8.3 Measuring Portfolio Performance

Evaluating investment performance requires understanding various return measures and risk-adjusted metrics.

Return Measures

Total Return

Total return captures all sources of investment return:

$$\text{Total Return} = \frac{\text{Ending Value} - \text{Beginning Value} + \text{Income}}{\text{Beginning Value}}$$

Time-Weighted Return (TWR)

Time-weighted return eliminates the effect of cash flows (deposits and withdrawals).

Why TWR? Managers don't control when clients add or withdraw money.

Dollar-Weighted Return (Money-Weighted / IRR)

Dollar-weighted return includes the effect of cash flows.

TWR vs. DWR Comparison

Exam Tip: Time-weighted return is used to compare MANAGERS because it eliminates cash flow timing that managers don't control. Dollar-weighted return measures the INVESTOR'S actual experience.

Risk-Adjusted Return Measures

Sharpe Ratio

The Sharpe ratio measures excess return per unit of total risk (standard deviation).

$$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$

Sharpe Ratio Interpretation

Treynor Ratio

The Treynor ratio measures excess return per unit of systematic risk (beta).

$$\text{Treynor Ratio} = \frac{R_p - R_f}{\beta_p}$$

When to Use Treynor vs. Sharpe

Alpha (Jensen's Alpha)

Alpha measures the difference between actual return and expected return based on CAPM.

$$\alpha = R_p - [R_f + \beta \times (R_m - R_f)]$$

Alpha Interpretation

Alpha Example

Given: Portfolio return = 12%, Risk-free = 3%, Market = 10%, Beta = 1.0

• Expected return = 3% + 1.0 x (10% - 3%) = 3% + 7% = 10%
• Alpha = 12% - 10% = +2% (outperformed)

Exam Tip: Sharpe uses TOTAL risk (standard deviation). Treynor uses SYSTEMATIC risk (beta). Use Sharpe for entire portfolios, Treynor for well-diversified portfolios.

Risk-Adjusted Measures Summary

Benchmarks

Purpose of Benchmarks

• Measure performance against a standard
• Evaluate manager skill
• Set client expectations
• Assess strategy effectiveness

Selecting Appropriate Benchmarks

Benchmark Requirements

Common Benchmark Issues

Standard Deviation

Standard deviation measures total volatility of returns.

Standard Deviation Example

Fund B has the same expected return but MORE risk.

Exam Tip: A portfolio with a POSITIVE alpha has outperformed what was expected based on its level of risk (beta). Positive alpha indicates the manager added value.