Sharpe ratio: definition and how to calculate it

• What is the Sharpe ratio?
• Why is the Sharpe ratio so important?
• How to calculate Sharpe ratio
• How is the Sharpe ratio used to manage risk?
• What is considered a good and bad Sharpe ratio?
• Limitations of the Sharpe ratio
• Sharpe ratio vs Sortino ratio

What is the Sharpe ratio?

The Sharpe ratio is a tool used to measure the risk-to-return ratio of an asset or portfolio in high-volatility markets. The ratio is especially helpful in comparing levels of risk in two different portfolios.

The Sharpe ratio is one of the most popular risk-to-return measures because of its simple formula. With just three simple metrics you can calculate risk-to-return via the Sharpe ratio. It was developed by William Sharpe, winner of the Nobel Memorial Prize in Economic Sciences.

Why is the Sharpe ratio so important?

The Sharpe ratio is important because it standardises the relationship between risk and reward for different portfolios. With it, you can easily calculate the risk level of different portfolios with standard definition of risks. This standardisation of risk is any easy way to judge the difference between markets.

Ultimately, the Sharpe ratio is a useful tool to help you gauge which portfolio or asset best fits into your trading plan according to the level of risk you want to incur.  

Typically, traders look to focus their strategy on risk management or trading volatility. Volatility inherently creates risk, so many traders play a balancing act of finding volatility to hopefully profit from while decreasing their exposure to risk.

While maximizing the rate of return may seem like the obvious bet, too much volatility can leave you in a dangerous position. Every rate has a level of standard deviation, meaning the amount returns can deviate from the expected rate. Standard deviation goes both ways, so a standard deviation of 15 means the asset could experience anywhere from a loss of 15 points to a gain of 15, or somewhere in between.

Risk vs reward: The Sharpe ratio is all about calculating the risk vs reward of an asset. Too much focus on either will slow your potential profits or, even worse, leave you exposed to huge losses. Typically, the higher upside to an asset’s return, the larger the downside as well.

How to calculate Sharpe ratio

To calculate the Sharpe ratio, you need to first find your portfolio’s rate of return: R(p). Then, you subtract the rate of a ‘risk-free’ security such as the current treasury bond rate, R(f), from your portfolio’s rate of return. The difference is the excess rate of return of your portfolio.

You can then divide the excess rate of return by the standard deviation of the portfolio’s performance: S(p). The figure left is Sharpe ratio of your portfolio. The entire calculation can be thought of as the excess return of the portfolio divided by its volatility, represented by the standard deviation.

The formula for the Sharpe ratio is: [R(p) – R(f)] / S(p)

Sharpe ratio example

To give an example of the Sharpe ratio in use, let’s imagine you’ve got two portfolios with various assets. Portfolio A’s current performance yields a 14% return, and the current gilt rate of return is 4%. Portfolio A’s volatility, or standard deviation, is 20%.

14% - 4% / 20% = 0.5

The Sharpe ratio is best used to compare multiple portfolios that have different levels of volatility and rates of return. Portfolio B may only have an expected return of 8% but its volatility is only 5%. If we plug Portfolio B into the Sharpe ratio:

8% - 4% / 5% = 0.8.

So, portfolio B has a higher risk-to-reward ratio despite a lower rate of return.

How is the Sharpe ratio used to manage risk?

The Sharpe ratio is most often considered a tool for institutional traders or hedge fund managers looking to gain maximum returns while minimising risks. Balancing the reward-to-risk ratio is a key element of any trading plan or investing portfolio.

Retail traders may take on a higher risk level to increase the possibility of high returns. Long-term investors may prefer to minimise risk in favour of ensuring consistent returns. However, the Sharpe ratio is useful for anyone looking to minimise risk without cutting too much upside potential.

When planning new trades or a change to your portfolio, the Sharpe ratio is a handy tool to test new strategies. One clear piece of trading advice evidenced by the Sharpe ratio is that a diversified portfolio greatly reduces your exposure to risk.

What is considered a good and bad Sharpe ratio?

A good Sharpe ratio rest between one and three. Anything below one is considered a bad Sharpe ratio. Most Sharpe ratios won’t be higher than three, but the higher the Sharpe ratio the higher the reward to risk. A ratio above two connotates an extremely good reward-to-risk ratio.

When calculating the Sharpe ratio, you want it to at least be above one, and beyond that the higher the better. 

Limitations of the Sharpe ratio

Some critics claim the Sharpe ratio is limited by the objectivity of the chosen ‘risk-free’ asset. There is always risk to different assets. For example, even treasury bonds backed 100% by the US government can have their rate of return eroded by rapidly rising inflation or completely wiped if the government was to default on its debts.

Market fluctuations are another consideration left out by the Sharpe ratio. Using the standard deviation to calculate market volatility means you are ignoring the worst possible outcomes. When volatility works against you, the actual Sharpe ratio is much lower.

The Sortino ratio is one way to combat these limitations. The Sortino ratio is set up like the Sharpe ratio, but its risk-adjusted return is calculated using only the downside variation. To do this it uses the lowest possible deviation in place of the average standard deviation.

Sharpe ratio vs Sortino ratio

The Sortino ratio is like the Sharpe ratio but only includes the downside risk to produce a lower ratio. By not accounting for the upside potential of volatility, the Sortino risk is thought of as providing a more realistic view of the negative risk. Because of this more realistic account of risk, many people prefer the Sortino ratio when calculating for high-risk assets like cryptocurrencies or equities.  

How to calculate the Sortino ratio

The formula for the Sortino ratio is identical to the Sharpe ratio formula, except the standard deviation in the denominator position is replaced with only the standard deviation of the downside.

Sortino ratio = (actual or expected return – risk free rate) / downside standard deviation

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