Portfolio Choice

The focus of this assignment is to construct portfolios. The topics correspond to Lectures

4 to 6. You will need to use a spreadsheet posted on Carmen called hw2data.xls. This

dataset contains the historical monthly returns of six stocks: Coca-Cola (KO), Eastman

Kodak (EK), General Electric (GE), Dow Chemical (DOW), Johnson & Johnson (JNJ), and

3M (MMM).

Please work in a group of 1 – 4 people. Each group should hand in one copy of their answers.

Please show your work and provide explanations where relevant. However, you do not need

to print out entire spreadsheets. Your answers should be summarized in a write-up with

relevant details of calculations, tables and charts (if applicable), and explanations.

The assignment can be turned in during class or via e-mail (chabi-yo 1@sher.osu.edu). If

you do submit your assignment via e-mail, please submit it either as a Word document or

as a PDF le. In particular, please do not e-mail an Excel spreadsheet if you feel that the

Excel spreadsheet is relevant to providing details of your work, please copy and paste the

relevant portions into your Word document.

Part 1: Preferences and the Equity Premium Puzzle

1

Suppose that you use a quadratic utility function, U = E (r) 2 A 2 , to make your nancial

decisions. The average historical return for large US stocks is 11.63% with a standard

deviation of 20.56%. Suppose that you also use this for your estimates of E (r) and .

1. Suppose that in choosing a portfolio consisting of a risk-free asset (where rf = 3%)

and large US stocks, you invest 60% of your money in large US stocks (and the rest in

the risk-free asset). What does this imply about your risk aversion coecient, A?

2. If your preferences are consistent (i.e. you use the same utility function, including the

same A as above), which would you prefer?

(a) an asset which has E (r) = 5% and = 0

(b) an asset with E (r) = 10% and = 20%

Assume that you are only investing in (a) or (b) and not mixing the two assets into a

portfolio.

3. Suppose that we interview a group of investors who chose to invest 60% of their portfolio

in large US stocks and 40% in the risk-free asset. We then ask them which asset from

(2) that they prefer. Most answer that they prefer (b). If we believe that the investors

in the group are consistent in their choices, what does this imply about the quadratic

utility function? If we believe that the quadratic utility function is the correct utility

function, what does this imply about the consistency of investors preferences?

Part 3: Diversication

Start with asset A which has an expected return of 10% and a volatility of 30%.

1. Suppose that we introduce asset B with an expected return of 10% and a volatility

of 30%. The correlation between the two asset returns is 0.9. What is the optimal

combination of A and B? What is the volatility of this portfolio? [Hint: The expected

return of any combination is 10%, so you want to minimize the portfolio volatility.]

2. Now suppose that we introduce asset C with an expected return of 10% and a volatility

of 30%. The returns of asset C are uncorrelated with both the returns of asset A and

of asset B. What is the optimal combination of A, B, and C? What is the volatility of

this portfolio?

3. Did the introduction of B or C have a greater eect in decreasing the portfolio volatility?

Why is this the case?