12.6 Quantitative Measures of Fund Manager Performance

Return Alone Is Not Performance

A scheme returning 21% while another returned 16% has not necessarily been better managed. If the first took far more risk to achieve it, the investor was compensated for risk rather than served by skill. Risk-adjusted measures ask whether the return justified the risk.

Sharpe Ratio

Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Standard Deviation

It measures excess return per unit of total risk. The numerator is the return above what a risk-free instrument would have earned; the denominator is total volatility.

Worked example.

Scheme A: return 21%, standard deviation 24%, risk-free rate 6.5%
Sharpe = (21 - 6.5) / 24 = 0.60

Scheme B: return 16%, standard deviation 13%, risk-free rate 6.5%
Sharpe = (16 - 6.5) / 13 = 0.73

Scheme B has the better risk-adjusted performance despite the lower absolute return. It delivered more excess return for each unit of volatility its investors experienced.

A higher Sharpe ratio is better. Because it uses total risk, Sharpe is the appropriate measure when the scheme is the investor's entire portfolio, where every source of volatility is felt.

Treynor Ratio

Treynor Ratio = (Portfolio Return - Risk-Free Rate) / Beta

Identical in structure, but the denominator is beta rather than standard deviation, so it measures excess return per unit of market risk only.

Worked example.

Scheme A: return 21%, beta 1.20, risk-free rate 6.5%
Treynor = (21 - 6.5) / 1.20 = 12.08

Scheme B: return 16%, beta 0.85, risk-free rate 6.5%
Treynor = (16 - 6.5) / 0.85 = 11.18

On this measure Scheme A looks better, which is the reverse of the Sharpe conclusion. The difference is instructive: Scheme A carries volatility beyond what its market exposure explains — concentration or style — and Sharpe penalises that while Treynor does not.

When to use which:

Jensen's Alpha

Alpha = Actual Return - [ Risk-Free Rate + Beta x (Benchmark Return - Risk-Free Rate) ]

Alpha measures the return earned above what the scheme's beta alone would predict. It is the most direct quantitative expression of manager skill.

Worked example.

Actual return       = 18.0%
Risk-free rate      =  6.5%
Beta                =  0.90
Benchmark return    = 14.0%

Expected return = 6.5 + 0.90 x (14.0 - 6.5)
                = 6.5 + 0.90 x 7.5
                = 6.5 + 6.75
                = 13.25%

Alpha = 18.0 - 13.25 = +4.75%

The manager delivered 4.75 percentage points more than the scheme's market exposure would have produced. Positive alpha indicates value added; negative alpha indicates value destroyed.

A caution the exam expects: alpha computed from a short period or against an inappropriate benchmark is unreliable, and a positive alpha over one year is far weaker evidence than a consistently positive alpha across a full cycle.

Information Ratio

Information Ratio = (Portfolio Return - Benchmark Return) / Tracking Error

Measures excess return per unit of active risk — how much outperformance the manager generated for each unit of deviation from the benchmark. It is the natural measure for an actively managed scheme judged against its index, and a higher ratio indicates more efficient use of the freedom to deviate.

Sortino Ratio

A refinement of Sharpe that uses only downside deviation in the denominator, on the reasoning that investors do not object to upside volatility. Useful where a scheme's return distribution is asymmetric.

Using the Measures Correctly

Four rules govern all of them:

1. Compare within a category only. A liquid fund's Sharpe ratio and a small cap fund's Sharpe ratio are not comparable, because the risk-free rate and the nature of the risk differ fundamentally.
2. Use identical periods. A three-year Sharpe and a five-year Sharpe describe different market environments.
3. Use a sufficient period. These are statistical measures, and short samples are unstable. Three years is a minimum.
4. Read them together. A high Sharpe with a low alpha, or a high alpha with a very high tracking error, each tells a story the single number does not.

Summary