10.
1 Calculating Returns Suppose a stock had an initial price of $76 per share,
paid a dividend of $1.95 per share during the year, and had an ending share price
of $84. Compute the percentage total return.
Ending share price+Dividend-Beginning price/Beginning price= % total return
(84+1.95-76)/76= 13.09%
10.2 Calculating Yields In Problem 1, what was the dividend yield? The capital
gains yield?
Dividend/Beginning price=Dividend Yield
1.95/76= 2.57%
Ending share price-Beginning/Beginning price/Beginning Price=Capital gain yield
(84-76)/76=10.53%
10.3 Calculating Returns Rework Problems 1 and 2 assuming the ending share
price is $68.
(68+1.95-76)/76= -7.96% (% total return)
1.95/76= 2.57% (dividend yield)
(68-76)/76= -10.53% (capital gain yard)
10.5 Nominal versus Real Returns What was the arithmetic average annual
return on large-company stocks from 1926 through 2017?
a. In nominal terms?
b. In real terms?
a. 12.1%; Inflation 3%
b. ((1+nominal rate of return)/(1+inflation rate))-1
This study source was downloaded by 100000892934504 from CourseHero.com on 03-12-2025 10:07:55 GMT -05:00
https://www.coursehero.com/file/157149930/WK5-IAdocx/
((1+12.1%)/(1+3%))-1= 8.83%
10.7 Calculating Returns and Variability Using the following returns, calculate
the arithmetic average returns, the variances, and the standard deviations for X
and Y:
Returns
Year X Y
1 12% 14%
2 24 29
3 -27 -33
4 14 17
5 19 37
√∑(X-Xmean)2/N
Total rtn / N Standard deviation
(Standard deviation)2
Mean X= 8.4 Y= 12.8
SD X= 18.18 Y= 24.35
Var. X= 330.64 Y= 592.96
11.2 Portfolio Expected Return You own a portfolio that has $3,100 invested in
Stock A and $4,600 invested in Stock B. If the expected returns on these stocks are 9.8
percent and 12.7 percent, respectively, what is the expected return on the portfolio?
3100+4600=7700 Total investment
respective rtn*respective weight= Portfolio return
(3100/7700*9.8)+(4600/7700*12.7)= 11.53%
11.6 Calculating Returns and Standard Deviations Based on the following
information, calculate the expected return and standard deviation:
This study source was downloaded by 100000892934504 from CourseHero.com on 03-12-2025 10:07:55 GMT -05:00
https://www.coursehero.com/file/157149930/WK5-IAdocx/
Summation of probability*Expected rate of return= Expected return
(0.15*-0.148)+(0.30*0.031)+(0.45*0.162)+(0.10*0.348) -
0.0222+0.0093+0.0729+0.0348= 0.0948
√(0.15*(0.0948 - -0.148)2+0.30(0.0948-0.031)2+0.45(0.0948-
0.162)2+0.10(0.0948-0.0348)2
√(0.008842776+0.001221132+0.002032128+0.00036
√0.012456036
=0.1116
11.9 Returns and Standard Deviations Consider the following information
a. Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is
the expected return of the portfolio?
b. What is the variance of this portfolio? The standard deviation?
11.10 Calculating Portfolio Betas You own a stock portfolio invested 20 percent in
Stock Q, 30 percent in Stock R, 15 percent in Stock S, and 35 percent in Stock T. The
betas for these four stocks are .75, 1.90, 1.38, and 1.16, respectively. What is the
portfolio beta?
Respective beta* respective weight= Portfolio beta
(0.2*0.75)+(0.3*1.9)+(0.15*0.38)+(0.35*1.16)= 1.33
11.12 Using CAPM A stock has a beta of 1.15, the expected return on the market is
11.1 percent, and the risk-free rate is 3.8 percent. What must the expected return on
this stock be?
3.8+1.15(11.1-3.8) 3.8+1.15(7.3) 3.8+8.40= 12.2%
This study source was downloaded by 100000892934504 from CourseHero.com on 03-12-2025 10:07:55 GMT -05:00
https://www.coursehero.com/file/157149930/WK5-IAdocx/
11.18 Reward-to-Risk Ratios Stock Y has a beta of 1.15 and an expected return of
11.8 percent. Stock Z has a beta of .85 and an expected return of 10.7 percent. If the
risk-free rate is 4.5 percent and the market risk premium is 7.1 percent, are these stocks
correctly priced?
Risk free rate+beta*market risk premium= Expected rtn.
4.5%+1.15*7.1%= 12.67% expected rtn of Y
4.5%+0.85*7.1%= 10.54% expected rtn of Z
So they are not correctly priced as expected rtn doesn't match CAPM rtn.
12.1 Factor Models A researcher has determined that a two-factor model is
appropriate to determine the return on a stock. The factors are the
percentage change in GNP and an interest rate. GNP is expected to grow by
3.5 percent and the interest rate is expected to be 2.9 percent. A stock has a
beta of 1.3 on the percentage change in GNP and a beta of −.47 on the
interest rate. If the expected rate of return on the stock is 10.2 percent,
what is the revised expected return on the stock if GNP actually grows by 3.2
percent and the interest rate is 2.7 percent?
Actual change in GNP-Expected change in GNP+Actual change in interest rate-
expected change in interest rate)
10.2%+1.30(3.2%-3.5%)+(-0.47)*(2.7%-2.9%)=9.90%
12.2 Factor Models Suppose a three-factor model is appropriate to describe the
returns of a stock. Information about those three factors is presented in the following
chart:
a. What is the systematic risk of the stock return?
b. Suppose unexpected bad news about the firm was announced that causes the stock
price to drop by .85 percent. If the expected return on the stock is 10.9 percent, what is
the total return on this stock?
.0000734(19,843-19,571)=0.90(2.70%-2.60%)-0.32(3.20%-3.40%)= 1.97%
This study source was downloaded by 100000892934504 from CourseHero.com on 03-12-2025 10:07:55 GMT -05:00
https://www.coursehero.com/file/157149930/WK5-IAdocx/
Expected rtn+unexpected rtn(systematic risk portion of rtn)-(unsystematic portion).
10.90%+1.97%-0.85%=12.02%
12.4 Multifactor Models Suppose stock returns can be explained by the
following three-factor model: R i = R F + β1 F 1 + β 2 F 2 − β 3
F 3
Assume there is no firm-specific risk. The information for each stock is presented here:
The risk premiums for the factors are 4.9 percent, 3.8 percent, and 5.3 percent, respec-
tively. If you create a portfolio with 20 percent invested in Stock A, 20 percent invested
in Stock B, and the remainder in Stock C, what is the expression for the return on your
portfolio? If the risk-free rate is 3.2 percent, what is the expected return on your
portfolio?
Portfolio 1
Stock A: 0.20*1.55=0.31 Stock B: 0.20*0.81=0.162 Stock C: 0.60*0.73=0.438 = 0.91
Portfolio 2
Stock A: 0.20*0.80=0.16 Stock B: 0.20*1.25=0.25 Stock C: 0.60*-1.4=-0.84 = 0.33
Portfolio 3
Stock A: 0.20*0.05=0.01 Stock B: 0.20*1.24=0.74 Stock C: 0.60*1.24=0.74 =0.71
3.2%+0.91*6.1%+0.33*5.3%-0.71*5.7%
3.2%+5.5%+1.75%-4%= 6.45%
This study source was downloaded by 100000892934504 from CourseHero.com on 03-12-2025 10:07:55 GMT -05:00
https://www.coursehero.com/file/157149930/WK5-IAdocx/
Powered by TCPDF (www.tcpdf.org)
