chapter

Part 2 Important Financial Concepts

CHAPTER 5

Risk and

Return

SOLUTIONS MANUALOverview

This chapter focuses on the fundamentals of the risk and return relationship of assets and their valuation. For the single asset held in isolation, risk is measured with the probability distribution and its associated statistics: the mean, the standard deviation and the coefficient of variation. The concept of diversification is examined by measuring the risk of a portfolio of assets that are perfectly positively correlated, perfectly negatively correlated, and those that are uncorrelated. Next, the chapter looks at international diversification and its effect on risk. The capital asset pricing model (CAPM) is then presented as a valuation tool for securities and as a general explanation of the risk-return trade-off involved in all types of financial transactions.

SUGGESTED ANSWERS TO CRITICAL THINKING QUESTIONS

Focus on Ethics What about moral risk?

Do you agree that the best protection against employee misdeeds is loyalty and empowerment?This is a difficult question and there are many conflicting views. Some people argue that the ultimate objective is to attract a loyal, honest and ethical workforce, and to build incentives into the workplace that encourage honest behaviour and empower employers to behave morally. If this can be achieved there is probably no doubt that it will provide the ultimate protection against dishonest conduct.

On the other hand, others have argued that, laudable as this objective is, human beings are often flawed and subject to temptation, and there will always be some employees, no matter how honest they appear, who will yield to the temptation to conduct themselves improperly. In this case, incentives for ethical behaviour must be combined with systems to prevent and/or detect dishonest conduct.

For example, Nick Leeson was able to get away with his behaviour because the Barings Bank Singapore operation was poorly structured and vulnerable to this sort of conduct. Leeson was responsible for both the front office (initiating trades on behalf of the bank) and the back office (recording transactions and processing the paperwork). A separation of these roles is the norm in the finance industry and would probably have prevented what occurred. Madoff got away with his deception because of blinding trust in his character and reputation.

Focus on Practice Risk reduction internationally

What are some of the negative consequences of international diversification?It seems quite clear that international diversification, in the long term, increases risk-adjusted return. That doesnt mean that higher returns are guaranteed every time. Risk is an inherent part of investing and it means that sometimes return will be higher than expected and sometimes they will be lower than expected. A lower return because of a downturn in foreign markets in a particular period, that becomes evident with the benefit of hindsight, isnt really a disadvantage of international diversification its just part and parcel of investing.

There are some disadvantages, however. It is more costly, in terms of transaction costs, to invest in foreign markets. There may be less information available about risk and return in other countries, which in itself is a type of risk. In some countries there is a certain amount of political risk, which is the risk that a foreign government will do something detrimental to foreign investors, such as nationalising (taking over) privately-owned assets. There are also intangible or emotional factors, such as the desire on the part of some people to own investments in their own country for nationalistic reasons, or a resistance on the part of people in other countries, for similar reasons, against foreign investment.

ANSWERS TO REVIEW QUESTIONS

5-1Risk is defined as the chance of financial loss, as measured by the variability of expected returns associated with a given asset. A decision-maker should evaluate an investment by measuring the chance of loss, or risk, and comparing the expected risk to the expected return. Some assets are considered risk-free; the most common examples are Australian Government Treasury securities.

5-2The return on an investment (total gain or loss) is the change in value plus any cash distributions over a defined time period. It is expressed as a per cent of the beginning-of-the-period investment. The formula is:

Realised return requires the asset to be purchased and sold during the time periods the return is measured. Unrealised return is the return that could have been realised if the asset had been purchased and sold during the time period the return was measured.

5-3a.The risk-averse financial manager requires an increase in return for a given increase in risk.

b.The risk-indifferent manager requires no change in return for an increase in risk.

c.The risk-seeking manager accepts a decrease in return for a given increase in risk.

Most financial managers are risk-averse.

5-4Scenario analysis evaluates asset risk by using more than one possible set of returns to obtain a sense of the variability of outcomes. The range is found by subtracting the pessimistic outcome from the optimistic outcome. The larger the range, the more variability or risk associated with the asset.

