MGMT 3412B Midterm 2
Conceptual: (50% of the total grade, 50 points)
Multiple choice questions (2 points each)
1- If interest rates are expected to rise, you would expect:
a. bond prices to fall more than stock prices.
b. bond prices to rise more than stock prices.
c. stock prices to fall more than bond prices.
d. stock prices to rise and bond prices to fall.
2- A major difference between real and nominal returns is that:
a. real returns adjust for inflation and nominal returns do not.
b. real returns use actual cash flows and nominal returns use expected cash flows.
c. real returns adjust for commissions and nominal returns do not.
d. real returns show the highest possible return and nominal returns show the
lowest possible return.
3- Liquidity risk:
a. is the risk that investment bankers normally face.
b. is lower for small OTC stocks than for large NYSE stocks.
c. is the risk associated with secondary market transactions.
d. increases whenever interest rates increase.
4- If a Canadian investor buys foreign stock, his dollar-denominated return will
increase if the dollar:
a. appreciates in value.
b. depreciates in value.
c. remains unchanged.
d. moves to a net gain position.
5- The bond default premium is measured by the difference between the:
a. return on long-term corporate bonds and short-term corporate bonds.
b. return on long-term government bonds and short-term government bonds.
c. return on long-term corporate bonds and long-term government bonds.
d. return on short-term corporate bonds and short-term government bonds.
6- Which of the following statements regarding the correlation coefficient is not true?
a. It is a statistical measure.
b. It measures the relationship between two securities’ returns.
c. It determines the causes of the relationship between two securities’ returns.
d. All of these are true.
7- The major difference between the correlation coefficient and the covariance is that:
a. the correlation coefficient can be positive, negative or zero while the covariance
is always positive.
b. the correlation coefficient measures relationships between securities and the
covariance measures relationships between a security and the market.
c. the correlation coefficient is a relative measure showing association between
security returns and the covariance is an absolute measure showing association
between security returns.
d. the correlation coefficient is a geometric measure and the covariance is a
statistical measure.
8- Under Markowitz analysis, the only variables that can be manipulated are the:
a. expected returns.
b. portfolio weights.
c. standard deviations.
d. correlation coefficients.
9- Markowitz’s main contribution to portfolio theory is:
a. that risk is the same for each type of financial asset.
b. that risk is a function of credit, liquidity and market factors.
c. risk is not quantifiable.
d. insight about the relative importance of variances and covariances in
determining portfolio risk.
10- Select the true statement from among the following:
a. The risk for a portfolio is a weighted average of individual security risks.
b. Three factors determine portfolio risk.
c. Having established the portfolio weights, the calculation of the expected return
depends on the calculation of portfolio risk.
d. When adding a security to a portfolio, the average covariance between it and the
other securities is not important.
11- The optimal portfolio for a risk-averse investor:
a. cannot be determined.
b. occurs at the point of tangency between the highest indifference curve and the
highest expected return.
c. occurs at the point of tangency between the highest indifference curve and the
efficient set of portfolios.
d. occurs at the point of tangency between the highest expected return and lowest
risk efficient portfolios.
12- Portfolios lying on the upper right portion of the efficient frontier are likely to be
chosen by:
a. aggressive investors.
b. conservative investors.
c. risk-averse investors.
d. defensive investors.
13- Under the separation theorem, all investors should:
a. hold the same portfolio of risky assets and therefore have the same risk/return
combination.
b. have different optimal portfolios.
c. hold the same portfolio of risky assets and achieve their own risk-return
combination through borrowing and lending.
d. hold the same portfolio of risky assets, and the same expected return but at
different levels of risk.
14- Markowitz’s portfolio theory is most concerned with the identification of:
a. undervalued portfolios.
b. utility curves.
c. unsystematic risk.
d. risk-return trade-offs.
15- An indifference curve shows:
a. the one most desirable portfolio for a particular investor.
b. all combinations of portfolios that are equally desirable to a particular investor.
c. all combinations of portfolios that are equally desirable to all investors.
d. the one most desirable portfolio for all investors.
