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21 Nov 2018

QUESTION 5

Today is your 25th birthday, and you want to save $1.5 Million by your birthday at age 70. If you expect to earn 7% APR compounded monthly in your retirement account, what constant payment at the end of each month must you deposit into the account through your 70th birthday in order to reach your retirement savings goal on your 70th birthday? (Answer to the nearest penny.)

QUESTION 46

Suppose you are comparing two portfolios of stocks to determine which is more appropriate for all of your investments. Portfolio A contains a large number of stocks, but each stock appears to have a relatively high amount of risk which you believe is unsystematic in nature and a relatively low level of systematic risk. Portfolio B also contains a large number of stocks, however each stock in that portfolio seems to contain a relatively large amount of systematic risk and a low level of unsystematic risk. If both portfolios have the same expected return, which portfolio would most likely be the best choice?

a.

Portfolio A
b.

Portfolio B
c.

There is no information that would indicate that one portfolio is better than the other.

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22 Nov 2018

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Q2: You own a portfolio that has $700 invested in Stock A and $2,400 invested in Stock B. If the expected returns on these stocks are 11 percent and 18 percent, respectively. 
 
Required:  
 
a) What is the expected return on the portfolio?
b) Why is some risk diversifiable? Why are some risks non-diversifiable? Does it follow that an investor can control the level of unsystematic risk in a portfolio, but not the level of systematic risk? 
c) Can the risk of a portfolio be reduced to zero by increasing the number of stocks in the portfolio? Explain.
d) If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain.

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. What’s the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%


3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?


a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?


a.

1.0
b.

-1.0
c.

0.0
d.

0.5


5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate


7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, what’s the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27


8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%


9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.


a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

Question 3. (10 Points) You have just graduated from Champlain College and have started a job which
offers to match your contributions into your retirement account up to 6% of your annual salary. You have
decided you want to deposit 6% of your salary each year into your retirement savings account. Your
retirement savings can be invested into three different funds: a risk-free US Treasury Fund, a U.S. Stock
Fund, and an Emerging Markets Stock Fund. The information regarding the three funds is below.
Investment Expected Return Standard Deviation
of Return


U.S. Treasury Fund 3.00% 0.00
U.S. Stock Fund 9.00% 0.25
Emerging Markets Stock Fund 15.00% 0.40

The correlation between the U.S. Stock Fund and the Emerging Markets Stock Fund is 0.51.
(a) If you invest 40% of your money in the U.S. Treasury Fund and 60% in the U.S. Stock Fund,
what will be the expected return on your portfolio? What will be the standard deviation of your
portfolio? What is the Sharpe Ratio of this portfolio?

(b) Rather than only investing in the U.S. market, you would like to invest in the Emerging Markets
Stock Fund as well. What is the highest Sharpe ratio you can achieve using both the U.S. Stock
Fund and the Emerging Markets Stock Fund in your portfolio? (Hint: Use solver in Excel and do
not allocate any money to the U.S. Treasury Fund) How much money, in percentage of the total
portfolio, is allocated to the U.S. Stock Fund and to the Emerging Markets Stock Fund in this
optimal risky portfolio?

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