5-5The decision-maker can get an estimate of project risk by viewing a plot of the probability distribution, which relates probabilities to expected returns and shows the degree of dispersion of returns. The more spread out the distribution, the greater the variability or risk associated with the return stream.

5-6The standard deviation of a distribution of asset returns is an absolute measure of dispersion of risk about the mean or expected value. A higher standard deviation indicates a greater project risk. With a larger standard deviation, the distribution is more dispersed and the outcomes have a higher variability, resulting in higher risk.

5-7The coefficient of variation is another indicator of asset risk, measuring relative dispersion. It is calculated by dividing the standard deviation by the expected value. The coefficient of variation may be a better basis than the standard deviation for comparing risk of assets with differing expected returns.

5-8An efficient portfolio is one that maximises return for a given risk level or minimises risk for a given level of return. Return of a portfolio is the weighted average of returns on the individual component assets:

where n = number of assets, wj = weight of individual assets, and = expected returns.

The standard deviation of a portfolio is not the weighted average of component standard deviations; the risk of the portfolio as measured by the standard deviation will be smaller. It is calculated by applying the standard deviation formula to the portfolio assets:

5-9The correlation between asset returns is important when evaluating the effect of a new asset on the portfolios overall risk. Returns on different assets moving in the same direction are positively correlated, while those moving in opposite directions are negatively correlated. Assets with high positive correlation increase the variability of portfolio returns; assets with high negative correlation reduce the variability of portfolio returns. When negatively correlated assets are brought together through diversification, the variability of the expected return from the resulting combination can be less than the variability or risk of the individual assets. When one asset has high returns, the others returns are low and vice versa. Therefore, the result of diversification is to reduce risk by providing a pattern of stable returns.

Diversification of risk in the asset selection process allows the investor to reduce overall risk by combining negatively correlated assets so that the risk of the portfolio is less than the risk of the individual assets in it. Even if assets are not negatively correlated, the lower the positive correlation between them, the lower the resulting risk.

5-10The inclusion of foreign assets in a domestic companys portfolio reduces risk for two reasons. When returns from foreign-currency-denominated assets are translated into Australian dollars, the correlation of returns of the portfolios assets is reduced. Also, if the foreign assets are in countries that are less sensitive to the business cycle, the portfolios response to market movements is reduced.

When the dollar appreciates relative to other currencies, the dollar value of a foreign-currency-denominated portfolio declines and results in lower returns in dollar terms. If this appreciation is due to better performance of the economy, foreign-currency-denominated portfolios generally have lower returns in local currency as well, further contributing to reduced returns.

Political risks result from possible actions by the host government that are harmful to foreign investors or possible political instability that could endanger foreign assets. This form of risk is particularly high in developing countries. Companies diversifying internationally may have assets seized or the return of profits blocked.

5-11The total risk of a security is the combination of non-diversifiable risk and diversifiable risk. Diversifiable risk refers to the portion of an assets risk attributable to firm-specific, random events (strikes, litigation, loss of key contracts, etc) that can be reduced or eliminated by diversification. Non-diversifiable risk is attributable to market factors affecting all firms (war, inflation, political events, etc). Some argue that non-diversifiable risk is the only relevant risk because diversifiable risk can be eliminated by creating a portfolio of assets which are not perfectly positively correlated.

5-12Beta measures non-diversifiable risk. It is an index of the degree of movement of an assets return in response to a change in the market return. The beta coefficient for an asset can be found by plotting the assets historical returns relative to the returns for the market. By using statistical techniques, the characteristic line is fit to the data points. The slope of this line is beta. Beta coefficients for actively traded stocks are published in Value Line Investment Survey and in brokerage reports. The beta of a portfolio is calculated by finding the weighted average of the betas of the individual component assets.

5-13The equation for the capital asset pricing model is: kj = RF + [bj (km - RF)],

where:

kj=the required (or expected) return on asset j

RF=the rate of return required on a risk-free security (a government security)

bj=the beta coefficient or index of non-diversifiable (relevant) risk for asset j

km=the required return on the market portfolio of assets (the market return)

The security market line (SML) is a graphical presentation of the relationship between the amount of systematic or non-diversifiable risk associated with an asset and the required return. Systematic risk is measured by beta and is on the horizontal axis while the required return is on the vertical axis.