16- What common variable is used in the calculation of both the cumulative wealth
index and the geometric mean return? How is the common variable calculated?
How is it used in each?
Answer: The total return (TR) is used in both calculations.
TR = [CFt + (PE – PB)] / PB.
CWIn = WI0 (1 + TR1)(1 + TR2) . . . (1 + TRn)
G
= [(1 + TR1)(1 + TR2) . . . (1 + TRn)]1/n – 1
17- What is the key assumption underlying the single-index model?
Answer: The key assumption of the single-index model is that securities are related only
in their common response to the return on the market; that is; the residual errors for
security i are uncorrelated with those of security j.
18- What variable is manipulated to determine efficient portfolios? Why are the other
variables not changed at will? What are the other variables?
Answer: Security weights. Other variables are characteristics of the individual securities, not a
portfolio decision. The other variables are expected return, standard deviation, and
correlation.
19- What are the three steps in building a portfolio of financial assets?
Answer: a. Use the Markowitz portfolio model to select an efficient, risky portfolio.
b. Consider borrowing and lending possibilities to construct a new efficient
set.
c. Choose the final portfolio based on individual preferences.
20- When, if ever, would a stock with a large risk (i.e., standard deviation) be desirable in
building a portfolio?
Answer: A stock with a large risk (standard deviation), could be desirable if it has high
negative correlation with other stocks. This will lead to large negative covariances, which
help to reduce portfolio risk.
Problems: (50% of the total grade, 50 points)
1- John buys 1 share of Telmex at 140 pesos when the value of the peso is stated in
dollars at $0.35. One year later, Telmex is selling for 155 pesos and paid a
dividend of 5 pesos during the year. If, after 1 year, the value of the pesos is
$0.29, what will John’s rate of return be in Canadian dollars? (7 points)
Solution:
Return Relative in pesos = [(155 – 140 + 5) / 140] + 1.0 = 1.1429
Domestic TR = 1.1429[0.29 / 0.35] – 1 = –0.0531 or –5.31%
2- Listed below are the end-of-year prices, annual dividends, and total returns for XYZ
Corp. (10 points)
Year
1988
1989
1990
1991
1992
End-of-Year
Price ($)
65.00
72.00
67.00
70.00
72.50
Annual
Dividends ($)
$1.20
$1.50
$1.50
$1.60
$1.60
Total
Return (%)
—
13.07
–4.86
6.87
5.86
(a) Calculate the arithmetic mean return over the holding period 1988-1992.
(b) Calculate the geometric mean return over the holding period 1988-1992.
(c) What is the dividend yield earned by an investor who purchases the stock at the end of
1988 and holds it till the end of 1989?
(d) Compute the cumulative wealth index (Wn) that would result over the four-year
holding period. (Assume W0 = $1).
Solution:
(a) Arithmetic Mean Return = Sum of %TR / 4
= [13.07 – 4.86 + 6.87 + 5.86] / 4 = 20.94% / 4 = 5.235%
(b)
Geometric Mean Return = [Product of Return Relatives]1/4 – 1
= [(1.1307) (.9514) (1.0687)(1.0586)]1/4 – 1
= [1.21702]1/4 – 1 = 1.050327 – 1 = .05033 or 5.033%
Note: The geometric mean is less than the arithmetic mean because of the variability in the
total returns over the four years.
(c)
For 1989, the Dividend yield = Dividends Received / Price Paid = 1.50 / 65 = 2.31%
(d) Cumulative Wealth Index
(CWIn) = WI0 (1 + TR1)(1 + TR2)...(1 + TRn)
Assuming WI0 = $1,
(CWIn) = $1(1.1307)(.9514)(1.0687)(1.0586) = $1.21702
This means that $1 would have grown to $1.217 or by approximately 21.70%.
