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BMAN20072 Investment Analysis 2021/22 Semester 2

Week 4 Problem Set

Topic: Portfolio Performance Evaluation and Capital Asset Pricing Model

Part A. Non-numerical questions

4.A.1 Portfolio Performance Evaluation

Which evaluation measure is most important for you? Sharpe, Treynor, or Jensen’s alpha? Why? Explain. Are there any other performance measures you would use?

4.A.2 CAPM

CAPM assumes that “all assets are tradable” . How would the violation of this assumption affect the model? Give an example of assets that are not tradeable in the real world.

4.A.3 CAPM and Passive investment strategy

What is the implication of CAPM for passive investment strategy? Discuss.

Part B. Numerical questions

4.B.1

In 2019 the average return on the Safety First Fund was 10%, while the average return on the market portfolio was 12% and the average risk-free return was 3%.  Standard deviation and Beta are shown in the table below.

Statistic

Safety First Fund

Market Portfolio

Standard deviation of return

7.5%

15%

Beta

0.75

1.00

Calculate the three measures. Does Safety First Fund outperform the market?

a)         The Sharpe ratio

b)        The Treynor ratio

c)         Jensen’s alpha

4.B.2

Consider the following information regarding the performance of a portfolio manager in a recent month. The table shows the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or

neutral sector allocation in column 3, and the returns of sector indices in column 4.

Actual return (%)      Actual weight     Benchmark weight     Index return (%)

Equity

Bond

Cash

2

1

0.5

0.7

0.2

0.1

0.6

0.3

0.1

2.5

1.2

0.5

a)  What was the manager’s over- or underperformance in the month?

b)  What was the contribution of security selection to his performance?

c)  What was the contribution of asset allocation to his performance?

4.B.3

If simple CAPM is valid, which of the following situations are possible? Explain.

a)

Portfolio

Expected return

beta

A

20%

1.4

B

25%

1.2

b)

Portfolio

Expected return

Standard deviation

Risk-free

10%

0

Market

18%

24

A

16%

12

 

c)

Portfolio

Expected return

Standard deviation

Risk-free

10%

0

Market

18%

24

A

20%

22


d)

 

Portfolio

Expected return

Beta

Risk-free

10%

0

Market

18%

1.0

A

16%

1.5