1. Of the alternatives available, __________ typically have the highest standard deviation of returns.
A. commercial paper
B. corporate bonds
C. stocks
D. treasury bills
2. The arithmetic average of 12%, 15% and 25% is _________.
A. 17.3%
B. 15%
C. 17.2%
D. 20%
3. The geometric average of 10%, 20% and 30% is __________.
A. 15%
B. 19.7%
C. 20%
D. 23%
4. The risk-free rate is usually approximated by ___________.
A. the return on bank savings accounts
B. the return on Treasury bills
C. the return on money market mutual funds
D. None of the above
5. The market risk premium is defined as ___________.
A. the difference between the return on an index fund and the return on Treasury bills
B. the difference between the return on a small firm mutual fund and the return on the Standard and Poor's 500 index
C. the difference between the return on the risky asset with the lowest returns and the return on Treasury bills
D. the difference between the return on the highest yielding asset and the lowest yielding asset.
6. The reward/variability ratio is given by __________.
A. the slope of the capital allocation line
B. the second derivative of the capital allocation line
C. the point at which the second derivative of the investor's indifference curve reaches zero
D. none of the above
7. Historical records regarding returns on stocks, Treasury bonds, and Treasury bills between 1926 and 1995 show that __________.
A. stocks offered investors greater rates of return than bonds and bills
B. stock returns were less volatile than those of bonds and bills
C. bonds offered investors greater rates of return than stocks and bills
D. bills outperformed stocks and bonds
8. Historical returns have generally been __________ for stocks of small firms as/than for stocks of large firms.
A. the same
B. lower
C. higher
D. There is no evidence of a systematic relationship between returns on small firm stocks and returns on small firm stocks
9. Historically small firm stocks have earned higher returns than large firm stocks. When viewed in the context of an efficient market, this suggests that ____________.
A. small firms are better run than large firms
B. government subsidies available to small firms produce effects that are discernible in stock market statistics
C. small firms are riskier than large firms
D. small firms are not being accurately represented in the data
10. Consider a treasury bill with a rate of return of 5% and the following risky securities:
Security A : E(r) = .15; σ2= .0400
Security B : E(r) = .10; σ2 = .0225
Security C : E(r) = .12; σ2 = .1000
Security D: E(r) = .13; σ2 = .0625
The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor would choose as part of his complete portfolio would be __________.
A. security A
B. security B
C. security C
D. security D
11. An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 4% and 60% in a treasury bill that pays 6%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively.
A. 8.0%, 12%
B. 9.6%, 8%
C. 9.6%, 10%
D. 11.4%, 12%
12. The holding period return on a stock was 37.50%. Its ending price was $26 and its cash dividend was $1.50. Its beginning price must have been __________.
A. $18.50
B. $20.00
C. $21.50
D. $23.00
13. You invest $100 in a complete portfolio. The complete portfolio is comprised of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. __________ of your money should be invested in the risky asset to form a portfolio with an expected rate of return of 9%
A. 87%
B. 77%
C. 67%
D. 57%
14. You invest $100 in a complete portfolio. The complete portfolio is comprised of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. The slope of the capital allocation line formed with the risky asset and the risk-free asset is __________.
A. .40
B. .47
C. .57
D. .80
15. You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should __________.
A. invest $125,000 in the risk-free asset
B. invest $375,000 in the risk-free asset
C. borrow $125,000
D. borrow $375,000
16. The return on the risky portfolio is 18%. The risk-free rate as well as the investor's borrowing rate is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is __________.
A. 16.00%
B. 16.40%
C. 19.20%
D. 20.00%
17. You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in treasury bills.
A. 19%
B. 25%
C. 50%
D. 65%
18. You are considering investing $1,000 in a complete portfolio. The complete portfolio is comprised of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. The dollar values of your positions in X, Y, and treasury bills respectively would be __________, __________ and __________ if you decide to hold a complete portfolio that has an expected return of 8%.
A. $162, $595, $243
B. $243, $162, $595
C. $595, $162, $243
D. $595, $243, $162
19. Diversification is most effective when security returns are __________.
A. high
B. negatively correlated
C. positively correlated
D. uncorrelated
20. The risk that can be diversified away is ___________.
A. beta
B. firm specific risk
C. market risk
D. systematic risk
21. __________ is a true statement regarding the variance of risky portfolios.
A. The higher the coefficient of correlation between securities, the greater will be the reduction in the portfolio variance
B. There is a direct relationship between the securities coefficient of correlation and the portfolio variance
C. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities
D. none of the above
22. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always __________.
A. equal to the sum of the securities standard deviations
B. equal to -1
C. equal to 0
D. greater than 0
23. Market risk is also called __________ and __________.
A. systematic risk, diversifiable risk
B. systematic risk, nondiversifiable risk
C. unique risk, nondiversifiable risk
D. unique risk, diversifiable risk
24. Firm specific risk is also called __________ and ___________.
A. systematic risk, diversifiable risk
B. systematic risk, non-diversifiable risk
C. unique risk, non-diversifiable risk
D. unique risk, diversifiable risk
25. The term efficient frontier refers to the set of portfolios which _________________.
A. yield the greatest return for a given level of risk
B. involve the least risk for a given level of return
C. Both a and b above
D. None of the above answers are correct
26. Portfolios that lie on the portion of the efficient frontier below the minimum-variance portfolio ___________________.
