Download Treasury bill rate - Chinhoyi University of Technology

CHINHOYI UNIVERSITY OF TECHNOLOGY
SCHOOL OF BUSINESS SCIENCES AND MANAGEMENT
DEPARTMENT OF ACCOUNTING SCIENCES AND FINANCE
INVESTMENT ANALYSIS & PORTIFOLIO MANAGEMENT
PRACTICE QUESTIONS
Question 1
A. Which of the following statements about the security market line (SML) are true?
i.
The SML provides a benchmark for evaluating expected investment
performance.[1]
ii.
The SML leads all investors to invest in the same portfolio of risky assets.[1]
iii.
The SML is a graphic representation of the relationship between expected
return and beta.[1]
iv.
Properly valued assets plot exactly on the SML. [1]
B. Risk aversion has all of the following implications for the investment process
except:
i. The security market line is upward sloping.
ii.
The promised yield on AAA-rated bonds is higher than on A-rated bonds.
iii.
Investors expect a positive relationship between expected return and risk.
iv.
Investors prefer portfolios that lie on the efficient frontier to other
portfolios with equal expected rates of return.[2]
1
C. What is the beta of a portfolio with E(Rp) - 20%, if Rf- 5% and E(Rm) -15%?[2]
D. Are the following statements true or false? Explain.
i.
Stocks with a beta of zero offers an expected rate of return of zero. [2]
ii.
The CAPM implies that investors require a higher return to hold highly
volatile securities. [2]
iii.
You can construct a portfolio with a beta of 0.75 by investing 0.75 of the
budget in T-bills and the remainder in the market portfolio. [2]
[15 marks]
Question 2
Hennessy & Associates manages a $30 million equity portfolio for the multimanager
Wilstead Pension Fund. Jason Jones, financial vice president of Wilstead, noted that
Hennessy had rather consistently achieved the best record among the Walstead’s six
equity managers. Performance of the Hennessy portfolio had been clearly superior to that
of the S&P 500 in four of the past five years. In the one less favorable year, the shortfall
was trivial.
Hennessy is a “bottom-up” manager. The firm largely avoids any attempt to “time the
market.” It also focuses on selection of individual stocks, rather than the weighting of
favored industries. There is no apparent conformity of style among the six equity
managers. The five managers, other than Hennessy, manage portfolios aggregating $250
million, made up of more than 150 individual issues.
Jones is convinced that Hennessy is able to apply superior skill to stock selection, but the
favorable results are limited by the high degree of diversification in the portfolio. Over
the years, the portfolio generally held 40–50 stocks, with about 2% to 3% of total funds
committed to each issue. The reason Hennessy seemed to do well most years was because
the firm was able to identify each year 10 or 12 issues that registered particularly large
gains. Based on this overview, Jones outlined the following plan to the Wilstead pension
committee:
“Let’s tell Hennessy to limit the portfolio to no more than 20 stocks. Hennessy
will double the
commitments to the stocks that it really favors and eliminate the
remainder. Except for this one new restriction, Hennessy should be free to manage the
portfolio exactly as before.”
All the members of the pension committee generally supported Jones’s proposal, because
all agreed that Hennessy had seemed to demonstrate superior skill in selecting stocks.
Yet, the proposal was a considerable departure from previous practice, and several
committee members raised questions.
Required
a. Will the limitation of 20 stocks likely increase or decrease the risk of the portfolio?
Explain.[4]
b. Is there any way Hennessy could reduce the number of issues from 40 to 20 without
significantly affecting risk? Explain. [3]
c. One committee member was particularly enthusiastic concerning Jones’s proposal.
He suggested that Hennessy’s performance might benefit further from reduction in
the number of issues to 10. If the reduction to 20 could be expected to be
2
advantageous, explain why reduction to 10 might be less likely to be advantageous.
(Assume that Wilstead will evaluate the Hennessy portfolio independently of the