5-14a.If there is an increase in inflationary expectations, the security market line will show a parallel shift upward in an amount equal to the expected increase in inflation. The required return for a given level of risk will also rise.

b.The slope of the SML (the beta coefficient) will be less steep if investors become less risk-averse, and a lower level of return will be required for each level of risk.

5-15The CAPM provides financial managers with a link between risk and return. Because it was developed to explain the behaviour of securities prices in efficient markets and uses historical data to estimate required returns, it may not reflect future variability of returns. While studies have supported the CAPM when applied in active securities markets, it has not been found to be generally applicable to real corporate assets. However, the CAPM can be used as a conceptual framework to evaluate the relationship between risk and return.

SOLUTIONS TO PROBLEMS

5-1LG 1: Rate of return:

a.

Investment X:Return

Investment Y:Return

b.Investment X should be selected because it has a higher rate of return for the same level of risk.

5-2LG 1: Return calculations:

Logistics Ltd doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. It does not represent cash flow in the hands of the shareholder.

5-3LG 1: Return calculations:

InvestmentCalculationrt (%)

A($1,100 $800 $100) ( $80025.00

B($118,000 $120,000 + $15,000) ( $120,00010.83

C($48,000 $45,000 + $7,000) ( $45,00022.22

D($500 $600 + $80) ( $600-3.33

E($12,400 $12,500 + $1,500) ( $12,50011.20

5-4LG 1: Return calculations

a.A = 30%

B = 21.74%

b.Based on rates of return, A is selected because of high rate for a given level of risk.5-5LG 1: Risk preferences

a.The risk-indifferent manager would accept Investments X and Y because these have returns at least equal to the 12% required return and the risk does not matter.

b.The risk-averse manager is likely to accept Investment X because it provides the highest return and has the lowest amount of risk. Investment X offers an increase in return for taking on more risk than what the firm currently earns. As long as the increase in return is seen to be sufficient compensation for the extra risk, Investment X would be chosen.

c.The risk-seeking manager would accept Investment Y, because it has more risk for the same return as existing investments. He is also likely to accept Investment Z, because it has more risk and the risk-seeking manager is prepared to accept a lower return in order to get access to more risk (as long as the extra risk is seen by the individual manager to be sufficient compensation for the lower return).

d.Traditionally, financial managers are risk-averse and would prefer Investment X, since it provides the required increase in return for an increase in risk.

5-6LG 1: Risk preferences

a) A because it has the highest return.

b) B because it offers the highest return for a given risk.

c) C because it offers the highest risk.

d) Most are risk averse and would select B.5-7LG 2: Risk analysis

a.Expansion

Range

A24% 16% =8%

B30% 10% =20%

b.Project A is less risky, since the range of outcomes for A is smaller than the range for Project B.

c.Since the most likely return for both projects is 20% and the initial investments are equal, the answer depends on your risk preference. A risk-averse manager would prefer Project A. A risk-seeking manager would prefer Project B. A risk-indifferent manager would be indifferent between the two projects.

d.The answer is no longer clear, since it now involves a risk-return trade-off. Project B has a slightly higher return but more risk, while A has both lower return and lower risk. A risk-averse manager might choose either project, depending on his level of risk aversion; i.e. how risk-averse he is. Someone who is more risk-averse requires a larger amount of extra return to compensate him for extra risk, and is less likely to choose Project B. This person is more likely to choose a low risk-low return option (i.e. Project A). Someone who is still risk-averse but has a lower level of risk aversion might find the additional return (1%) sufficient compensation for the extra risk and is more likely to choose Project B.

5-8LG 2: Risk and probability

a.Camera

Range

V30% 20% =10%

Z35% 15% =20%

b.PossibleProbabilityExpected ReturnWeighted

OutcomesPrikiValue (%)

(ki Pri)

Camera VPessimistic0.25205.00

Most likely0.502512.50

Optimistic0.2530

7.50

1.00Expected Return25.00Camera ZPessimistic0.20153.00

Most likely0.552513.75

Optimistic0.2535

8.75

1.00Expected Return25.50c.Camera Z is considered more risky than Camera V because it has a much broader range of outcomes. The risk-return trade-off is present because Camera Z is more risky and also provides a higher return than Camera V.