A. add nothing to the investment opportunity set
B. are sometimes useful in implementing sophisticated hedging techniques
C. represent opportunities for arbitrage
D. None of the above answers is correct
27. The optimal risky portfolio can be identified by finding _____________.
A. the minimum variance point on the efficient frontier
B. the maximum return point on the efficient frontier
C. the tangency point of the capital market line and the efficient frontier
D. None of the above answers is correct
28. A portfolio is comprised of two stocks, A and B. Stock A has a standard deviation of return of 25% while stock B has a standard deviation of return of 5%. Stock A comprises 20% of the portfolio while stock B comprises 80% of the portfolio. If the variance of return on the portfolio is .0080, the correlation coefficient between the returns on A and B is __________.
A. -.975
B. -.025
C. .025
D. .975
29. The standard deviation of return on investment A is .20 while the standard deviation of return on investment B is .05. If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is __________.
A. .12
B. .28
C. .30
D. .75
30. A portfolio is comprised of two stocks, A and B. Stock A has a standard deviation of return of 5% while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is .2778. Stock A comprises 40% of the portfolio while stock B comprises 60% of the portfolio. The variance of return on the portfolio is __________.
A. .0035
B. .0055
C. .0075
D. .0095
Part 2
1.) Two securities have the following characteristics:
E(Ra)=.06 σa = .04
E(Rb)=.08 σb = .10
1A) Fill in the missing cells (A through O) in the table. For each of two correlation cases, corr. = -1 and corr. = 0, calculate the attainable portfolios' mean and standard deviation from combining the two assets together using weights in increments of 25% from 1 to 0. Also, calculate the minimum risk portfolio's weights, mean and standard deviation for the correlation= 0 case (for the case of the correlation = -1, I have already calculated the weights for you!). Assume that the risk free rate is .04. Hint: in some of the cases, filling in the cells requires no calculations. Note, throughout this problem, returns are in decimal form, i.e., 1%=0.01.
|
|
|
Corr = 0
|
|
Corr = -1
|
|
|
Weight in A
|
Weight in B
|
E(Rp)
|
σp
|
E(Rp)
|
σp
|
|
1.0
|
0.0
|
0.06
|
E)
|
H)
|
M)
|
|
0.75
|
0.25
|
A)
|
0.03905
|
I)
|
0.005
|
|
0.50
|
0.50
|
0.07
|
0.05385
|
J)
|
N)
|
|
0.25
|
0.75
|
0.075
|
F)
|
K)
|
0.065
|
|
0.0
|
1.0
|
B)
|
0.10
|
L)
|
0.10
|
|
Minimum risk portfolio for corr=0
|
|
|
|
|
|
|
C)
|
D)
|
0.06275
|
G)
|
NA
|
NA
|
|
Minimum risk portfolio for corr=-1
|
|
|
|
|
|
|
0.7143
|
0.2857
|
NA
|
NA
|
0.0657
|
O)
|
1B) Consider the data in part A for the case of the correlation = 0. Below is the formula for the weight in asset A in the tangency portfolio (that is, the tangency portfolio that is found from extending a line from the risk-free rate to the tangency point of the attainable portfolios curve):
WA = [E(RA) - rf]σ2b - [E(Rb) - rf]σaσbcorr(Ra,Rb)/ [E(RA) - rf]σ2b + [E(Rb) - rf]σa2 - [E(Ra) - rf + E(Rb) - rf]σaσbcorr(Ra,Rb)
E(Ra)=.06 σa = .04
E(Rb)=.08 σb = .10
For the tangency portfolio, find the weight in asset A and B, the portfolio mean, and the standard deviation. Assume that the risk free rate is .04.
1C) Find the reward-to-variability ratio (the slope) of the tangency line (i.e., the capital allocation line).
1D) You want to invest in a portfolio along the capital allocation line that will earn an expected return of 0.11. What will be the portfolio's standard deviation?
2. Assume that security returns are generated by the single index model
Ri = αi + βiRM + εi
where Ri is the excess return for security and RM is the market's excess return. Suppose also that there are three securities A, B, and C characterized by the following data:
|
Security
|
Beta
|
Expected Return
|
σ2(εi)
|
|
A
|
0.8
|
0.10
|
0.05
|
|
B
|
1.0
|
0.12
|
0.01
|
|
C
|
1.2
|
0.14
|
0.10
|
A.) If σ2M =0.04 calculate the variance (e.g. the total risk) of returns of securities A, B, and C.
B.) Now assume there are an infinite number of assets with the return characteristics identical to those of A, B, and C, respectively. If one forms a well-diversified portfolio of type A securities, what will be the variance of the portfolio's return? Similarly, what will the variance of the portfolio's return for portfolios formed only from type B? type C?
C) Listed below are the characteristic lines and correlation's (correlation of each fund with the market) for three mutual funds:
R1 =-0.5 + 1.25Rm p=0.8
R2 =1.25 + 0.95Rm p=0.75
R3 =0.75 + 1.35Rm p=0.7
Which fund has the most non-diversifiable risk?
D) What percent of each fund's risk is systematic and non-systematic?
3) Consider two assets, A and B. The correlation of returns between asset A and B is zero. Starting with the formula for the variance of a portfolio composed of the two assets, derive an expression for the weight placed in asset A and the weight placed in asset B for the minimum risk portfolio. Firm A is a factory that makes models of tiny factories, and firm B is a factory that makes models of factories that make models of tiny factories.