Risk Parity Basics: The Sharpe Ratio

“Sharpe Ratio” is used often on this blog, but not all readers may be familiar with what it is, what it can tell you, and its limitations. So, a Risk Parity Basics post to make sure everyone is on board. In short: it’s a measure of risk-adjusted return that we use to compare assets and portfolios.

One of the most important investing statistics, the Sharpe Ratio allows investors (looking backwards) to compare the return they have gotten according to the risk they took on to get there or (looking forward) to project return according to expected risk. It is so useful because it allows us to compare different types of assets according to the same basic standard: for the risk you took, how did the asset do? You might have a super-volatile asset that has great returns, compared to a pretty blah performer without many ups and downs, and the Sharpe Ratio allows you to compare them (by the way, you’d be surprised how many times the “blah” asset is actually better!).

Named after William Sharpe, winner of the 1990 Nobel Prize in Economics, the Sharpe Ratio (or just “SR”) can be calculated for portfolios or for individual assets. Here at Risk Parity Chronicles, we emphasize SR results for the test portfolios, since they provide us with a common standard to judge very different portfolios. The RPC Stability portfolio is designed to be pretty boring and flat, while the RPC Growth uses a lot of leveraged assets in pursuing higher returns, but the SR gives me a metric for apples-to-apples comparison. Despite being so different, their SRs are very close: .52 for the RPC Stability and .51 for the RPC Growth.

As for the nuts and bolts, it is a straight-forward calculation with just three numbers needed: the rate of return for an asset or portfolio, the standard deviation of it over that time period, and the rate of cash or short-term Treasuries. The result is a number usually between 0 and 1, with the higher the better. The longer the data set, the more reliable the number will be in assessing past performance, and the more reliable it can be for judging future expectations, keeping in mind (as always) that there are no crystal balls telling you what the future will hold.

It is not difficult to calculate by hand, though it can be a lot of work to assemble the data if you want to do it yourself. Luckily, there are sites that will calculate it for you and I’ll walk you through that process below using Portfolio Visualizer.

To come up with the Sharpe Ratio on your own, you’ll need three numbers going in:

1) The return of the asset or portfolio over a given time period. If you calculate this number by hand (you don’t have to!), you’ll need your own way to find this number. We can call the asset or portfolio’s return “Rp” (Rate of the portfolio).

2) the return of a “risk-free” asset, such as cash in the bank, or very short-term Treasury bills. There are different ways to figure this out (you can look at the rate on your savings account), but I look here and find the Treasury rate at the time at the start of the investment. It’s like I’m going back in time - what would I have made if I had just chosen the safest thing around? We’ll call this “Rf” (Risk-free Rate).

3) the standard deviation of the asset or portfolio’s return over the same time period as #1. Again, you’ll need to know this number from your own sources. This number gets the lower-case Greek letter sigma: 𝛔, in the form of  𝛔p (standard deviation of the portfolio).

Then, a simple formula:

Example: A given portfolio returned 8% over the year, when a simple Treasury bill would have given you 2%. The standard deviation of the portfolio was 12%, so you have (8-2)/12, or .5. The Sharpe Ratio would be .5.

Limitations of the Sharpe Ratio

The Sharpe Ratio is not the only way to measure risk-adjusted return, and in some cases, alternative measures are better. One frequent critique of the Sharpe Ratio is the use of standard deviation as the risk measure. Standard deviation treats all ups and downs of an asset over time as equivalent, but really, it’s not the ups which anyone cares about - it’s the downs. The Sortino Ratio was developed to express this, as it considers only the downward deviation in asset prices. Great news for you: if you want to focus on Sortino Ratio instead of Sharpe, that’s easy - on Portfolio Visualizer it is located just next to the Sharpe!

It gets silly when you have negative returns, because now a larger standard deviation (the denominator in the equation) will result in a “better” Sharpe Ratio. Maybe there is a fancy way to figure out risk-adjusted return in this case, but for me, if we are talking about negative returns, then I avoid this metric.

We haven’t yet focused on leverage in Risk Parity portfolios (but trust me, that’s coming), but if you are comfortable using leverage, then the projected Sharpe Ratio becomes even more valuable as a metric. With the second path of Risk Parity, we can use leverage to boost returns on a portfolio that would have low returns but a high Sharpe Ratio. I’m not suggesting necessarily that using leverage in a portfolio is a good idea, but if it is, it is with safe but modest portfolios. As an example, compare the Golden Butterfly (great Sharpe Ratio but low projected returns) with the Levered Butterfly. I used the same basic framework, but added in leveraged funds to boost returns. The result is a higher expected return than the original, with just a slightly lower Sharpe Ratio (.53 compared to .59).

Addtional Resources

Here is Investopedia’s write-up of the Sharpe Ratio, if you want a second opinion:

Understanding the Sharpe Ratio
The Sharpe ratio is a measure of risk-adjusted return. It describes how much excess return you receive for the volatility of holding a riskier asset.

If you want an explanation of SR straight from the source, here is the 1966 paper where Sharpe introduced the ratio:

And here is William Sharpe’s summary explanation of the Sharpe Ratio from 1994:

The Sharpe Ratio