Is your fund doing better this year so far than the average of a large number of traders tossing coins to trade the market? Given that the buy and hold return (less dividends) of SPY is close to 20% YTD, how does the performance of your trading, or fund manager, compare to that? The simulation in this blog post provides some interesting statistics that should not be surprising, however, given the strength of this bull market.

Suppose that instead of buying SPY at the start of the year and holding it, you instead decided to toss a coin near the close of the first trading day. If heads came up you fully invested your capital and then you tossed the coin at the following close (or just in time for an MOC order). If heads came up again, then you stayed long but if tails came up, then you sold everything (commission \$0.01 per share is assumed). Then you repeated again the same coin tossing next day, and so on. Obviously, your coin tossing outcomes will represent just one possible random sequence out of infinitely many possibilities. However, if one simulates a very large number of such sequences, some interesting statistics can be obtained for the net percent return, which is calculated as 100 x net profit/initial capital. The statistics shown on the graph below are for 20,000 such sequences, a number large enough to obtain convergence to the actual distribution of random returns in the SPY case:

The results of the simulation are shown on the above graph of the distribution of net returns of the random systems corresponding to the random tossing sequence outcomes. The first interesting fact to notice is that 95.11% of all random traders made a profit greater than 0. This is much better than in a casino and shows that a bull market is the ultimate gambling environment. Just toss a coin and you may make up to 30% in 10 months or lose up to -11%. But the probability of a loss is less than 5%.