Below I have displayed the results of an analysis of drawdowns in SPY. I used SPY as a proxy for the S&P 500 index. I looked at the historical performance of SPY and I used historical data as input to a simulation to do forecasts of SPY drawdowns. I used a threshold of 5% to define drawdowns in the forecasts and the historical data, so any drawdowns of less than 5% from the peak are not included. The drawdown time refers to the number of trading days it takes to fully recover the drawdown and get to new highs. The historical data contained 7,338 days of data. 25 drawdowns, were found in the historical data based on the definitions above. The forecast simulation does 1,000 runs each simulating SPY performance for 7,338 days and collecting the list of drawdowns in each run. In all, the simulation returned 29,725 drawdowns. I display graphs of the results and then a brief discussion of observations.
First, there appears to be more drawdown size risk in the forecast data than in the historical data. At every point in the curves, the forecast is more risky than what we observe historically. The median size historically is 7%, but in the forecast the median expected drawdown size is 10%. This is true at every point on the curve except the 90th percentile, where the forecast and the historical data are the same at 34%.
Second, there is a high correlation between the drawdown size and the time it takes to recover. So the deeper the drawdown, the longer it will probably take to recover.
Finally, all the distributions of the forecast and of the historical data contain a lot of tail risk. If a drawdown is within what I consider to be the normal range (the middle 70%, between percentiles 15 and 85), the relationship between the probability and the absolute risk is somewhat linear. However in the tail beyond the 85th percentile, the risk in both the drawdown size and days to recover goes parabolic. For the size risk forecast, when you move from the 85th to the 90th percentile, the risk increases 61%. For the days to recover forecast, going from the 85th to the 90th percentile results in a 260% increase in risk. The distributions of drawdowns in the historical data are even more skewed. So it seems that a given drawdown is likely to fall within our normal range and thus our forecasts about it are likely to be accurate, but if it is a rare occurrence that is deeper or longer than “normal”, the estimate for just how deep it will go and how long it will last is anyone’s guess.