MORITZ PUTZHAMMER

23 December 2022 • 7 min read

Is a 0.5 a good Sharpe ratio? Or is 1.5 considered a good Sharpe ratio? And what exactly is a Sharpe ratio in crypto? Given the complexity of crypto trading, you understandably have questions, and we aim to provide some answers (hopefully!).

As we’ve all learned from painful experience, investing in crypto carries risks, ones which are nevertheless quite similar to other types of investments, including market volatility, the possibility of significant unexpected losses (as we’ve seen with FTX and Terra Luna, for example), and ever-present threats from bad actors within the space.

Thankfully, however, there are myriad ways to evaluate volatility and mitigate risk when developing investment strategies and designing a diversified portfolio. In fact, there are many good books and articles on the topics of quantitative portfolio management and strategy optimization.

While modern portfolio theory (MPT) or even portfolio optimization models are beyond the scope of this article, we will take a brief look at one of the most widely used methods for measuring risk-adjusted relative returns—the Sharpe ratio.

Let’s begin at the beginning. The “Sharpe” in Sharpe ratio owes its name to William Forsyth Sharpe, an American economist, academic, and Nobel Memorial Prize in Economic Sciences recipient (the award is commonly referred to as the Nobel Prize in Economics).

In 1961, Sharpe completed his PhD in economics from UCLA; from 1957-1961 he worked at the RAND Corporation; during the 1960s and 1970s he taught economics at various universities; and in the 1980s he founded Sharpe-Russell Research, an investment consulting firm.

In 1990, Sharpe was awarded the Nobel Prize for his work on the so-called “capital asset pricing model,” which is a financial model outlining the manner in which the prices of securities tends to reflect possible risks and returns. According to his theory, the pricing of risky assets by a market allowed investors to incorporate them into their portfolios when combined with investments that were less risky, and this insight led to the idea of “beta,” or the measurement of a portfolio’s risk. When comparing the risk of an asset to the risk of the broader market, an investor will often make use of a beta coefficient.

One can safely argue that the Sharpe ratio is the most commonly used metric of the historical performance of financial assets, be they mutual funds, hedge funds, stocks, or otherwise.

More to the point, the Sharpe ratio is a measure of risk-adjusted return that compares the return of an investment to the risk-free rate of return (typically represented by the yield on short-term US Treasury bonds).

As Steven E. Pav outlines in his book *The Sharpe Ratio: Statistics and Applications* (Palgrave 2021), for most investors, the Sharpe ratio is typically useful when trying to answer certain questions, which include:

- Should the investor invest a predetermined amount of money (long) in a given asset?
- Should the investor replace strategy A with strategy B?
- Should the investor invest in asset B given that s/he will keep their investment in asset B?

As Pav notes, all of these questions involve a binary. In other words, the point is not to ask how much an investor allocate to any given asset (in our case, cryptocurrencies). Nor is the concern over whether to short an asset (although one can certainly do that with margin trading).

Rather, the amount and side are predetermined, and a salient point to bear in mind is the fact that the Sharpe ratio is a historical measure. But it’s one that is used to inform future investments. An associated point to consider is that historical performance does not guarantee future results, and every investor must necessarily be aware of certain assumptions regarding historical data underlying their use of the Sharpe ratio.

The Sharpe ratio is calculated by taking the excess return (also known as the "risk premium") of the investment over the risk-free rate and dividing it by the standard deviation of the investment's returns.

You might even encounter slight variations in terms of how the formula is represented, as in the following example:

In this case, the value “µ̂” is the historical (or sample) mean return of the asset, while “σ̂” is the sample standard deviation of returns, and “r0” is some fixed risk-free rate of return.

Once you’ve done the calculation by dividing the excess return by the standard deviation, the resultant ratio is indicative of how much extra return an investor is receiving for each unit of risk taken. In other words, if an investment has a Sharpe ratio of 1, it means that the investor is receiving 1 unit of excess return for every unit of risk taken.

For example, let’s suppose that an investor is considering two different investments: a crypto asset with a return of 20% and a standard deviation of 10%, and a government bond with a return of 5% and a standard deviation of 0%.

The Sharpe ratio for the crypto asset would be (20% - 5%) / 10% = 1.5, while the Sharpe ratio for the government bond would be (5% - 5%) / 0% = 0.

There is no one "good" Sharpe ratio that applies to all investments, including cryptocurrencies. It will depend on the specific investment and the investor's risk tolerance and investment objectives.

