1. Discuss the investor preference assumptions underpinning the first and the second degree

stochastic dominance rules. Briefly discuss two cases where the mean-variance criterion

provides an efficient decision rule.

2. An investor is making portfolio selection based on a single-index model with the stock and

index prices provided in the accompanying Excel file, under tab “Question 2”. Assuming

short sale is permitted, and the risk free rate is 2% per annum continuously compounded,

determine the investor’s portfolio.

3. Discuss the separation of investment and financial decisions under certainty and uncertainty.

Use graphs and/or functions to illustrate your answers.

4. An asset manager has the prior beliefs of the expected return and covariance matrix of the

four assets in his portfolio P:

Now the asset manager also has the following subjective views on these asset characteristics

going forward (in the following we use the term “confidence” to denote the uncertainty

surrounding these views, as also used in the lecture notes):

• The expected return of the first asset will exceed the expected return of the second asset by

1% with a confidence of 0.0009.

• The expected return of the fourth asset will exceed the expected return of the third asset by

1% with a confidence of 0.0004.

• The expected return of the first asset will reach to 10% with a confidence of 0.0003.

• The expected return of the third asset will reach to 1.5% with a confidence of 0.0002.

Assuming the risk-free rate is 0%, please answer the following three questions:

a. Compute and report back the posterior expected return and covariance matrix

based on these subjective views using the Black-Litterman model. As the

posterior expected return matrix also relies on the weights of the four assets in a

market cap-weighted portfolio, you may use the following information for your

calculation:

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765N1 Portfolio Management

Market Cap ACN AIN ANF DGICA

In billion dollars 162.80 1.55 70.91 13.73

b. Assume that portfolio P is constructed as the all-long tangent portfolio given the

prior expected return and covariance matrices. Please compute and submit its

asset allocation.

c. Given the posterior expected return and covariance matrix you have just

calculated, what is the new asset allocation of portfolio P as the all-long tangent

portfolio?