I'm trying to determine which of my portfolio simulations/backtests if any are good enough to put some money into. I outline an approach below and I'm interested in knowing: What problems are there with my approach if any? How big are these problems? Could you recommend a better approach, and explain it with sufficient detail so that I could implement it? - Thanks!!
I ran several portfolio simulations with portfolio sizes ranging from 1 stock to 20 stocks and average holding periods ranging from 2 days to 3 months. The criteria involve various buy/sell/ranking rules and the sims account for all trading costs. Each simulation is run over the prior 10 years, so I have 10 years of the portfolio equity curve. I take the daily simple return (r) of the portfolio equity curve and convert it to the daily lognormal return [LN(1+r)] which I place in column C of a spreadhseet. I want to calculate with 80% confidence what the minimum CAGR of the sim will be 6 months from now. I believe this would be called the 80% VaR. I use the following formula:
80% 6-mo VaR CAGR = [AVERAGE(C:C)-0.69*STDEV(C:C)/SQRT(125)+1]^251-1
I'm interpreting the result as follows: If 80% 6-mo VaR > Benchmark's 10-yr CAGR, then the strategy has an 80% chance of producing alpha 6 months from now and it's worth putting some money into it. I choose 10-year CAGR for the benchmark to match up with the 10-years of data in the backtest. I chose 6-mo VAR because 6-mo is probably the most I'd be willing to wait for confirmation that the strategy is producing alpha. I chose 80% confidence level because I was trying not to be so conservative that I throw away strategies that will most probably produce alpha. After all, having an 80% chance of producing alpha is probably a lot better than the norm. If my purpose was risk measurement, I'm thinking that 99% VaR or 99.9% VaR would be more appropriate.
Note: I used a 0.69 z-score in the above formula, which is different from the normal distribution z-score. In order to account for stock returns having fat tails at the edges, I examined the last 7 years of SPY and IWM daily returns to create my own custom Z-score index that better matches historical LN(1+R) probability distributions. I also examined a highly volatile 1-stock price history as well to account for the fact that portfolios with <20 stocks could have fatter tails than the SPY and IWM. I summarize the custom z-scores I use below:
VaR %-level / Normal Distribution Z-score / Custom Z-Score:
99.9% / 3.09 / 6.25
99% / 2.33 / 3.12
95% / 1.64 / 1.70
80% / 0.84 / 0.69