other portfolios in the fund.) [4]
d. Another committee member suggested that, rather than evaluate each managed
portfolio independently of other portfolios, it might be better to consider the
effects of a change in the Hennessy portfolio on the total fund. Explain how this
broader point of view could affect the committee decision to limit the holdings in
the Hennessy portfolio to either 10 or 20 issues. [5]
[15 marks]
Question 3 [ASGT 2]
a. Within the context of CAPM, assume;
 Expected return on the market
=
15%
 Risk free rate
=
8%
 Expected rate of return on RTG security
=
17%
 Beta of RTG security
=
1.25
i. What is the alpha of RTG? Plot the SML? [5]
ii. Is RTG overpriced, under priced or fairly priced? Why? [3]
b. i. A portfolio has an expected rate of return of 20% and standard deviation of 20%.
Bills offer a sure rate of return of 7%. Which investment alternative will be
chosen by an investor whose A=4? What if A=8.[4]
ii. You have the following information about the following corporations, Circle
Cement and TN Holdings.
RATES OF RETURN
PROBABILITY
0.1
0.4
0.5
Risk free return (Rf)
A
=
WCIRCLE =
WTN
=
Circle Cement
%
20
10
-5
=
5
40%
60%
TN Holdings
%
10
40
45
15%
Draw a pie chart to show how the investor will allocate their funds between the
risky portfolio (P) and the risk free asset. Illustrate your answer with a CAL.
comment on your findings. [8]
[20 marks]
3
Question 4
A pension fund manager at Old Mutual Zimbabwe is considering investing in 3
mutual funds. The first is a stock fund, the second is a long-term corporate bond
fund, and the third is a T-Bill money market fund that yields a rate of 8%. The
return probability distributions of the risky funds are as follows
Expected Return %
Stock Fund [S]
Standard deviation %
30
20
15
Bond Fund [B]
12
Correlation coefficient between Stock Fund and Bond Fund =0.20
a) Solve numerically for the proportions invested in each asset, the
expected return and standard deviation of the optimal risky
portfolio.[10]
b) Find the reward to variability ratio of the CAL supported by T-Bills and Portfolio P.
[2]
c) Calculate the complete portfolio allocated to P and to T-Bills if A=4. Outline your
answer with a pie chart.[8]
[20 marks]
Question 5
I.
Consider the two (excess return) index model regression for A and B
RA= 1%+1.2RM
R-SQR=0.576
RESID STD DEV-N=10.3%
RB=-2%+0.8RM
R-SQR=0.436
RESID STD DEV-N=9.1%
a)
Which stock has more firm specific risk? (4)
b)
Which stock has greater market risk? (4)
Comment in each case.
[8 marks]
Question 6
Estimate the index model and the total variance when given the following information
about the 6 month performance of the Airplus Corporation and the ZSE Index below.
Comment on the significance of your results and illustrate your answer with a Security
Characteristic Line (SCL). [22]
Month
JANUARY
FEBRUARY
MARCH
APRIL
Star CorporationHPR (%)
10
9
12
15
4
ZSE Index- HPR Treasury bill rate
(%)
(%)
4
5
6
5.5
9
7.4
13.4
11
MAY
JUNE
16
8.9
11
11.5
12
11.9
Question 7
A. Which of the following assumptions imply (i.e.) an informationally efficient
market?[2]
i.
Many profit-maximizing participants, each acting independently of the
others, analyze and value securities.
ii.
The timing of one news announcement is generally dependent on other
news announcements.
iii.
Security prices adjust rapidly to reflect new information.
iv.
A risk-free asset exists, and investors can borrow and lend unlimited
amounts at the risk-free rate.
B. Which of the following most appears to contradict the proposition that the stock
market is weakly efficient? Explain.[2]
i.
Over 25% of mutual funds outperform the market on average.
ii.
Insiders earn abnormal trading profits.
iii.
Every January, the stock market earns above normal returns.
C. Suppose, after conducting an analysis of past stock prices, you come up with the
following observations. Which one would appear to contradict the weak form of the
efficient market hypothesis? Explain.[1]
i.
The average rate of return is significantly greater than zero.
ii.
The correlation between the market return one week and the return the
following week is zero.
iii.
One could have made superior returns by buying stock after a 10% rise in
