Why Investing is Not Only About Returns
Sharpe ratio, risk-adjusted investment performance
Two hypothetical investments below returned the same ~40%. Which is better?
Since returns are identical, we must look elsewhere to answer this. One place to look that is different between the two is the path each took to reach that ~40%.
BLACK certainly “wiggles” more. You probably already intuitively know that the wiggles are bad. Here are a few reasons why.
First, it makes BLACK much more painful to hold. Sure, sometimes it’s beating GREEN (Sept 2019). But other times, it underperforms horrendously (July 2020). And because of prospect theory / loss aversion (see Kahneman) we know that sadness from losses > happiness from gains. The losses will outweigh the gains and makes any holding experience very unpleasant. Anyone who has actually traded can confirm.
Second, after wiggling around so much, doesn’t it almost seem “lucky” that BLACK returned the same as GREEN? And in the next moment, it feels like BLACK could be anywhere, whereas GREEN seems it would make steady gains. So the wiggles also make us less confident in our investment going forward.
Third, what happens if we suddenly needed cash. BLACK wiggles so much it could be down when we need the money, and we would be forced to close the position at a loss.
By now many will recognize that the “wiggles” here represent risk, and we can answer our initial question more explicitly: BLACK is a worse investment than GREEN, despite having returned the same, because it took on much more risk to get that return.
We need a performance metric that reflects this. Simple % returns fails.
Risk-Adjusted Investment Performance
First, we must quantify risk. Our risk metric should capture our intuition that if the returns graph wiggles a lot like BLACK, there is more uncertainty/pain/luck involved; thus, it is riskier.
One of the simplest and most common ways to do this is by calculating the standard deviation of returns, known as volatility.
Now, to obtain a risk-adjusted measure of performance we can simply divide returns by volatility. This is known as the Sharpe ratio (SR). The factor of 252 is to annualize the Sharpe assuming we are using daily returns. We use 252 because there are 252 trading days in a year (excluding weekends and holidays). If we were using monthly returns, for instance, we would use 12 instead of 252
We calculated the Sharpe of GREEN vs BLACK as 2.0 vs. 0.5. So the Sharpe ratio “works”. It reflects our intuition that GREEN is the better investment, while this would be unknowable from returns.
It does this by incorporating volatility to tell you how much return you actually earn per unit of risk you took.
To get a better sense of what the Sharpe ratio is measuring, we’ve plotted hypothetical investments with increasing Sharpes below: 2, 5 and 20 Sharpes. As the Sharpe increases, the wiggles in the curve get smaller. At a 20 Sharpe, you basically have a straight line going up and to the right. A 20 Sharpe would be extremely difficult to capture at scale and represents a near perfect arbitrage.
Realistic Sharpe Numbers
So what’s a realistic or good Sharpe then?
The trailing ~20 year Sharpe of SPY (an ETF that tracks US large caps) is around 0.45. We want to at least beat that. Warren Buffet, one of the world's most popular investors, has a long-term Sharpe of around 0.75. Good hedge funds have Sharpes in the 1-2 range. Excellent ones will target long-term Sharpes of 2-4.
That's it for this post! To learn more about how Sharpe ratios are used in practice, check out our next post!