. The numbers in "Crossing the average" (below) illustrate in more detail the spread for various stock market indexes for the two different scenarios when the index is above or below its 100-day SMA.
As expected, the implied and realized volatility both are lower for all indexes when the market trades above its 100-day SMA. In this case, the implied-to-realized spread is, on average, positive for all the indexes.
The difference in the spread between the above and below SMA scenarios is with 0.6% the smallest reading (for the Nikkei225). The Nikkei is the only index that trades more often below the moving average in this time period because of the long-term downturn of Japanese equities (49.4% vs. 50.6%). The values in the table are derived from overlapping daily data for the whole period. However, similar results are obtained when fewer data points with non-overlapping monthly intervals are used.