price and selling
after a 10% fall.
iv.
One could have made higher than average capital gains by holding stock
with low dividend yields.
D. State if the following statements are true or false if the efficient market
hypothesis holds?
i.
It implies perfect forecasting ability.[0.5]
ii.
It implies that prices reflect all available information.[0.5]
iii.
It implies that the market is irrational.[0.5]
iv.
It implies that prices do not fluctuate.[0.5]
E. A market anomaly refers to:[2]
i.
An exogenous shock to the market that is sharp but not persistent.
ii.
A price or volume event that is inconsistent with historical price or volume
trends.
iii.
A trading or pricing structure that interferes with efficient buying and
selling of securities.
iv.
Price behaviour that differs from the behaviour predicted by the efficient
market
hypothesis.
5
F. “If the business cycle is predictable, and a stock has a positive beta, the stock’s
returns also must be predictable.” Respond explaining your reasoning.[2]
G. Some scholars contend that professional managers are incapable of outperforming
the market. Others come to an opposite conclusion. Compare and contrast the
assumptions about the stock market that support
(a) Passive portfolio management and [2]
(b) Active portfolio management.[2]
H. You are a portfolio manager meeting a client. During the conversation that
followed your formal review of her account, your client asked the following
question:
“My grandson, who is studying investments, tells me that one of the best ways to
make money in the stock market is to buy the stocks of small-capitalization firms
late in December and to sell the stocks one month later. What is he talking
about?”
i.
ii.
Identify the apparent market anomalies that would justify the proposed
strategy.[3]
Explain why you believe such a strategy might or might not work in the
future.[2]
[20 marks]
Question 8
As director of research for a medium-sized investment firm, Jeff Cheney was concerned
about the mediocre investment results experienced by the firm in recent years. He met
with his two senior
equity analysts to consider alternatives to the stock selection
techniques employed in the past.
One of the analysts suggested that the current literature has examined the relationship
between Price– Earnings (P/E) ratios and securities returns. A number of studies had
concluded that high P/E stocks tended to have higher betas and lower risk-adjusted
returns than stocks with low P/E ratios.
The analyst also referred to recent studies analyzing the relationship between security
returns and company size as measured by equity capitalization. The studies concluded
that when compared to the S&P 500 index, small-capitalization stocks tended to provide
above-average risk-adjusted returns, while large-capitalization stocks tended to provide
below-average risk adjusted returns. It was further noted that little correlation was found
to exist between a company’s P/E ratio and the size of its equity capitalization.
Jeff’s firm has employed a strategy of complete diversification and the use of beta as a
measure of portfolio risk. He and his analysts were intrigued as to how these recent
studies might be applied to their stock selection techniques and thereby improve their
performance .Given the results of the studies indicated above:
6
a) Explain how the results of these studies might be used in the stock selection and
portfolio management process. Briefly discuss the effects on the objectives of
diversification and on the measurement of portfolio risk.[10]
b) List the reasons and briefly discuss why this firm might not want to adopt a new
strategy based on these studies in place of its current strategy of complete
diversification and the use of beta as a measure of portfolio risk.[10]
[20 marks]
Question 9
I.
Consider the following table, which gives a security analyst’s expected return on
two stocks for two particular market returns:
Market Return,Rm
Aggressive Stock, A
Defensive Stock ,B
5%
2%
3.5%
20%
32%
14%
a) What are the betas of the two stocks?[2]
b) What is the expected rate of return on each stock if the market return is equally
likely to be 5% or 20%?[3]
