Problem 5 Efficient frontier and portfolio choice Consider t

Problem 5 (Efficient frontier and portfolio choice)

Consider the following expected returns, volatilities, and correlations:

Stock

Expected return

Standard deviation

Correlation with Duke Energy

Correlation with Microsoft

Correlation with Wal-Mart

Duke Energy

14%

6%

1

-1

0

Microsoft

44%

24%

-1

1

0.7

Wal-Mart

23%

14%

0

0.7

1

 

(a) Consider a portfolio consisting of only Duke Energy and Microsoft. The percentage of your investment (portfolio weights) that you would place in Microsoft stock to achieve a risk-free investment should be closest to:

(1) 15%
(2) 4%
(3) 23%
(4) 10%


(b) The expected return of a portfolio that is equally-invested in Duke Energy and Microsoft is closest to:

(1) 28%
(2) 29%
(3) 24%
(4) 23%


(c) The volatility of a portfolio that is equally-invested in Duke Energy and Microsoft is closest to:

(1) 8%
(2) 9%
(3) 11%
(4) 6%


(d) The expected return of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short position of $2,000 in Microsoft is closest to:

(1) 21%
(2) 12%
(3) 27%
(4) 18%


(e) The volatility of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short-position of $2,000 in Microsoft is closest to:

(1) 9%
(2) 14%
(3) 11%
(4) 12%

(f) Consider a portfolio consisting of only Microsoft and Wal-Mart. Calculate the expected return on such a portfolio when the weight on Microsoft is 0%, 25%, 50%, 75%, and 100%.

(g) Consider a portfolio consisting of only Microsoft and Wal-Mart. Calculate the volatility of such a portfolio when the weight on Microsoft is 0%, 25%, 50%, 75%, and 100%.


(h) Plot the efficient frontier.
Problem 5 (Efficient frontier and portfolio choice)
Consider the following expected returns, volatilities, and correlations:

Stock	Expected return	Standard deviation	Correlation with Duke Energy	Correlation with Microsoft	Correlation with Wal-Mart
Duke Energy	14%	6%	1	-1	0
Microsoft	44%	24%	-1	1	0.7
Wal-Mart	23%	14%	0	0.7	1

Solution

(a) (3)