7. Fund Performance

Question 1

Fund return

Answer 1

• Fund’s return over investment period
• Advantage: Easy to compute and readily available
• Disadvantage: No risk-adjustment

Question 2

Excess return

Answer 2

• Fund’s raw return minus the return of some benchmark
• Benchmarks include market return, benchmark index return and average return of all funds from the same investment objective
• Problem: Strategic benchmark selection

Question 3

Sharpe ratio

Answer 3

• SR = (Return - RF) / standard deviation of fund returns
• Interpretation: Expected return per unit of risk
•Advantages:
  - easy to compute
  - intuitive economic interpretation
  - takes the fund's risk into account
• Disadvantage: 
  - Based on the fund's total risk

Question 4

Treynor ratio

Answer 4

• TR = (Return - RF) / beta of fund
• Interpretation: Expected return per unit of systematic risk
• Advantages:
- Solid measure of risk-adjusted performance
- Relatively easy economic interpretation
• Disadvantages:
- Computations more evolved
- Does not account for additional risk factors

Question 5

Jensen’s alpha / CAPM alpha

Answer 5

• Accounts for the fund’s systematic risk measured by the CAPM
• Alpha is the fund’s expected excess return that is not explained by systematic risk
• Advantages:
- Prominent measure of risk-adjusted performance
- Easy economic interpretation
• Disadvantages:
- Computations more evolved
- Does not account for additional risk factors

Question 6

Multifactor alphas

Answer 6

• Account comprehensively for fund’s systematic risk
•Multifactor model instead of CAPM
• Advantages:
- Most comprehensive measure of risk-adjusted returns
- One can analyze which strategies a fund manager is using
• Disadvantages:
- Computations more evolved
- Not clear what relevant risk factors are
- Economic interpretation is more advanced

Question 7

Information ratio

Answer 7

• IR = (Return - benchmark return) / volatiity of active return
• Does not assume any specific benchmark
• The information ration combines elements of alpha and the Sharpe ratio
• Economic interpretation: How consistently is the outperformance obtained

Question 8

How are the Sharpe and the Treynor ratio computed in the real world?

Answer 8

1. Select sufficiently long sample period (at least on year)
2. Compute the performance measure
   I. Calculate mean fund return and substract risk-free rate
   II. Determine the standard deviation of fund returns (Sharpe) or the beta of the fund return with the market return.

Question 9

How are Alphas computed in the real world

Answer 9

1. Select sufficiently long sample period (at least on year)
2. Compute the performance measure
   I. Regress the monthly fund excess returns on the monthly factor returns. The number of observations equals the number of time periods
   II. The intercept of the regression is the fund’s alpha