5-9LG 2: Bar charts and riska.Bar Chart-Line J

Probability

Expected Return (%)

Bar Chart-Line K

Probability

Expected Return (%)

b.Weighted

MarketProbabilityExpected ReturnValue

AcceptancePriki(ki Pri)

Line JVery Poor0.050.00750.000375

Poor0.150.01250.001875

Average0.600.08500.051000

Good0.150.14750.022125

Excellent0.050.16250.008125

1.00Expected Return0.083500Line KVery Poor0.050.0100.000500

Poor0.150.0250.003750

Average0.600.0800.048000

Good0.150.1350.020250

Excellent0.050.1500.007500

1.00Expected Return0.080000c.Line K appears less risky due to a slightly tighter distribution than Line J, indicating a lower range of outcomes.

5-10LG 2: Risk and probability

a) A = 0.04B = 0.16

b) B is more risky; it has the greater range.

c) rA = 15.8%

rB = 15.2%

5-11LG 2: Expected returnAnalystProbabilityReturnWeighted Value

10.355%1.75%

20.055%0.25%

30.2010%2.0%

40.403%1.2%

Total1.00Expected Return4.70%

5-12LG 2: Risk measures:

CV1 0.10 ( 0.15 0.6667

CV2 0.05 ( 0.12 0.4167

Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment.

5-13LG 2: Coefficient of variation:

a.A

B

C

D

b.Asset C has the lowest coefficient of variation and is the least risky relative to the other choices.

5-14LG 2: Standard deviation versus coefficient of variation as measures of risk

a.Project A is least risky based on range, with a range of 0.04.b.Project A is least risky based on standard deviation, with a value of 0.029. Standard deviation is not the appropriate measure of risk since the projects have different returns.

c.A

B

C

D

In this case Project A is the best alternative since it provides the least amount of risk for each percent of return earned. Coefficient of variation is probably the best measure in this instance since it provides a standardised method of measuring the risk/return trade-off for investments with differing returns.

5-15LG 1, 2: Rate of return, standard deviation, coefficient of variation

a)2007 = 50.07%; 2008 = 200.60%; 2009 = 11.73%; 2010 = 26.83%.

b)72.31%.

c)Standard deviation = 86.97%.

d)Coefficient of variation = 1.20.e)The share is riskier than what Mike normally buys, but if he believes that Oxbo will continue to rise then he should include it in his portfolio.

5-16LG 2: Return and risk

a)Asset R = 3.29% Asset Q = 4.49%

b)Asset R = 0.2742 Asset Q = 0.3742

c)Asset R has less risk as shown by a lower standard deviation and a lower coefficient of variation.5-17LG 2: Assessing return and risk

a.Project 7

i.Range: 1.00 (0.10) = 1.10

ii.Expected return:

Rate of ReturnProbabilityWeighted ValueExpected Return

kiPriki Pri

-0.100.01-0.001

0.100.040.004

0.200.050.010

0.300.100.030

0.400.150.060

0.450.300.135

0.500.150.075

0.600.100.060

0.700.050.035

0.800.040.032

1.00

0.010.010

1.00

0.450

iii.Standard Deviation: Priki

2Pri

Pri

-0.100.450-0.5500.30250.010.003025

0.100.450-0.3500.12250.040.004900

0.200.450-0.2500.06250.050.003125

0.300.450-0.1500.02250.100.002250

0.400.450-0.0500.00250.150.000375

0.450.4500.0000.00000.300.000000

0.500.4500.0500.00250.150.000375

0.600.4500.1500.02250.100.002250

0.700.4500.2500.06250.050.003125

0.800.4500.3500.12250.040.004900

1.000.4500.5500.30250.010.003025.

0.027350(Project 257 = = 0.165378

iv.

