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A Certain Ratio – Sharpe Ratio

A Certain Ratio – Sharpe Ratio

Written by Tina Winter

A Certain Ratio

We’ve previously looked at three measures:

Standard Deviation (Sigma, σ) – a measure of the volatility of an investment or portfolio

Alpha (α) – how well an investment has performed relative to the market

Beta (β) – how risky an investment is relative to the market

There are a range of other measures that are used in quantitative analysis of investment performance.

Sharpe Ratio adjusts the rate of return of an investment to take account of risk and is calculated:

Return – risk free return
Standard Deviation

Sharpe ratio is normally computed on an annual basis so it is possible to compare investments on a like with like basis. Looking at a calculation assuming return of 8%, risk free return 3%, σ =2.5%

Sharpe ratio = (8 – 3) / 2.5 = 2

Sharpe ratio reflects both the performance of the markets on a risk adjusted performance  and the value added by the fund manager – high is good, low is bad. Sharpe ratio can be negative which means the investment has underperformed risk free assets – you really would have been better off in cash.

Information ratio is a risk adjusted measure used to evaluate active fund managers’ relative performance. The risk taken relative to the benchmark is measured by tracking error, the standard deviation of relative returns. It is calculated as follows:

Average annual portfolio return – Average annual benchmark return
Tracking error

So when portfolio return is 8%, benchmark return is 6%, and tracking error is 3%

Information ratio = (8 – 6) / 3 = 0.67

The higher the positive Information ratio (IR) the better the risk rated return. An IR of above 0.5 would generally be very good, and above 1.0 exceptional. A negative IR means you really would have been better off with a tracker fund.