3- Assume that the expected return on the S&P/TSX Composite Index is 12 per cent
with a standard deviation of 16 per cent. Given the following information for
stocks A, B, and C and the single index model: [calculate the variance of each stock
using this formula: (i2 = βi2M2 + ei2)] (12 points)
Security
A
B
C
αi
20%
16%
15%
βi
1.37
1.08
1.18
ei
20%
14.14%
10%
(a) Calculate the expected return for each stock.
(b) Calculate the variance and standard deviation for each stock.
(c) Indicate which of the three securities is the riskiest and which is least risky
when added to a well-diversified portfolio.
Solution:
(a) E(Ri) = αi + βiE(RM)
E(RA) = 20% + 1.37(12%) = 36.44%
E(RB) = 16% + 1.08(12%) = 28.96%
E(RC) = 15% + 1.18(12%) = 29.16%
(b)
i2 = βi2M2 + ei2
A2 = (1.37)2(0.16)2 + (0.2)2 = 8.8049%
A = 29.67%
B2 = (1.08)2(0.16)2 +(0.1414)2 = 4.985%
B = 22.32%
C2 = (1.18)2(0.16)2 + (0.1)2 = 4.56%
C = 21.36%
(c) When added to a well-diversified portfolio, it is only systematic risk or beta that
is relevant. Hence, stock A would be the riskiest [βA = 1.37] and Stock B would
be the least risky [βB = 1.08].
4- Three securities have the following expected returns: X = 10%, Y = 18%, and Z =
25%. (9 points)
(a) Calculate the expected return for a portfolio consisting of all three securities if
equal amounts are placed in each security.
(b) Assume that the standard deviations for these three securities are, respectively,
12%, 14%, and 18%. The correlation coefficients are as follows: XY = +0.6,
YZ = +0.2, and XZ = –0.3. Assuming equal weights, calculate the standard
deviation for the portfolio.
Solution:
(a) E(Rp) = .333(.10) + .333(.18) + .333(.25)
= .0333 + .05994 + .08325
= .1765 or 17.65%
(b) p2 = (.333)2(.12)2 + (.333)2(.14)2 + (.333)2(.18)2 + 2(.333)(.333)(.6)(.12)(.14)
+ 2(.333)(.333)(.2)(.14)(.18) + 2(.333)(.333)(–.3)(.12)(.18)
= .009298
p = (.009298)1/2 = 9.64%
5- You are given the following information for stock A and stock B: (12 points)
State of the
economy
High growth
Moderate growth
No growth
Recession
Probability of
occurrence (%)
10
20
50
20
E(RA) (%)
E(RB) (%)
40
30
10
-20
20
15
8
-5
Calculate the expected return and standard deviation for a portfolio composed of
40% invested in stock A and 60% invested in stock B.
Solution:
E (Ra) = 0.4 (0.1) + 0.3 (0.2) + 0.1 (0.5) + (-0.2) (0.2) = 0.11
E (Rb) = 0.2 (0.1) + 0.15 (0.2) + 0.08 (0.5) + (-0.05) (0.2) = 0.08
E (Rp) = 40% (0.11) + 60% (0.08) = 0.044 + 0.048 = 0.092
σAB = [(0.4 – 0.11) (0.2 – 0.08)] (0.1) + [(0.3 – 0.11) (0.15 – 0.08)]
(0.2) + [ (0.1 – 0.11) (0.08 – 0.08)] (0.5) + [(-0.2 – 0.11) (-0.05 –
0.08)] (0.2)
= 0.0142
 A  .10(40  11) 2  .20(30  11) 2  .50(10  11) 2  .20(20  11) 2
 84.1  72.2  0.5  192.2  349  0.1868
 B  .10(20  8) 2  .20(15  8) 2  .50(8  8) 2  .20(5  8) 2
 14.4  9.8  0  33.8  58  0.0762
 P  (0.4) 2 (0.1868) 2  (0.6) 2 (0.0762) 2  2(0.4)(0.6)(0.0142)  0.01448  0.12