Project 12i.Range: 0.50 0.10 = 0.40

ii.Expected return:

Rate of ReturnProbabilityWeighted ValueExpected Return

kiPriki Pri

0.100.050.0050

0.150.100.0150

0.200.100.0200

0.250.150.0375

0.300.200.0600

0.350.150.0525

0.400.100.0400

0.450.100.0450

0.50

0.050.0250

1.00

0.300iii.Standard Deviation: Priki

2Pri

Pri

0.100.300-0.200.04000.050.002000

0.150.300-0.150.02250.100.002250

0.200.300-0.100.01000.100.001000

0.250.300-0.050.00250.150.000375

0.300.3000.000.00000.200.000000

0.350.3000.050.00250.150.000375

0.400.3000.100.01000.100.001000

0.450.3000.150.02250.100.002250

0.500.3000.200.04000.050.002000

0.011250(Project 432 = = 0.106066

iv.

b.Bar ChartsProject 257

Probability

Rate of Return

Project 432

Probability

Rate of Return

c.Summary statistics

Project 257Project 432Range1.1000.400

Expected Return ()0.4500.300

Standard Deviation ()0.1650.106

Coefficient of Variation (CV)0.36750.3536

Since Projects 257 and 432 have differing expected values, the coefficient of variation should be the criterion by which the risk of the asset is judged. Since Project 432 has a smaller CV, it is the opportunity with lower relative risk.

5-18LG 2: Integrated expected return, standard deviation and coefficient of variation

a.Expected return:

Rate of ReturnProbabilityWeighted ValueExpected ReturnkiPriki Pri

Asset F0.400.100.04

0.100.200.02

0.000.400.00

-0.050.20-0.01

-0.100.10-0.01

0.04Asset G0.350.400.14

0.100.300.03

-0.200.30-0.06

0.11Asset H0.400.100.04

0.200.200.04

0.100.400.04

0.000.200.00

-0.200.10-0.02

0.10Asset G provides the largest expected return.

b.Standard Deviation: Pri

Pri(2(kAsset F0.400.04=0.360.12960.100.01296

0.100.04=0.060.00360.200.00072

0.000.04=-0.040.00160.400.00064

-0.050.04=-0.090.00810.200.00162

-0.100.04=-0.140.01960.100.00196

0.017900.1338

Pri(2(kAsset G0.350.11=0.240.05760.400.02304

0.100.11=-0.010.00010.300.00003

-0.200.11=-0.310.09610.300.02883

0.051900.2278

Pri(2(kAsset H0.400.10=0.300.09000.100.009

0.200.10=0.100.01000.200.002

0.100.10=0.000.0000-0.400.000

0.000.10=-0.100.01000.200.002

-0.200.10=-0.300.09000.100.009

0.0220.1483Based on standard deviation, Asset G appears to have the greatest risk.

c.

Asset F:

Asset G:

Asset H:

As measured by the coefficient of variation, Asset F has the largest relative risk.

5-19LG 2: Normal probability distribution

a.Coefficient of variation: CV =

Solving for standard deviation:0.75=(k ( 0.189

(k=0.75 0.189=0.14175

b.i.68% of the outcomes will lie between

1 standard deviation from the expected value:

+l(=0.189+0.14175=0.33075

-l(=0.1890.14175=0.04725

ii.95% of the outcomes will lie between ( 2 standard deviations from the expected value:

+2(=0.189+(2 0.14175)=0.4725

-2(=0.189(2 0.14175)=-0.0945

iii.99% of the outcomes will lie between ( 3 standard deviations from the expected value:

+3(=0.189+(3 0.14175)=0.61425

-3(=0.189(3 0.14175)=-0.23625

c.Probability Distribution

Probability

Return

5-20LG 2: Portfolio standard deviation

Standard deviation for a portfolio of R and Q = 3.18% which is less than either individual standard deviation (see problem 5-16).