c) If the T-bill rate is 8%, and the market return is equally likely to be 5% or 20%,
draw the SML for this economy.[5]
d) Plot the two securities on the SML graph. What are the alphas of each and advise
on the significance of the alpha measure?[5]
e) What hurdle rate should be used by the management of the aggressive firm for a
project with the risk characteristics of the defensive firm’s stock?[5]
[20 marks]
Question 10
An investor has gathered the following information about the Zimbabwean market
Bond Fund
Equity Fund
E( R)
𝝈
25%
30%
45%
60%
Covariance between bonds and equities is - 125
Expected return on Treasury bills is 15%
Investor’s risk aversion coefficient is 4
7
Required
i. Calculate the weight invested in the bond fund, equity fund and the money
market. Illustrate your answer graphically in a pie chart. [7]
ii. Calculate the expected return and standard deviation of the risky portfolio and
the complete portfolio. Draw a Capital allocation Line to illustrate your
answer. Calculate the Reward to Variability ratio supported by the risk free
asset and the risky portfolio. [8]
iii. Briefly describe the action to be taken by the investor [5]
[20 marks]
Question 11 [ASGT2]
Outline the differences and similarities between the Single Index model and the Capital
Asset Pricing model. In your opinion, which of the two models makes a better assessment
of the return on a security? [20]
Question 12
An investor has gathered the following information about the Zimbabwean market
Bond Fund
Equity Fund
E( R)
25%
45%
Std dev
30%
60%
Covariance between bonds and equities is - 125
Expected return on Treasury bills is 15%
Investor’s risk aversion coefficient is 4
Required
i. Calculate the weight invested in the bond fund, equity fund and the money
market. Illustrate your answer graphically in a pie chart. [7]
ii. Calculate the expected return and standard deviation of the risky portfolio and
the complete portfolio. Draw a Capital allocation Line to illustrate your
answer. Calculate the Reward to Variability ratio supported by the risk free
asset and the risky portfolio. [8]
iii. Briefly describe the action to be taken by the investor [5]
[20 marks]
Question 13
Outline the differences and similarities between the Single Index model and the Capital
Asset Pricing model. In your opinion, which of the two models makes a better assessment
of the return on a security? [20]
8
Question 14
1(a)
(b)
Track the performance of any counter of your choice from the Zimbabwe Stock
Exchange for a period of at least five years (can track annually, semi annually,
quarterly, monthly) and comment on your findings. Advise shareholders and
prospective shareholders on the course of action to take. Your comment should
include the movement of the share price, Earnings per Share, Net Asset Book
Value, Return on Average Shareholders’ funds, P/E ratios, PBV ratios, PS ratios,
Return on Average Assets and Dividends paid or not paid. (90)
How has the operating environment affected your counter (positively or negatively)
for the years under study? What should the management do to counter or take
advantage of the operating environment affecting your counter? (10)
QUESTION 15
a) A portfolio has an expected rate of return of 20% and standard deviation of 20%.
Bills offer a sure rate of return of 7%. Which investment alternative will be chosen
by an investor whose A=4? What if A=8. (5)
b) You have the following information about the following corporations, PPC and
Econet .
RATES OF RETURN
PPC
PROBABILITY
ECONET
%
%
0.1
0.4
0.5
20
10
-5
10
40
45
Risk free return (Rf)
=
15%
A
=
5
WPPC =
40%
WECONET =
60%
Draw a pie chart to show how the investor will allocate their funds between the
risky portfolio (P) and the risk free asset. Illustrate your answer with a CAL.
comment on your findings. [10]
QUESTION 16
A pension fund manager is considering three mutual funds. The first is a stock fund,
the second is a long-term corporate bond fund, and the third is a T-Bill money market
fund that yields a rate of 8%. The probability distribution of the risky fund is as follows
Expected Return %
Standard deviation %
30
Stock Fund [S]
20
15
Bond Fund [B]
12
Correlation coefficient between Stock fund and Bond fund
