1 The returns on shares S and T vary depending on the state of economic growth. a Calculate the…

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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