Why the Sharpe Ratio Matters
Most investors at some point have heard of the term Sharpe Ratio being thrown around as a measure of a hedge fund manager’s level of skill. Measuring skill is obviously correctly motivated; if we’re going to pay someone to manage our money, naturally, we’d like to know how good they are at it and if they are better or worse than other managers.
This sounds great, but what does skill mean in an investment context? Surely high skill managers must be generating higher returns than low skill managers? Or perhaps high-skill managers lose less money than low-skill managers? It turns out neither are necessarily true. The difference is in the risk required to generate the returns.
Investment returns certainly are not free. Indeed, investors do pay for their returns and they pay for them in the form of risk. In finance, we typically measure risk as the volatility of returns. The intuition here is that investments that tend to move up and down rapidly are more risky than investments that are more stable. For example, Tesla stock is much riskier than the S&P 500. In practice, this is typically calculated from historical data by taking the sample standard deviation of recent daily returns.
Note that this calculated term can change over time with market conditions — often considerably. Let’s apply this transformation to the semiconductor sector ETF (symbol SMH) and visualize the result:
The above chart shows that semiconductor sector risk is generally moderate, but went up considerably during the start of the covid-19 pandemic and waned over the course of 2020, before returning in early 2021 during the tech selloff in March.
Now that we have a feel for measuring risk, let’s evaluate two hypothetical investment managers with differing risk and return profiles.
In this scenario, investment manager B generates about 60% greater returns, but does so by taking about 100% more risk. The greater returns come at a heavy cost! Looking at the annualized returns alone does not capture this. We need a metric that measures investment return against how much risk was required to generate it. This is exactly where the Sharpe ratio comes in. If we assume a risk-free rate of zero, the Sharpe ratio is simply return over risk, or more precisely, mean of the return stream over variance of the return stream. With this new metric, let’s measure our investment managers once again.
Clearly investment manager A is more efficient in their risk taking than investment manager B and is consequently rewarded with a higher Sharpe Ratio.
Unfortunately, there is still one loose end that needs to be tied up. There are still a lot of investors out there reading this that would still prefer manager B because of the higher return. Maybe they are OK running their investment at a vol (volatility) of 10%. Does this mean that a better Sharpe isn’t necessarily better in practice?
No actually — because hedge fund managers (and most individuals) have access to a tool called leverage. This simply means borrowing money against existing securities in order to buy more securities. It can be thought of as a mortgage for one’s portfolio. At the time of writing this we are in a very low interest rate environment, so this borrowing can be done at a very modest interest rate of about 1% (about LIBOR + 80bps). If a hedge fund wants to take more risk, it’s trivial to do so. They can lever up and take on more risk. Conversely, if they want less risk, they can move a part of the portfolio into cash.
Suppose investment manager A decides to utilize this idea and 2x lever his fund. Neglecting interest fees, let’s see how this impacts our comparison:
Investment manager A now matches the risk level of investment manager B, but significantly outperforms it because they have a higher Sharpe ratio. Since taking on leverage or moving a part of the portfolio into cash allows for a virtually arbitrary risk level, the determinant of investment performance becomes the Sharpe Ratio. The more efficient risk taker wins.
Comparing the mean of the return stream to the standard deviation of the return stream, that is, the ratio of the first and second statistical moments, is a concept that appears elsewhere in the sciences. A scaled version of this is used in statistics and is the commonly used t-test which is used for hypothesis testing — a higher observed Sharpe Ratio also means the returns were less likely to be generated by luck.
In electrical engineering, comparing the squared ratio of the first and second statistical moments is known as the signal-to-noise ratio (SNR). The SNR can be used with the Shannon-Hartley theorem to determine the maximum rate of which information can be reliably transmitted over a communication channel — a higher Sharpe Ratio return stream is much more discernible from the background noise than a lower one.
Additional Considerations
- Insurance style payoffs: The Sharpe ratio is not relevant when investment performance is defined by a small number of rare events. These strategies are generally not common. One example is selling options. These are not strategies we pursue at TPC.
- Illiquid assets: The Sharpe Ratio requires a calculation of a volatility, which is not availible for illiquid investments like those in private equity or venture capital. That said, approximations are possible and the result is pretty interesting.
Questions or comments? Email: patrick at titanpointcapital.com