Some investors may be willing to accept higher levels of volatility and potentially higher returns, while others may prefer lower volatility and more consistent returns. Ultimately, it's up to the individual investor to determine the level of risk they are comfortable with and the Sharpe ratio that is appropriate for their investment strategy.

Having said the aforementioned, however, many seem to agree that a good Sharpe ratio is 1 or higher. Climbing from a good Sharpe ratio to a very good Sharpe ratio, then, is anything between 1 and 2, while an excellent Sharpe ratio is typically considered to be above 3.

In the examples cited thus far, the ratio has always been either a positive number or zero. However, what does it mean if your calculations result in a negative Sharpe ratio?

A negative Sharpe ratio occurs if the investment return is lower than the risk-free rate.** **As outlined, the Sharpe ratio is understood as the portfolio excess return divided by standard deviation of portfolio returns. Now, since the standard deviation (or crypto market volatility) cannot result in a negative, an excess negative return means that the Sharpe ratio will be negative.

As we can see, a negative Sharpe ratio means that * Rp < Rf* (the return on the asset is lower than the risk-free interest rate).

There are advantages and disadvantages when using the Sharpe ratio and below are some of the main advantages.

- Adjusting for risk by dividing the excess return by the standard deviation, the Sharpe ratio allows investors to compare different investments with different levels of risk.
- The Sharpe ratio provides a single metric for evaluating the performance of an investment, which can be fairly easy to calculate and understand (although there can be layers of complexity).
- Since it considers
*both*the return*and*the risk of an investment, the Sharpe ratio provides a more comprehensive evaluation of an investment's performance. - As it is both well-known and used widely, it represents a popular measure of risk-adjusted return, allowing investors to compare investments easily.
- Its ubiquity speaks to another advantage: investors can use it across asset classes, whether crypto, stocks, bonds, and even real estate.

For these reasons and others, the Sharpe ratio can be a powerful tool when evaluating the performance of a particular cryptocurrency, especially when it’s combined with additional forms of technical analysis and fundamental analysis.

The Sharpe ratio should not be understood as a plug-and-play formula in which you crunch some numbers and receive the magical key to beating the crypto market. It can become very complex very quickly depending on how deep you dive down the rabbit hole of portfolio management and optimization.

When optimizing the Sharpe ratio, you’ll also need to consider things such as whether you’ll invest fractional amounts, long or short, in a number of different assets. What about the relationship between the Sharpe ratio and signal-noise ratio?

How good are you with linear algebra, (multivariate) probability distributions, or statistical practices? And what about Gaussian returns and Gaussian dynamic weights or signals? Just because the Sharpe ratio is the most commonly used metric of the historical performance of financial assets (crypto or otherwise), it doesn’t necessarily mean that it’s easy to understand and use properly.

In terms of specific disadvantages, investors should be aware of the following points regarding the Sharpe ratio:

- There is an assumption of a normal distribution of returns, which is obviously not always the case. In the real world, returns may be skewed or have a different distribution, which can affect the Sharpe ratio’s accuracy.
- Extraneous costs, such as taxes or transaction costs, are often excluded. Naturally, these can affect the net return of an investment (often significantly).
- Since the Sharpe ratio is based on historical data, it may not accurately reflect future returns. As you’ll read repeatedly (and for good reason), past performance is not necessarily indicative of future results.
- The Sharpe ratio does not consider the specific risks or unknowns associated with a particular investment. For example, a high Sharpe ratio might be due to a lack of diversification or a concentration of risk in a single asset.
- Since it’s a one-size-fits-all tool, the Sharpe ratio does not consider the investor's personal risk tolerance or investment objectives. A “good” risk-adjusted return will obviously vary among investors.

As an investor, it’s always crucial to know the strengths and limitations of any given investment tool.

Keep in mind that the Sharpe ratio is just one measure among many of risk and return. With this point in mind, crypto investors would be wise to consider a variety of factors when making crypto investment decisions.

Factors such as the overall level of risk in a portfolio, the correlation between different investments, and the investor's risk tolerance and investment goals should all be taken into account when devising and implementing investment decisions.

Moreover, as Pav notes in *The Sharpe Ratio: Statistics and Applications*, backtesting is also a crucial component, one that we haven’t even mentioned thus far. As he writes, “the goal of backtesting is to produce an unbiased estimate of historical returns of a basket, portfolio, or trading strategy. You will almost certainly backtest a quantitative strategy before allocating money to it.”

Just when you think that you’ve nailed your strategy, there’s always more work to be done.