9
=0.10
a. Solve numerically for the proportions of each asset and for the expected
return
and standard deviation of the optimal risky portfolio.(10)
b. Find the reward to variability ratio of the CAL supported by T-Bills and
Portfolio P. (2)
c. Calculate the complete portfolio allocated to P and to T-Bills if A=4. Outline
Your answer with a pie chart.(8)
QUESTION 16
A universe of available securities includes two risky stock funds, A and B, and Treasury
Bills. The data for the universe are as follows:
A
B
Treasury bills
Expected Return %
Standard deviation %
10
30
5
20
60
0
The correlation coefficient between A, B
=
-0.2
a) Find the optimal risky portfolio, P, and its expected return and standard
deviation.(10)
b) Find the slope of the CAL supported by T-Bills and Portfolio P. (2)
c) How much will an investor with A=5 invest in funds A, B and in T-Bills? (8)
QUESTION 17
Consider the two (excess return) index model regression for A and B
RA= 1%+1.2RM
R-SQR=0.576
RESID STD DEV-N=10.3%
RB=-2%+0.8RM
R-SQR=0.436
RESID STD DEV-N=9.1%
c)
Which stock has more firm specific risk? (5)
d)
Which stock has greater market risk? (5)
Comment in each case.
QUESTION 18 [ASGT 2]
Estimate the index model and the total variance when given the following
information about the 6 month performance of the Star Corporation and the ZSE
Index below. Comment on the significance of your results and illustrate your
answer with a Security Characteristic Line (SCL). [25]
Month
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
Star CorporationHPR (%)
100
99
121
154
166
87
10
ZSE Index- HPR
(%)
44
69
91
150
111
177
Treasury bill rate
(%)
50
50
75
110
120
120
QUESTION 19 [ASGT 1]
A fund manager is considering investing in three mutual funds. The first is a stock
fund, the second is a long-term corporate bond fund, and the third is a T-Bill
money market fund that yields a rate of 8%. The probability distribution of the
risky fund is as follows
Expected Return %
Standard deviation %
30
Stock Fund [S]
20
15
Bond Fund [B]
12
Correlation coefficient between Stock fund and Bond fund
=0.10
d) Solve numerically for the proportions of each asset , the expected
return
and standard deviation of the optimal risky portfolio. (10)
e) Find the reward to variability ratio of the CAL supported by T-Bills and
Portfolio P. (2)
f) Calculate the complete portfolio allocated to P and to T-Bills if A=4.
Outline
your answer with a pie chart.(8)
QUESTION 20
A fund manager is considering investing in three mutual funds. The first is a
stock fund, the second is a long-term corporate bond fund, and the third is a TBill money market fund that yields a rate of 8%. The probability distribution of
the risky fund is as follows
Expected Return %
Standard deviation %
30
Stock Fund [S]
20
15
Bond Fund [B]
12
Correlation coefficient between Stock fund and Bond fund
=0.10
g) Solve numerically for the proportions of each asset , the expected
return
and standard deviation of the optimal risky portfolio. (10)
h) Find the reward to variability ratio of the CAL supported by T-Bills and
Portfolio P. (2)
i) Calculate the complete portfolio allocated to P and to T-Bills if A=4.
Outline
your answer with a pie chart.(8)
[20
marks]
11
QUESTION 21 [ASGT1]
A pension fund manager is considering three mutual funds. The first is a stock fund,
the second is a long-term government and corporate bond fund, and the third is a
T-bill money market fund that yields a sure rate of 5.5%. The probability
distributions of the risky funds are:
Expected Return
Standard Deviation
Stock fund (S)
15%
32%
Bond fund (B)
9
23
The correlation between the fund returns is 0.15.
a. Tabulate and draw the investment opportunity set of the two risky funds.
b. Use investment proportions for the stock fund of 0 to 100% in increments of 20%.
c. What expected return and standard deviation does your graph show for the
minimum variance portfolio?
d. Draw a tangent from the risk-free rate to the opportunity set. What does your
graph show for the expected return and standard deviation of the optimal risky
portfolio?
e. What is the reward-to-variability ratio of the best feasible CAL?