5-21LG 3: Portfolio return and standard deviation

a.Expected portfolio return for each year: kp = (wL kL) + (wM kM)

Expected

Asset LAsset MPortfolio Return

Year(wL kL)+(wM kM)kp

2007(14% 0.40 =5.6%)+(20% 0.60 =12.0%)=17.6%

2008(14% 0.40 =5.6%)+(18% 0.60 =10.8%)=16.4%

2009(16% 0.40 =6.4%)+(16% 0.60 =9.6%)=16.0%

2010(17% 0.40 =6.8%)+(14% 0.60 =8.4%)=15.2%

2011(17% 0.40 =6.8%)+(12% 0.60 =7.2%)=14.0%

2012(19% 0.40 =7.6%)+(10% 0.60 =6.0%)=13.6%

b.Portfolio return:

c.Standard deviation:

EMBED Equation.2

d.The assets are negatively correlated.

e.Combining these two negatively correlated assets reduces overall portfolio risk.

5-22LG 3: Portfolio analysis

a.Expected portfolio return:

Alternative 1: 100% Asset F

Alternative 2: 50% Asset F + 50% Asset G

Asset FAsset GPortfolio Return

Year(wF kF)+(wG kG)kp

2007(16% 0.50 = 8.0%)+(17% 0.50 = 8.5%)=16.5%

2008(17% 0.50 = 8.5%)+(16% 0.50 = 8.0%)=16.5%

2009(18% 0.50 = 9.0%)+(15% 0.50 = 7.5%)=16.5%

2010(19% 0.50 = 9.5%)+(14% 0.50 = 7.0%)=16.5%

Alternative 3: 50% Asset F + 50% Asset H

Asset FAsset HPortfolio Return

Year(wF kF)+(wH kH)kp

2007(16% 0.50 = 8.0%)+(14% 0.50 = 7.0%)=15.0%

2008(17% 0.50 = 8.5%)+(15% 0.50 = 7.5%)=16.0%

2009(18% 0.50 = 9.0%)+(16% 0.50 = 8.0%)=17.0%

2010(19% 0.50 = 9.5%)+(17% 0.50 = 8.5%)=18.0%

b.Standard deviation:

EMBED Equation.2

Alternative 1: 100% Asset F

Alternative 2: 50% Asset F + 50% Asset G

Alternative 3: 50% Asset F + 50% Asset H

c.Coefficient of variation: CV=

d.Summary:kp: Expected Value

of Portfolio(kpCVp

Alternative 1 (F)17.5%1.2910.0738

Alternative 2 (FG)16.5%0.00.0

Alternative 3 (FH)16.5%1.2910.0782

Since the assets have different expected returns, the coefficient of variation should be used to determine the best portfolio. Alternative 3, with positively correlated assets, has the highest coefficient of variation and therefore is the riskiest. Alternative 2 is the best choice; it is perfectly negatively correlated and therefore has the lowest coefficient of variation.

5-23LG 4: Correlation, risk and return

a.i.Range of expected return: between 8% and 13%

ii.Range of the risk: maximum risk = 10%, minimum risk = 5%

b.i.Range of expected return: between 8% and 13%

ii.Range of the risk:maximum risk = 10%

minimum risk = a number greater than 0% and less than 5%

(in this case, 4.47%)

c.i.Range of expected return: between 8% and 13%

ii.Range of the risk:maximum risk = 10%, minimum risk = 0%

5-24LG 1, 4: International investment returns

a.Returnpesos =

b.

c.Returnpesos =

d.The two returns differ due to the change in the exchange rate between the peso and the NZ dollar. The peso depreciated (and thus the NZ dollar appreciated) between the purchase date and the sale date, causing a decrease in total return. The answer in part (c) is the more important of the two returns for Derek, because it indicates his return in his home currency. An investor in foreign securities will carry exchange-rate risk that will add to or subtract from his return on the shares.

5-25LG 5: Total, non-diversifiable and diversifiable riska and b.

Portfolio

Risk

((kp)

(%)

Diversifiable

Nondiversifiable

Number of Securities

c.Only non-diversifiable risk is relevant because, as shown by the graph, diversifiable risk can be virtually eliminated through holding a portfolio of at least 20 securities that are not positively correlated. Davids portfolio, assuming diversifiable risk could no longer be reduced by additions to the portfolio, has 6.47% relevant risk.

