I see why sharpe of 3 is so desirable

[traider]

Excellent OP sir. You gave a very good practical consideration and explanation of Sharpe and the relation to risk and return.

I do have a question for you, consider two strategies: Both have the exact same Sharpe. One has a 50% return and the other 25%. Professional investors would say they have identical "risk adjusted returns" so are the same. For me, a retail investor, the 50% return is intuitively better even though it has the same Sharpe as the 25%. Where do I go wrong if I pick the 50% strategy?

The reason I ask is: I think the Sharpe for small cap is not as good as SPY's but if you buy and hold small cap index for 30-40 yrs, the absolute return is so much better than buy and hold SPY, a puzzle I don't quite understand.

Regards,

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.

 

[Kevin Schmit]

I think the Sharpe for small cap is not as good as SPY's but if you buy and hold small cap index for 30-40 yrs

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.

 

[SabreMan]

I do have a question for you, consider two strategies: Both have the exact same Sharpe. One has a 50% return and the other 25%. Professional investors would say they have identical "risk adjusted returns" so are the same. For me, a retail investor, the 50% return is intuitively better even though it has the same Sharpe as the 25%. Where do I go wrong if I pick the 50% strategy?

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

 

[ironchef]

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.

Excellent points. However, been there done that in 2000 and 2008.

 

[ironchef]

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.

Thank you for your suggestions.

 

[ironchef]

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!

 

[marcela 2020]

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.