Tutorial topic 7

Question 1

Suppose the risk-free rate is 6 per cent. The expected return on the market is 12%. If a particular share has a beta of 0.8, what is its expected return based on the CAPM? If another share has an expeted return of 22% what must its beta be?

Answer 1

The expected return is 10.8%

Beta = 2.67

Question 2

If there is investment in two securities and the total risk of the portfolio is less than the total risk of either security what has caused to this happen?

Answer 2

Total risk = portfolio variance
= x σ2A + [1 –x] σ 2A + 2 x [1 – x] Covariance [A, B]
For the portfolio variance to be less than the variance of A or B the covariance term must be negative. This means that the non-systematic risks of the securities are negatively correlated.

Question 3

If a portfolio has a positive investment in every asset, can the expected return on the portfolio be greater than that on every asset in the portfolio? Can it be less than that on every asset in the portfolio? If you answer yes to one or both of these questions, give an example to support your answer

Answer 3

No to both questions.

Question 4

The most important characteristic in determining the variance of a well-diversifited portfolio is the variances of individual assets in the portfolio. Is the statement true or false? Explain

Answer 4

False. The variance of individual assets is a measure of total risk. The return of a well-diversified portfolio is a function of systematic risk only.

Question 5

Suppose the government announces that, based on a just-completed survey, the growth rate in the economy is likely to be 4% in the coming year, as compared to 6% for the year just completed. Would security prices increase, decrease, or stay the same following this announment

Answer 5

It depends on what expectations were. If the market had ‘priced’ securities for 4 per cent growth, then there would be no change. If, for example, the market had expected zero growth, then the prices would, in all likelihood, increase.

Question 6

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

The Reserve Bank announces an unexpected increase in inflation

Answer 6

Systematic—market-wide

Question 7

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

The managing director announces an increase in expenses unexpectedly

Answer 7

Unsystematic—firm-specific

Question 8

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

The interest rate a company pays on its short-term borrowing is increased by its bank.

Answer 8

Unsystematic—if firm-specific and not a result of general increases

Question 9

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

Electricity prices unexpectedly rise

Answer 9

Both—probably mostly systematic

Question 10

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

There is a change in goverment with a major shift in policies

Answer 10

Systematic—likely to influence the whole market

Question 11

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

An oil tanker ruptures, creating a large oil spill

Answer 11

Unsystematic—firm-specific

Question 12

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

A manufacturer loses a multimillion-dollar customer

Answer 12

Unsystematic—firm-specific

Question 13

Clasify the following events as mostly systematic or mostly non-systematic. Is the distinction clear in every case?

A High Court decision substantially broadens producer liability for injuries suffered by product users.

Answer 13

Systematic—market-wide.

Question 14

beta of the portfolio = Covariance/________ of the market

Answer 14

variance

Question 15

Correlation = covariance/product of __________

Answer 15

standard deviations

Question 16

In broad terms, why is some risk diversifiable? Why are some risks non-diversifiable? Does it follow that an investor can control the level of non-systematic risk in a portfolio, but not the level of systematic risk?

Answer 16

Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique risk is eliminated at little cost. On the other hand, there are some risks that affect all investments and cannot be avoided without cost. Thus, systematic risk can be controlled, but only by a costly reduction in expected returns.

Question 17

The beta for the Family Company is 1.45. Its expected return is 20 %, and the risk-free is 4%. If Family plots on the SML, what is the market risk premium?

Answer 17

(0.20 – 0.04)/1.45 = 0.11 = 11%

Question 18

Suppose Jacoba Industries has a beta of 1.25 and an expected return of 14%. The expected return on the market is 12. If this security plots on the SML, what is the risk-free rate? What is the slope of the SML?

Answer 18

0.14  = Rf + 1.25(0.12 – Rf)
Rf	= 4.0%

(0.14 – 0.04)/1.25 = 0.08