×QvantCase
← All techniques

Statistics for finance · level 1

Sharpe ratio & coefficient of variation

Return per unit of risk. Subtract the risk-free rate, divide by σ. The coefficient of variation is the same shape without the risk-free leg — σ / mean.

Theory: Portfolio Theory

Worked example: Return 11%, risk-free 3%, σ = 16%. Sharpe ratio?

excess return8%
σ16%
Sharpe0.5

Step by step

  1. 1

    Excess return first

    11% − 3% = 8%

  2. 2

    Divide by risk

    8 / 16 = 0.5

  3. 3

    Read it

    Above ~1 is strong, below ~0.3 is thin compensation for the risk taken.

Return 11%, risk-free 3%, σ = 16%. Sharpe ratio? = 0.5

The theory behind it

Intuition

Return per unit of risk. Dividing excess return by volatility makes strategies of different sizes comparable.

Common pitfalls

  • ×Forgetting to subtract the risk-free rate.
  • ×Comparing Sharpe ratios computed over different horizons without annualising.

In the interview

Investment-case rounds comparing two strategies.