A common practice to evaluate a fund manager is to identify a benchmark asset of similar investment style and compare the fund manager's performance against the benchmark. Good-performing fund managers should outperform the benchmark by generating higher returns. The fund manager performance evaluation can be implemented using a typical simple linear regression model, where the return of the target fund is regressed upon the return of its benchmark. Suppose the monthly return of a fund is denoted as R_fund and the monthly return on the style benchmark is denoted as R_s.

The mathematical expression of the linear regression model used for fund performance evaluation, can be formulated as

R_fund = ₀ + ₁R_s +

Three different fund (i.e. A, B, C) are evaluated. Fund A mainly invests in high-growth large-cap equities. For example, Fidelity Contrafund. As such, it is benchmarked against Large Growth style. Fund B mainly invests in small-cap firms. For example, JPMorgan Small Cap Growth Fund. Therefore, it is benchmarked against Small Growth Fund.Fund C mainly invests in US bonds. For example, PIMCO Total Return Fund. So it is benchmarked against Intermediate-Term Bond. In addition, each fund is also benchmarked against S&P 500 for comparison. The following table shows the fitted model coefficients and R-square values. It is assumed that all coefficients are statistically significant.

Fund	benchmark	0	1	R2
A	Large Growth Fund	4.12	0.76	0.74
S&P 500	5.63	0.96	0.81
B	Small Growth Fund	1.23	0.95	0.93
S&P 500	3.02	1.05	0.62
C	Intermediate-Term Bond	-1.17	1.01	0.90
S&P 500	6.56	-0.95	0.03

(a)

The pre-condition for an accurate evaluation of fund performance is to make sure the choice of benchmark is appropriate, according to the risk-return trade-off. This can be reflected from the model results, in particular the beta coefficients and R-square. For a good choice of benchmark, the ₁ value should be

1. close to ;
2. close to;
3. close to ;
4. it depends;

and the R² should be

1. large.
2. small.
3. it depends.

Explain the reasons for your choice.

B.

For Fund B, evaluate which benchmark (namely 'Small Growth Fund' and 'S&P 500') is more appropriate. Briefly explain why you think one benchmark is more appropriate than the other.

C.

For each fund, identify the more appropriate benchmark, between the two candidates. Fill in the table below by writing down the name of the appropriate benchmark.

Fund	Appropriate benchmark
A
B
C

D.

Based on your chosen benchmark in part (c), evaluate which fund (among A, B, and C) is superior (it means the fund outperforms its benchmark) and inferior (it means the fund underperforms its benchmark).Explain your judging criteria.

Fund	Superior or Inferior	Explain your judging criteria
A
B
C

Further, can we determine which fund manager has the best performance? Explain why.