I would allocate half of my capital to each of 2 strategies same sharpe, assuming they are uncorrelated. Reason is backtest are not indicative of results going forward, so is the historical sharpe. Due to uncertainty you want to diversify strategies as much as possible since most strategies without superior alpha(think hft, insider knowledge, hard to obtain data sources) have low sharpe. Are you really able to stick to your strategy when it goes through a 50% drawdown? The bigger your position is the more likely you will bail. Sharpe does a good job of ensuring that you pick the smoothest equity curve possible so that you won't have to experience this type of mental torment when trading live.
Leverage SPY so that the denominator (stdev) is equal to that pf the small cap ETF. Cumulative return over the 40 years for the leveraged SPY will be much much more than for the unleveraged small cap ETF with the exact same risk. Financing cost of the leverage is built into the Sharpe (assuming you can borrow at the risk-free rate, which you probably cannot. But you are still better off with the leveraged SPY). Edit: forgot to mention that you'll have to reset every quarter to maintain your leverage ratio relatively constant over the 40 year period.
Over the long run the 50% strategy is essentially the 25% strategy traded with 2x leverage. Profit will be double but so will the drawdowns. The risk is during a very bad spell/outlying losing period you will abandon the 50% strategy due to emotions. Where as you might not abandon the 25% strategy in the same type of scenario. This is a real issue as traders often abandon strategies at precisely the wrong time. As for small caps vs large caps. The situation is similar. You get more upside but you also get more downside. A quick google reveals that in 2011 the russell 2000 fell 30%. I don't remember the S&P 500 falling anywhere near that much. If the Sharpe of the small cap index is lower than the large cap index then this means the larger upside in the small caps does not fully compensate for the larger downside volatility
Thank you for the explanations. So, if I can stomach the ups and downs, I can get much better returns by leverage, that makes a lot of sense to me. What about time horizon, does that increase my odds of been up when I decide to quite the game? If so, why aren't more folks do this? This is a great thread!
Sharpe's ratio was originally developed as a prediction tool, but it can also be used to calculate a risk-adjusted historical return. When calculating the Sharpe ratio, investors must first ensure that they have a large amount of consistent and comparable data.