f. Suppose now that your portfolio must yield an expected return of 12% and be
efficient, that is, on the best feasible CAL.
i. . What is the standard deviation of your portfolio?
ii.. What is the proportion invested in the T-bill fund and each of the two risky
funds?
g. If you were to use only the two risky funds and still require an expected return of
12%, what would be the investment proportions of your portfolio? Compare its
standard deviation to that of the optimal portfolio in the previous problem. What
do you conclude?
[30
marks]
QUESTION 22
a. Several mechanisms have been put in place to mitigate the principal agency
problem. Explain in detail these mechanisms. (4)
b. Who are the clients of the financial system? Elaborate on the needs of each
of these clients. Also highlight how the environment has responded to the
clients’ demands.(5)
c.
Calculate the gross proceeds, total costs and net proceeds of a bankers
Acceptance with the following details.(6)
Nominal value, N
Discount rate, I
Term to maturity, d
Stamp duty, sd
Commission, c
d.
$10 000 000
10.5%
90 days
0.03%
0.6%
Assume you bought a government $10 000 000 value Treasury bond on July
12
16,2006. The T-Bond matures on January 2,2009 and has a coupon rate of 11%
payable semi-annually and a yield (discount rate) of 7%. Calculate the TBonds dirty price, accrued interest and clean price. Assuming that the bond is
Cum- interest and we use an actual/365 day convention.(10)
QUESTION 23
Bear
Normal
Probability
0.2
Rate of return on stock X -20%
Rate of return on stock Y -15%
0.5
18%
20%
Bull
0.3
50%
10%
a) What are the expected return of shares of stocks X and Y and also their
respective standard errors.(5)
b) Calculate the expected return as well as the
standard deviation of the
Portfolio. (5)
NB. Assume that the portfolio is equally weighted between X and Y
QUESTION 24
Suppose we have two securities
E (rA)
E (rB)
A
B
=20%
=30%
=25%
=40%
Construct the following portfolios. Comment on your findings. (20)
a.
b.
c.
WA
(%)
WB
(%)
0
100
40
100
0
60
P
rA,B=25%
E(rP)
(%)
P
rA,B=75%
QUESTION 25
A portfolio has an expected rate of return of 20% and standard deviation of 20%. Bills offer
a sure rate of return of 7%. Which investment alternative will be chosen by an investor
whose A=4? What if A=8. (5)
13
QUESTION 26
PPC
Rates of Return (%)
Probability
0.10
0.40
0.50
20
10
-5
ECONET
10
40
45
Risk free return
=
15%
A
=
5
WPPC =
40%
WEC
=
60%
Draw a pie chart to show how the investor will allocate their funds between the risky
portfolio (P) and the risk free asset. Illustrate your answer with a CAL. comment on
your findings. (20)
QUESTION 27
An analyst estimates that a stock has the following probabilities of return
depending on the state of the economy.
State of the economy
Probability
Good
Normal
Poor
Return%
0.1
0.6
0.3
15
13
7
a) Calculate the expected return as well as the standard error of the stock.
Comment on your findings. (5)
QUESTION 28
Based on the scenarios below, what is the expected return and standard deviation
for a portfolio with the following return profile? Comment. (5)
Bear
Probability
0.2
Rate of return on stock Y -25%
Normal
Bull
0.5
10%
0.3
24%
QUESTION 29
Suppose we have two securities
E (rX)
E (rY)
X
Y
=
=
=
=
40%
60%
20%
30%
Construct the following portfolios. Comment on your findings. (20)
14
WX
(%)
a.
b.
c.
100
0
30
WY
(%)
P
rX,Y=30%
E(rP)
(%)
P
rXY=80%
0
100
70
QUESTION 30
A portfolio has an expected rate of return of 20% and standard deviation of 20%. Bills offer
a sure rate of return of 10%. Which investment alternative will be
chosen by an
investor whose A=3? What if A=10? (5)
QUESTION 31
A universe of available securities includes two risky stock funds, A and B, and Treasury
Bills. The data for the universe are as follows:
Expected Return (%)
Standard Deviation (%)
A
B
10
30
20
60
T-bills
5
0
The correlation coefficient between A, B
=
-0.2
c) Find the optimal risky portfolio, P, and its expected return and standard
deviation.(10)
d) Find the slope of the CAL supported by T-Bills and Portfolio P. (2)
c) How much will an investor with A=5 invest in funds A, B and in T-Bills? (8)
15
Formulas: Investment Analysis and Portfolio Management
1.
  d  i 
MV  P 1  


