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Ratios



Sharpe Ratio

This is a commonly-used measure which calculates the level of a fund's return over and above the return of a notional risk-free investment, such as cash or Government bonds. The difference in returns is then divided by the fund's standard deviation - it's volatility, or risk measurement. The resulting ratio is an indication of the amount of excess return generated per unit of risk.
Sharpe is useful, when comparing similar portfolios or instruments. There is no absolute definition of a 'good' or 'bad' Sharpe ratio, beyond the thought that a fund with a negative Sharpe would have been better off investing in risk-free government securities. But clearly the higher the Sharpe ratio the better: as the ratio increases, so does the risk-adjusted performance. In effect, when analysing similar investments, the one with the highest Sharpe has achieved more return while taking on no more risk than its fellows.

Worked Example: The Sharpe Ratio – a risk-adjusted performance measure
As a basis for choosing between investments, the headline return of a fund is rather a blunt instrument. Investors could reasonably expect to know how much risk had to be taken on in order to achieve the return and, indeed, if they would have been better off putting their cash into a risk-free instrument instead. Sharpe seeks to address these questions in a single performance ratio. We can see how it works from the following examples.
This table includes three funds with very similar returns (1) over a three-year period.

Table 5. Total Return - Standard performance table from Unit Trust/OEIC universe
Name 1m 3m 6m 1y 3y
Sector: UT UK Smaller Cos -3.39 0.42 13.28 16.62 35.97(1)
Halifax Smaller Cos -3.26 -1.33 13.01 18.81 35.88(1)
Rathbone Smaller Cos -2.71 1.7 13.96 18.34 35.76(1)
Cazenove UK Smaller Cos -3.02 -0.18 16.76 18.33 9.11

So what's to choose? Let's take a look at their ratios:

Table 6. Ratios table over 36 months against benchmark "UT UK Smaller Companies" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Ann Volatility Ann Alpha Beta Sharpe
Sector: UT UK Smaller Cos 16.65 0 1 0.51
Halifax Smaller Cos 17.29(3) -0.31 1.02 0.48(2)
Rathbone Smaller Cos 19.2(3) -1.87 1.11 0.39
Cazenove UK Smaller Cos 19.72(4) -9.39 0(4)

The Halifax fund has highest Sharpe (2), indicating that it has generated the best return, per unit of risk taken on. Sharpe tells us we have lower risk (3) for the same performance, and that performance is superior to a risk-free rate.

And it is worth noting Cazenove's zero Sharpe – the fund is taking on 19.72% volatility for no gain over a risk-free rate.

We can also approach this kind of examination from the opposite direction, by looking at funds in the next table exhibiting similar levels of risk (1).

Table 7. Ratios table over 36 months against benchmark "UT UK Smaller Companies" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Ann Volatility Ann Alpha Beta Sharpe
Marlborough Special Situations 19.61(1) 15.11 1.11 1.35(2)
Sector: UT UK Smaller Cos 16.65 0 1 0.51
Capita Canlife UK Smaller Cos 19.36(1) -2.57 1.12 0.35(2)

Marlborough has higher Sharpe, and should prove to be the more rewarding investment. We can see the returns Marlborough is generating below (3).

Table 8. Total Return - Standard performance table from Unit Trust/OEIC universe
Name 1m 3m 6m 1y 3y
Marlborough Special Situations -4.42 1.95 17.04 25.69 111.84(3)
Sector: UT UK Smaller Cos -3.39 0.42 13.28 16.62 35.97
Capita Canlife UK Smaller Cos -2.96 0.6 8.91 7.38 32.22

So, Marlborough has achieved a substantial level of outperformance while taking on no more risk than its competitor, and this has been reflected in its Sharpe Ratio.
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