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A.

The following data, relating to the performance of the Fantastic Fund and the Market Portfolio over the calendar year, 2020, are available.

Measure	Fantastic Fund	Market Portfolio
Average return	16%	13%
Standard deviation of returns	25%	20%
Beta	1.40	1.00

The risk-free rate (T-bills) during 2020 was 3%.

REQUIRED:

1. Calculate the following measures of performance evaluation for the Fantastic Fund and the Market Portfolio over the observation year.
   1. The Sharpe ratio
   2. The Treynor ratio
   3. The Jensen alpha
   4. The M² measure for the relevant adjusted portfolio

2. On the basis of your calculations, would you prefer to invest in the Fantastic Fund, the Market portfolio or the relevant adjusted portfolio in i. IV. above? State why.

ANSWER:

B.

Reputable Fund Managers operates a Balanced Fund and wishes to compare its performance over the 2020-21 financial year relative to the benchmark of a (Bogey) Index Fund. The table below presents, for the 2020-21 financial year:

• the component asset classes of the Reputable Balanced Fund and Index Fund in column 1;
• the actual fraction (or weight) - and the actual return - of each asset class of the Reputable Balanced Fund in columns 2 and 3 respectively; and
• the actual fraction (or weight) and actual return of - each asset class of the Index Fund in columns 4 and 5 respectively.

Reputable Balanced Fund - Cols (2) & (3) (Bogey) Index Fund Cols (4) & (5)

Asset Class (1)	Actual Weight (2)	Actual Return (3)	Actual Weight (4)	Actual Return (5)
Equity	0.65	20%	0.55	22%
Bonds	0.25	4%	0.35	2%
Cash	0.10	1%	0.10	1%

REQUIRED:

1. What was the Reputable Balanced Funds return for 2020-21?
2. Did the Reputable Balanced Fund outperform or underperform against the (Bogey) Index Fund, and by what percentage amount?
3. What was the percentage contribution of asset allocation to the above relative performance?
4. What was the percentage contribution of security selection to the above relative performance?
5. Confirm that the sum of the asset allocation and the security selection allocations (in

iii. and iv. above) equals the total outperformance or underperformance relative to the Bogey Index Fund (in ii. above).

ANSWER.

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