  365  100 
Issuing certificates of deposits
MV
  d  i 
1   365  100 


 
Dealing in certificates of deposits
C
2.
Treasury Bills
 360  D 
Y 
 
 t  F 
  Yt 
P  F 1  

  360 
365 * y 
360   y * t 
360 * y 
CDeY 
BeY 
360  yt
d 

Tender Price= F  1 *

 365 
 P  TP  365
* 100
Required discount rate= 
*
 100  d
Actual yield=
F  TP 365
*
* 100
TP
d
i
d 

*
Consideration= N   N *
100 365 

3.
Bankers Acceptances
 d
c  i   sd 
TC  N 
 365

i
d 

GP  N   N *
*
100 365 

16
3.
ER A    Pr* RA
4.
 A 2   R A  E R A 2 Pr
5.
rA, B 
6.
ERp   ERi Wi
7.
 2 p  W 2 A 2 A  W 2 B 2 B 2COV A, BWAWB
8.
Sp 
E Rp   Rf
p
9.
Y* 
E Rp   Rf
0.01 * A *  2 p
10.
Y
11.
WD 
12.
  ER  Rf  ERm 
13.
HPR 
14.
Ri     i Rm  ei
15.
Rp  p  pRm  ep
16.
 2 i   2 i 2 m   2 ei 


COV A, B
 A B
E ( Rm )  Rf
0.01 * A *  2 p
ERD   Rf  2 E  ERE   Rf COVD, E
ERD   Rf  2 E  ERE   Rf  2 D  ERD   Rf  ERE   Rf COVD, E
D1 P1  P0

P0
P0
Variance of the rate of return on a security
17.
COV Ri Rm   i 2 m
18.
COV Ri , R j   COV  i Rm;  j Rm 
 ij 2 m
19.

COV Ri Rm 
 2m
17
20.
 1 n 2
 e t
 n  2  t 1
Variance attributable to firm specific factors
 2 ei   
2
21.
_
1


 m
RM

RM



n 1 

2 2
  m  Variance attributable to market forces
2
1
t 1  n 
n
22.
23.
24.
2
 2 ep       2 ei
 2 2 m
R 
2
 2 ei 
R2 1
 2i
2
 X Y
XY   

n

 X 
X  
2
2
n
_
_
_
25.
 Y  X
26.
h
27.
U  e
28.
d
Cu  Cd
uS  dS
T
n
1
u
30.
1  rf  d
ud
C 0  N d 1 S  Xe  rft N d 2 
31.
P0  X e  rfT N  d 2   SN  d 1 
32.
S
In
X
29.

 2



r



 2

T

18
33.
d 2  d1   T
34.
P0 
D1
Ke  g
35.
d
D 365
*
S
T
36.
Yield 
37.
rbd 
S  P 365
*
P
T
N  P 360
*
N
T
1
 n  1
 n  Q2  
Q ji
n
 n 
2
38.
Q
2
P
19