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Home > Asset Management Calculations > Risk-Adjusted Rate of Return

Asset Management Calculations

# Risk-Adjusted Rate of Return

Knowing an investment’s risk-adjusted return goes a long way toward determining just how much “bang for the buck” is really being generated.

## What It Measures

How much an investment returned in relation to the risk that was assumed to attain it.

## Why It Is Important

Being able to compare a high-risk, potentially high-return investment with a low-risk, lower-return investment helps to answer a key question that confronts every investor: Is it worth the risk?

By itself, the historical average return of an investment, asset, or portfolio can be quite misleading and a faulty indicator of future performance. Risk-adjusted return is a much better barometer.

The calculation also helps to reveal whether the returns of the portfolio reflect smart investment decisions, or the taking on of excess risk that may or may not have been worth what was gained. This is particularly helpful in appraising the performance of money managers.

## How It Works in Practice

There are several ways to calculate risk-adjusted return. Each has its strengths and shortcomings. All require particular data, such as an investment’s rate of return, the risk-free return rate for a given period (usually the performance of a 90-day US Treasury bill over 36 months), and a market’s performance and its standard deviation.

Which one to use? It often depends on an investor’s focus, principally whether the focus is on upside gains or downside losses.

Perhaps the most widely used is the Sharpe ratio. This measures the potential impact of return volatility on expected return and the amount of return earned per unit of risk. The higher a fund’s Sharpe ratio, the better its historical risk-adjusted performance, and the higher the number the greater the return per unit of risk. The formula is:

Sharpe ratio = (Portfolio return – Risk-free return) ÷ Standard deviation of portfolio return

Take, for example, two investments, one returning 54%, the other 26%. At first glance, the higher figure clearly looks the better choice, but because of its high volatility it has a Sharpe ratio of 0.279, while the investment with a lower return has a ratio of 0.910. On a risk-adjusted basis the latter would be the wiser choice.

The Treynor ratio also measures the excess of return per unit of risk. Its formula is:

Treynor ratio = (Portfolio return – Risk-free return) ÷ Portfolio’s beta

In this formula (and others that follow), beta is a separately calculated figure that describes the tendency of an investment to respond to marketplace swings. The higher the beta, the greater the volatility, and vice versa.

A third formula, Jensen’s measure, is often used to rate a money manager’s performance against a market index, and whether or not an investment’s risk was worth its reward. The formula is:

Jensen’s measure = Portfolio return – Risk-free return – Portfolio beta × (Benchmark return – Risk-free return)

## Tricks of the Trade

• A fourth formula, the Sortino ratio, also exists. Its focus is more on downside risk than potential opportunity, and its calculation is more complex.

• There are no benchmarks for these values. In order to be useful the numbers should be compared with the ratios of other investments.

• No single measure is perfect, so experts recommend using them broadly. For instance, if a particular investment class is on a roll and does not experience a great deal of volatility, a good return per unit of risk does not necessarily reflect management genius. When the overall momentum of technology stocks drove returns straight up in 1999, Sharpe ratios climbed with them, and did not reflect any of the sector’s volatility that was to erupt in late 2000.

• Most of these measures can be used to rank the risk-adjusted performance of individual stocks, various portfolios over the same time, and mutual funds with similar objectives.

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