Question 1

Question #1: Capital Allocation:

Consider the following capital market: a risk-free asset yielding 1.00% per year and a mutual fund consisting of 65% stocks and 35% bonds. The expected return on stocks is 11.75% per year and the expected return on bonds is 4.25% per year. The standard deviation of stock returns is 36.00% and the standard deviation of bond returns 11.50%. The stock, bond and risk-free returns are all uncorrelated.

1. What is the expected return on the mutual fund?

2. What is the standard deviation of returns for the mutual fund?

Now, assume the correlation between stock and bond returns is 0.40 and the correlations between stock and risk-free returns and between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).

3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?

Now, assume that the standard deviation of the mutual fund portfolio is exactly 26.50% per year and a potential customer has a risk-aversion coefficient of 2.50.

4. What correlation between the stock and bond returns is consistent with this portfolio standard deviation?

5. What is the optimal allocation to the risky mutual fund (the fund with exactly 26.50% standard deviation) for this investor?

6. What is the expected return on the complete portfolio?

7. What is the standard deviation of the complete portfolio?

8. What is the Sharpe ratio of the complete portfolio?

Question 2

Question #2: Markowitz Optimization:

Open the associated Excel file named QPS2 Data Fall I 2015 Problem 2 in My Course Content: Problem Set Spreadsheets. The data file includes 60 months of returns for 11 exchange traded funds; their names and ticker symbols follow:

Ticker

Name of Exchange Traded Fund

1

SPY

SPDR S&P 500 ETF

2

MDY

SPDR S&P MidCap 400 ETF

3

IWM

iShares Russell 2000 ETF

4

QQQ

Power Shares QQQ ETF

5

EFA

iShares MSCI EAFE ETF

6

VWO

Vanguard FTSE Emerging Markets Stock Index ETF

7

VNQ

Vanguard REIT Index ETF

8

BND

Vanguard Total Bond Market ETF

9

PFF

iShares US Preferred Stock ETF

10

GLD

SPDR Gold Shares ETF

11

JNK

SPDR Barclays High Yield Bond ETF

All students will do problem 2 using 9 of the above ETFs; all students will include the first 8 ETFs listed above: SPY, MDY, IWM, QQQ, EFA, VWO, VNQ, and BND. All students will include one of the last 3 ETFs: PFF, GLD, and JNK as instructed on your version.

Version A: Include PFF and exclude GLD and JNK.

Use the data on your 9 ETFs to answer the following questions:

1. What is the average return for each of the nine indexes?

2. Show the covariance matrix of returns. Briefly describe how you constructed the covariance matrix.

Consider the simple case where short sales are allowed, but short positions must be greater than or equal to 50% and long positions must be less than or equal to 50%. Use Excel Solver to find the Minimum Variance Portfolio (MVP).

Question 1
Question #1: Capital Allocation:
Consider the following capital market: a risk-free asset yielding 1.00% per year and a mutual fund consisting of 65% stocks and 35% bonds. The expected return on stocks is 11.75% per year and the expected return on bonds is 4.25% per year. The standard deviation of stock returns is 36.00% and the standard deviation of bond returns 11.50%. The stock, bond and risk-free returns are all uncorrelated.
1. What is the expected return on the mutual fund?
2. What is the standard deviation of returns for the mutual fund?
Now, assume the correlation between stock and bond returns is 0.40 and the correlations between stock and risk-free returns and between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).
3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?
Now, assume that the standard deviation of the mutual fund portfolio is exactly 26.50% per year and a potential customer has a risk-aversion coefficient of 2.50.
4. What correlation between the stock and bond returns is consistent with this portfolio standard deviation?
5. What is the optimal allocation to the risky mutual fund (the fund with exactly 26.50% standard deviation) for this investor?
6. What is the expected return on the complete portfolio?
7. What is the standard deviation of the complete portfolio?
8. What is the Sharpe ratio of the complete portfolio?
Question 2
Question #2: Markowitz Optimization:
Open the associated Excel file named QPS2 Data Fall I 2015 Problem 2 in My Course Content: Problem Set Spreadsheets. The data file includes 60 months of returns for 11 exchange traded funds; their names and ticker symbols follow:
	Ticker	Name of Exchange Traded Fund
1	SPY	SPDR S&P 500 ETF
2	MDY	SPDR S&P MidCap 400 ETF
3	IWM	iShares Russell 2000 ETF
4	QQQ	Power Shares QQQ ETF
5	EFA	iShares MSCI EAFE ETF
6	VWO	Vanguard FTSE Emerging Markets Stock Index ETF
7	VNQ	Vanguard REIT Index ETF
8	BND	Vanguard Total Bond Market ETF
9	PFF	iShares US Preferred Stock ETF
10	GLD	SPDR Gold Shares ETF
11	JNK	SPDR Barclays High Yield Bond ETF
All students will do problem 2 using 9 of the above ETFs; all students will include the first 8 ETFs listed above: SPY, MDY, IWM, QQQ, EFA, VWO, VNQ, and BND. All students will include one of the last 3 ETFs: PFF, GLD, and JNK as instructed on your version.
Version A: Include PFF and exclude GLD and JNK.
Use the data on your 9 ETFs to answer the following questions:
1. What is the average return for each of the nine indexes?
2. Show the covariance matrix of returns. Briefly describe how you constructed the covariance matrix.
Consider the simple case where short sales are allowed, but short positions must be greater than or equal to 50% and long positions must be less than or equal to 50%. Use Excel Solver to find the Minimum Variance Portfolio (MVP).