1 The

returns on shares S and T vary depending on the state of economic growth.

a Calculate the expected return and standard

deviation for share S.

b Calculate the expected return and standard

deviation for share T.

c What are the covariance and the correlation

coefficient between returns on S and returns on T?

d Determine a portfolio expected return and standard

deviation if two-thirds of a fund are devoted to S and onethird

devoted to T.

(An Excel spreadsheet showing the

calculations for Question 8 is available at www.pearsoned.co.uk/arnold)

Q76;

1 The

returns on shares S and T vary depending on the state of economic growth.

a Calculate the expected return and standard

deviation for share S.

b Calculate the expected return and standard

deviation for share T.

c What are the covariance and the correlation

coefficient between returns on S and returns on T?

d Determine a portfolio expected return and standard

deviation if two-thirds of a fund are devoted to S and onethird

devoted to T.

(An Excel spreadsheet showing the

calculations for Question 8 is available at www.pearsoned.co.uk/arnold)

Q76;

1 Using the results

generated in Question 8 and three or four additional calculations, display the

efficient frontier for a

two-asset portfolio consisting of S and T. Show a set

of indifference curves for a highly risk-averse investor and select an optimal

portfolio on the assumption that the investor can only invest in these two

shares.

2* (Examination level)

Horace

Investments

Your Uncle Horace is a wealthy man with investments

in a variety of businesses. He is also a generous person, especially to his

nieces and nephews. He has written explaining that he will be distributing some

of his shareholdings amongst the next generation. To your surprise, he has

offered you 100,000 of shares in two firms of great sentimental value to him:

Ecaroh and Acehar. You may allocate the 100,000 in any one of four ways. The

first two options are to put all of the money into one of the firms. An

alternative is to allocate half to Ecaroh and half to Acehar. Finally you may

have 90,000 of Ecaroh shares and 10,000 of Acehar shares. During the week you

are given to make your decision you contact a friend who is a corporate analyst

with access to extensive brokers and other reports on firms. The information he

provides could help you to allocate this generous gift. He tells you that the

market consensus is that Ecaroh is a relatively unexciting but steady, reliable

firm producing profits which do not vary in an erratic fashion. If the economy

is growing strongly then the returns on Ecaroh are expected to be 10 per cent

per year. If normal economic growth occurs then the returns will be 15 per cent

and if poor growth is the outcome the returns will be 16 per cent. Acehar, a

consumer electronics firm, is a much more exciting and dynamic but risky firm.

Profits vary in dramatic ways with the general level of activity in the

economy. If growth is strong then Acehar will return 50 per cent; if normal, 25

per cent; and, if poor, there will be no return. You generate your own

estimates of the probabilities of particular economic growth rates occurring by

amalgamating numerous macroeconomic forecasts and applying a dose of scepticism

to any one estimate. Your conclusions are that there is a 30 per cent chance of

strong growth, a 40 per cent chance of normal growth and the probability of

slow growth is put at 30 per cent. Because of Horaces emotional attachment to

these firms he insists that these are the only investment(s) you hold, as he puts

it, to engender commitment and interest in the success of his corporate

babies.

Required

a For each of the alternatives on offer calculate

returns and standard deviation.

b Draw a risk and return diagram on graph paper

displaying the four options and then add a reasonable riskreturn line for all

possible allocations between Acehar and Ecaroh. (This is hypothetical to some

extent because you do not know the minimum standard deviation point.) State

which of the four options are efficient portfolios and which are inefficient

given your risk-return line.

c You are young and not as risk averse as most

people, because you feel you will be able to bounce back from a financial

disaster should one occur. Draw indifference curves on the diagram for a person

who is only slightly risk averse. Demonstrate an optimal risk-return point on

the risk-return line by labelling it point J.

d Briefly discuss the benefits of greater

diversification. Do these benefits continue to increase with ever greater diversification?

Q77;

1 (Examination level)

You

have been bequeathed a legacy of 100,000 and you are considering placing the

entire funds

either in shares of company A or in shares in company

B. When you told your stock broker about this plan he suggested two alternative

investment approaches.

a Invest some of the money in A and some in B to give

you at least a small degree of diversification. The proportions suggested are

given in Table 2 below.

b Invest the entire sum in a broad range of

investments to reduce risk. This portfolio is expected to produce a

return of 23 per cent per year with a standard

deviation of 6 per cent.

To assist your final decision the broker provides you

with forecasts by expert City analysts for shares in A and

B given various states of the economy see

Table 1.

a Compare the risk and return of the alternatives

(including your original intention of putting all the money into either A or

B).

b Display the results on graph paper and draw an

estimated portfolio risk-return line based on the plot points for the two-share

portfolio. (There is no requirement to calculate the minimum risk portfolio.)

c Describe the efficient and inefficient region.

d Use indifference curves to select the optimal

portfolio to give the highest utility assuming that you are highly risk averse.

e Define the Market Portfolio in Modern

Portfolio Theory.

Q78;

1 If you have access

to information on financial security return probability profiles then draw up a

report showing the efficient frontier for a two-asset portfolio. Draw

indifference curves based on canvassed opinion and/or subjective judgement and

select an optimal portfolio.

2 If you have access

to the estimated probability distribution of returns for some projects within

the firm, consider the impact of accepting these projects on the overall

risk-return profile of the firm. For instance, are they positively or

negatively correlated with the existing set of activities?

Q79;

1 Outline the

difference between systematic and unsystematic risk.

2 Explain the

meaning of CAPM-beta.

3 State the equation

for the security market line.

4 If a share lies

under the security market line is it overor under-valued by the market

(assuming the CAPM to be correct)? What mechanism will cause the share return

to move towards the security market line?

5 What problems are

caused to the usefulness of the CAPM if betas are not stable over time?

Q80;

1 What influences

the CAPM-beta level for a particular share according to the theory?

2 Describe how the

characteristic line is established.

3 What are the

fundamental differences between the CAPM and the APT?

4 Is the firms

existing cost of capital suitable for all future projects? If not, why not?

5 List the

theoretical and practical problems of the CAPM.

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