The Sharpe Ratio is a very common way of measuring and comparing portfolios. The starting assumption is that it’s possible to invest in a risk-free asset and achieve a return.

An example of this would be leaving your money in a UK savings account with an interest rate of 3%. Since the Financial Services Compensation Scheme guarantees that up to £85,000, your UK-authorised bank holdings will be compensated in the event of default, you can assume your money is pretty safe.

It then means that, in general, you will only invest in a portfolio of riskier assets if they have a chance of generating more than 3%. Why would you invest in a risky asset if the prospected return was lower, or the same, as the riskless one? And by extension, you’d want to know how much additional risk you were taking in order to achieve the excess return that a risk portfolio is expecting.

The Sharpe Ratio, when using historical data, simply computes the amount of additional annualised return that a portfolio has generated for each additional unit of risk.

Let’s say Portfolio A achieved an annual return of 12% with a 4% volatility.

Meanwhile, Portfolio B achieved an annual return of 14% with a 6% volatility.

The Sharpe Ratio of Portfolio A is its excess return over the riskless investment, which remember, was 3%, divided by its volatility. So that’s (12% - 3%) / 4% , which is 2.25.

The Sharpe Ratio of Portfolio B is its excess return over the riskless investment, divided by its volatility. So that’s (14% - 3%) / 6% , which is 1.83.

So Portfolio B, while having a higher annual return, has a lower Sharpe Ratio, because of its more than proportional increase in volatility. The Sharpe Ratio allows us to normalise and compare portfolios with different return and risk profiles, and assess them all relative to a risk-free investment.