Performance Evaluation

Question 1

•••••••Performance Evaluation•••••••

A portfolio return can be broken up into three components

Answer 1

P_ortfolio = M_arket + S_tyle + A_{ctive management decisions}

A = P - B_enchmark

Style Return = B_enchmark - M_arket (in a broad market index, the benchmark is equal to the market and style return = 0)

Pure index strategy = Rf + R_{asset category} (any benchmark return shall be attributed to style)

Question 2

•••••••Performance Evaluation•••••••

Properties of a Valid Benchmark

Answer 2

SAMURAI

1. Specified in advance – known before being measured
2. Appropriate – consistent with managers style and expertise
3. Measurable – calculate in a frequent basis
4. Unambiguous – known participants and weights
5. Reflective of current investment opinions
6. Accountable
7. Investable – can be purchased

Question 3

•••••••Performance Evaluation•••••••

Performance Attribution - Micro Performance Attribution

Answer 3

R_V = value-added return (impact on performance)

(+) ∑ (w_P − w_B) * (R_B – R_M) pure sector allocation – o/u sector weighting decisions

(+) ∑ (w_P − w_B) * (R_P − R_B) allocation/selection interaction – Combination

(+) ∑ w_B * (R_P − R_B) within-sector selection – o/u impact on security selection

Overall benchmark return (RM), Sector Benchmark return (RB), Sector Portfolio Return (RP)

Question 4

•••••••Performance Evaluation•••••••

Performance Appraisal - Risk-Adjusted Performance Measures

Answer 4

Risk-Adjusted Performance Measures

Ex post alpha uses the security market line (SML) to appraise performance (α>0 above SML). α_p = R_p − [R_F + β_p(R_m − R_F)]

Treynor measure = T_P = (R_P − R_F) / β_P Appropriate for portfolio where nonsystematic risk has been diversified and β is most relevant

Sharpe ratio = S_P = (R_P − R_F) / σ_P Appropriate for an undiversified portfolio, where total risk is more relevant

M² = R_F + Sharpe Ratio * σ_M

Question 5

•••••••Performance Evaluation•••••••

Manager Continuation Policies Guidelines (H₀ / H_A)

Answer 5

H₀: The manager adds no value | H_A: The manager adds positive value

Type I error − Rejecting the null hypothesis when it is true. (Keeping managers who are not adding value.)

o Higher significance means more Type 1 error (from 5% to 15%)

Type II error − Failing to reject the null when it is false. (Firing good managers who are adding value.)

o Smaller significance means more Type 2 error (from 15% to 5%)

Question 6

•••••••Performance Evaluation•••••••

Time Weighted Return vs Money Weighted Return

Answer 6

TWR unaffected by cash-flow (contribution & withdraw)

• Best when manager does not control timing and size of cash flow
• Harder to calculate
• Geometric chain link sub-periods
• (END - CF_END - BEG ) / BEG | (END - BEG + CFBEG) / BEG + CFBEG

MWR = IRR = average rate to each position exposure

• Best when manager controls cash flow
• Higher when there is a large contribution right before the asset goes up or withdraw before it going down

Question 7

•••••••Performance Evaluation•••••••

Incremental return contribution

Answer 7

Incremental return contribution =

[total fund incremental value contribution - net contributions] / MV_beg