Assignment
1. What is the key difference between speculation and gambling?
2. You play a game where if the flip of a fair coin results in heads, you get $1,000 but get nothing if it comes up tails. What is the expected value of the game? You're offered a choice -receive $400 and not play the game or play the game and live with the outcome. If you're risk neutral, do you take the $400 or do you play the game? Why? If you're risk averse, what is the amount (specify a range) someone would have to pay you to NOT play the game? If you're risk seeking, what is the amount (specify a range) someone would have to pay you to NOT play the game?
3. Use the following information for question 3: You manage a risky fund with expected return of 18% and standard deviation of 28%. The T-Bill rate is 8%. (You much show your work in the calculations to receive credit).
a. Your client invests 70% in your risky fund and 30% in T-Bills. What is the expected return and standard deviation your client's portfolio?
b. Suppose your risky portfolio includes the following stocks: Stock A: 25%; Stock B: 32%; Stock C: 43%. What are the investment proportions of your client's portfolio including the position in T-Bills?
c. What is the Sharpe Ratio of your risky fund? What is the Sharpe ratio of your client's portfolio?
d. Draw the CAL of your risky fund on the expected return vs. standard deviation diagram and show the position of your client's portfolio on the graph. What is the slope of the CAL? (Don't worry about precision of the data points.)
e. As you learn more about your client's investment behavior, you estimate that her degree of risk aversion is A = 3.5. What proportion of your client's portfolio should now be invested in your risky fund and how much in T-Bills. What is the expected return and risk of this portfolio?
Use the graph below to answer questions 4 & 5. The indifference curves shown all have the same risk aversion coefficient (A).
4. Rank the indifference curves (1, 2. 3, & 4) in order of highest to lowest Utility. Which curve represents the greatest utility that can be achieved by the investor? Which point represents the optimal complete portfolio?
5. According to the graph, portfolio E has a higher expected return than portfolio F. Is E preferable to F based on the investor's utility function? Why or why not?
Use the following table to answer question 6:
|
Portfolio
|
Expected Return (%)
|
Standard Deviation (%)
|
|
W
|
15
|
36
|
|
X
|
12
|
15
|
|
Z
|
5
|
7
|
|
Y
|
9
|
21
|
6. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz? Why?
7. Portfolio theory as described by Markowitz is mostly concerned with:
a. The elimination of systematic risk
b. The effect of diversification on portfolio risk.
c. The identification of unsystematic risk.
d. Using active portfolio management to enhance returns.
8. Select the best response. Assume that an investor currently holding stock in Miller Corporation wants to add the stock of either Mac Corporation or Green Corporation to her portfolio.
All three stocks have the same expected return and volatility. The correlation between Miller and Mac is -0.05; and between Miller and Green is +0.05. Portfolio risk is expected to:
a. Decline more when the investor buys Mac
b. Decline more when the investor buys Green
c. Increase when either Mac or Green is bought
d. May decline or increase depending on other factors
9. Stocks A, B & C have the same expected return and standard deviation. The correlations between the returns of these stocks are shown in the table below.
|
Stock A
|
Stock B
|
Stock C
|
|
Stock A
|
+1.0
|
|
|
|
Stock B
|
+0.9
|
+1.0
|
|
|
Stock C
|
+0.1
|
-0.4
|
+1.0
|
Given these correlations, the portfolio constructed from these stocks having the lowest risk is a portfolio:
a. Equally invested in stocks A & B
b. Equally invested in stocks A & C
c. Equally invested in stocks B & C
d. Totally invested in stock C
10. George has a $2 million diversified portfolio invested in domestic large and small cap stocks and short term investment grade bonds. The expected return of this portfolio is 13.8% with an expected volatility of 23.1 %. George expects to receive an additional $2 million and wants to invest the new money in an index fund that best complements his current portfolio. He hires you to evaluate the four index funds shown in the table below for their ability to meet two criteria relative to George's current portfolio: 1) maintain or enhance the expected return; and 2) maintain or reduce the expected volatility. Each index fund below is invested in asset classes that are not substantially represented by George's current portfolio.
|
Index Fund
|
Expected Annual Rett
|
Expected Annual Volabrrelation
|
w/ Current Pc
|
|
Fund A
|
15%
|
25%
|
+0.80
|
|
Fund B
|
11%
|
22%
|
+0.60
|
|
Fund C
|
16%
|
25%
|
+0.90
|
|
Fund D
|
14%
|
22%
|
+0.65
|
State which fund you would recommend to George and justify your choice by describing how your chosen fund best meets both of George's criteria. No calculations are required.
11. Statistics for three stocks A, B & C are shown in the following tables:
|
|
Stock A
|
Stock B
|
Stock C
|
|
Standard Deviation
|
40%
|
20%
|
40%
|
|
Stock
|
A
|
B
|
C
|
|
A
|
1.00
|
0.90
|
0.50
|
|
B
|
|
1.00
|
0.10
|
|
C
|
|
|
1.00
|
Only on the basis of the information provided in the tables and given the choice between a portfolio made up of equal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B & C, which portfolio would you recommend? Justify your answer.
12. Which statement about portfolio diversification is correct?
a. Proper diversification can reduce or eliminate systematic risk.
b. Diversification reduces the portfolio's expected return because it reduces the portfolio's total risk.
c. As more securities are added to a portfolio, total risk would be expected to fall at a decreasing rate.
d. The measure of risk for a security held in a diversified portfolio is standard deviation
13. Assume you have two risky assets A & B. Asset A has high risk and high expected return and B has lower risk and lower expected return. The correlation between these two assets is small (assumed to be zero). Your client is a risk-averse investor (A > 0). Show these two assets on a return vs. risk graph and draw a hypothetical efficient frontier connecting the two. Also draw the Capital Allocation Line and an indifference curve that shows a possible optimal complete portfolio. No values are needed on the x & y axis. Label the following:
Assets A & B
Opportunity set of risky assets
Optimal Risky Portfolio
Indifference Curve
CAL
Optimal Complete Portfolio (based on investor's utility function)