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.

1

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]

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.

2

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 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 

  Circle Cement TN HoldingsPROBABILITY % %0.1 20 100.4 10 400.5 -5 45

Risk free return (Rf) = 15%A = 5

3

WCIRCLE = 40%WTN = 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. [8]

[20 marks]

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

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 BRA= 1%+1.2RMR-SQR=0.576 RESID STD DEV-N=10.3%RB=-2%+0.8RMR-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]

4

 Expected Return % 

Standard deviation %

Stock Fund [S] 2030 

Bond Fund [B] 1215 

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 Star Corporation-HPR (%)

ZSE Index- HPR (%)

Treasury bill rate (%)

JANUARY 10 4 5FEBRUARY 9 6 5.5MARCH 12 9 7.4APRIL 15 13.4 11MAY 16 11 12JUNE 8.9 11.5 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?

5

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.

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. Identify the apparent market anomalies that would justify the proposed strategy.[3]

ii. 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.

6

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:

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]

7

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 FundE( R) 25% 45%𝝈 30% 60%

Covariance between bonds and equities is - 125Expected return on Treasury bills is 15%Investor’s risk aversion coefficient is 4Required

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 FundE( R) 25% 45%Std dev 30% 60%

Covariance between bonds and equities is - 125

8

Expected return on Treasury bills is 15%Investor’s risk aversion coefficient is 4Required

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]

Question 14

1(a) 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)

(b) 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 ECONETPROBABILITY % %

9

0.1 20 100.4 10 400.5 -5 45

Risk free return (Rf) = 15%A = 5WPPC = 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

Correlation coefficient between Stock fund and Bond fund =0.10a. 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:

 Expected Return % 

Standard deviation %

A 10 20

B 30 60 Treasury bills 5 0

The correlation coefficient between A, B = -0.2a) Find the optimal risky portfolio, P, and its expected return and standard

deviation.(10)

10

 Expected Return % 

Standard deviation %

Stock Fund [S] 2030

 

Bond Fund [B] 1215

 

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 BRA= 1%+1.2RMR-SQR=0.576 RESID STD DEV-N=10.3%RB=-2%+0.8RMR-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 Star Corporation-HPR (%)

ZSE Index- HPR (%)

Treasury bill rate (%)

JANUARY 100 44 50FEBRUARY 99 69 50MARCH 121 91 75APRIL 154 150 110MAY 166 111 120JUNE 87 177 120

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

Correlation coefficient between Stock fund and Bond fund =0.10d) 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)

11

 Expected Return % 

Standard deviation %

Stock Fund [S] 2030

 

Bond Fund [B] 1215

 

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 T-Bill money market fund that yields a rate of 8%. The probability distribution of the risky fund is as follows

Correlation coefficient between Stock fund and Bond fund =0.10g) 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]

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%.

12

 Expected Return % 

Standard deviation %

Stock Fund [S] 2030

 

Bond Fund [B] 1215

 

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 22a. 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 $10 000 000Discount rate, I 10.5%Term to maturity, d 90 daysStamp duty, sd 0.03%Commission, c 0.6%

d. Assume you bought a government $10 000 000 value Treasury bond on July

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 T-Bonds 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 Bull

Probability 0.2 0.5 0.3

13

Rate of return on stock X -20% 18%50% Rate of return on stock Y -15% 20%

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) =20%E (rB) =30%A =25%B =40%

Construct the following portfolios. Comment on your findings. (20)

WA WB E(rP) P P(%) (%) (%) rA,B=25% rA,B=75%

a. 0 100b. 100 0c. 40 60

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)

QUESTION 26

PPC ECONETRates of Return (%)

Probability0.10 20 10

14

0.40 10 400.50 -5 45

Risk free return = 15%A = 5WPPC = 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 Return%

Good 0.1 15Normal 0.6 13Poor 0.3 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 Normal Bull

Probability 0.2 0.5 0.3Rate of return on stock Y -25% 10%24%

QUESTION 29

Suppose we have two securities

E (rX) = 40%E (rY) = 60%X = 20%Y = 30%

Construct the following portfolios. Comment on your findings. (20)

WX WY E(rP) P P(%) (%) (%) rX,Y=30% rXY=80%

15

a. 100 0b. 0 100c. 30 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 31A 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 10 20B 30 60

T-bills 5 0

The correlation coefficient between A, B = -0.2c) 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)

Formulas: Investment Analysis and Portfolio Management

16

1.MV=P[1+( d

365 )( i100 )]

Issuing certificates of deposits

C= MV

[1+( d365 )( i

100 )]Dealing in certificates of deposits

2. Treasury Bills

Y=(360t )( DF )

P=F [1−( Yt360 )]

BeY=(365∗y )

360− ( y∗t )

CDeY=(360∗y )360− yt

Tender Price=F−[1∗ d

365 ]

Required discount rate=[ P−TP100 ]∗365

d∗100

Actual yield=

F−TPTP

∗365d

∗100

Consideration=N−[N∗ i

100∗ d

365 ]3. Bankers Acceptances

TC=N [ d365

(c+i )+sd ]GP=N−[N∗ i

100∗ d

365 ]

17

3. E (R A )=∑ Pr*R A

4.σ

A2=∑ [RA−E (RA )2] Pr

5.rA ,B=

COV A , B

σ A σB

6. E (Rp )=E (Ri )Wi

7. σ 2 p=W2A σ

2A+W

2B σ

2B2COV A ,BW AW B

8.Sp= E (Rp )−Rf

σp

9.Y ¿=

E (Rp )−Rf0. 01∗A∗σ2 p

10.Y=

E (Rm )−Rf0 . 01∗A∗σ 2 p

11.WD=

[E (RD )−Rf ]σ2E−[E (RE )−Rf ]COV D, E

[ E (RD )−Rf ]σ2E+ [E (RE )−Rf ]σ

2D−[E (RD )−Rf +E (RE )−Rf ]COV D, E

12. α=ER−[Rf +βE (Rm ) ]

13.HPR=

D1

P0+P1−P0

P0

14. Ri=α+ βi Rm+ei

15. Rp=αp+β pRm+ep

16. σ 2 i=β2 iσ2m+σ2

(ei )

Variance of the rate of return on a security

17. COV (Ri Rm)=βiσ 2m

18. COV (Ri , R j )=COV (β iRm ;β j Rm)=βiβjσ 2m

18

19.β=

[COV (Ri Rm )]σ2m

20.σ 2 (e i )=( 1

n−2 )∑t=1

n

e2t

Variance attributable to firm specific factors

21.σ

2m= 1n−1∑ (RM−RM

¿ )2

β2σ2 m=Variance attributable to market forces

22.σ 2 (ep )=∑

t=1

n

(1n )

2σ2 ei

23.R2= β2 σ2m

σ2

R2=1−σ 2(ei )

σ2i

24.

β=∑ XY−

(∑ X∑Y )n

∑ X2−(∑ X2 )

n

25. α=Y¿−β X

¿¿

26.h=Cu−Cd

uS−dS

27.U=e σ√Tn

28.d=1

u

29.∏ ¿ 1+rf−d

u−d

30. C0=N (d1) S−Xe−rft N (d2)

31. P0=X e−rfT N (−d2)−SN (−d1)

19

32.In( SX )+r+( σ 2

2 )T33. d2=d1−σ √T

34.P0=

D1

Ke−g

35.d=D

S∗365

T

36.Yield=S−P

P∗365

T

37.rbd=N−P

N∗360

T

38.Q

2P=n [ 1n ]

2

Q2+[ n−1n ]Q ji

20