# Portfolio Management

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.
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?