5-26LG 5: Graphic derivation of beta

Derivation of Beta

a.b.To estimate beta, the rise over run method can be used:

Taking the points shown on the graph:

A financial calculator with statistical functions, or a spreadsheet, can be used to perform linear regression analysis. The beta (slope) of line A is 0.79; of line B, 1.379.

c.With a higher beta of 1.33, Asset B is more risky. Its return will move 1.33% times for each 1% the market moves. Asset As return will move at a lower rate, as indicated by its beta coefficient of 0.75.

5-27LG 5: Beta calculation

5-28LG 5: Interpreting beta

Effect of change in market return on asset with beta of 1.20:

a.1.20(15%)=18.0% increase

b.1.20(-8%)=9.6% decrease

c.1.20 (0%)=no change

d.The asset is more risky than the market portfolio, which has a beta of 1. The higher beta makes the return move more than the market.

5-29LG 5: Betas

a and b.

Increase inImpact onDecrease inImpact on

AssetBetaMarket ReturnAsset ReturnMarket ReturnAsset Return

A0.500.100.05-0.10-0.05

B1.600.100.16-0.10-0.16

C-0.200.10-0.02-0.100.02

D0.900.100.09-0.10-0.09

c.Asset B should be chosen because it will have the highest increase in return.

d.Asset C would be the appropriate choice because it is a defensive asset, moving in opposition to the market. In an economic downturn, Asset Cs return is increasing.

5-30LG 5: Betas and risk rankings

a.ShareBetaMost riskyB1.40

A0.80

Least riskyC-0.30

b. and c.

Increase inImpact onDecrease inImpact on

AssetBetaMarket ReturnAsset ReturnMarket ReturnAsset Return

A0.800.120.096-0.05-0.04B1.400.120.168-0.05-0.07C-0.300.12-0.036-0.050.015d.In a declining market, an investor would choose the defensive share, Share C. While the market declines, the return on C increases.

e.In a rising market, an investor would choose Share B, the aggressive share. As the market increases by 1%, Share B increases 1.4%.

5-31LG 5: Portfolio betas: bp=

a.

Portfolio A

Portfolio B

AssetBetawAwA bAwBwB bB

11.300.100.1300.300.39

20.700.300.2100.100.07

31.250.100.1250.200.25

41.100.100.1100.200.22

50.900.400.3600.20

0.18

bA=0.935bB=1.11

b.Portfolio A is slightly less risky than the market, while Portfolio B is more risky than the market. Portfolio Bs return will move more than Portfolio As for a given increase or decrease in market return. Portfolio B is the more risky.

5-32LG 6: Capital asset pricing model CAPM: kj = RF + [bj (km RF)]

Casekj=RF + [bj (km - RF)]

A8.9%=5% + [1.30 (8% 5%)]

B12.5%=8% + [0.90 (13% 8%)]

C8.4%=9% + [-0.20 (12% 9%)]

D15.0%=10% + [1.00 (15% 10%)]

E8.4%=6% + [0.60 (10% 6%)]

5-33 LG 6: Beta and CAPM

Expected return = 18%

Risk Premium = 6%

5-34 LG 6: Beta and CAPM

a) x = 13.0%

b) x = (6.5%)

y = 7.5% y = (3.75%)

z = (9.5%) z = 4.75%

5-35LG 5, 6: Beta coefficients and the capital asset pricing model

To solve this problem you must take the CAPM and solve for beta. The resulting model is:

a.

b.

c.

d.

e.If Katherine is willing to take a maximum of average risk then she will be able to have an expected return of only 16%. (k = 5% + 1.0(16% 5%) = 16%)

5-36LG 6: Manipulating CAPM: kj = RF + [bj (km RF)]

a.kj=8% + [0.90 (12% 8%)]

kj=11.6%

b.15%=RF + [1.25 (14% RF)]

RF=10%

c.16%=9% + [1.10 (km 9%)]

km=15.36%

d.15%=10% + [bj (12.5% 10%)

bj=2

5-37LG 1, 3, 5, 6: Portfolio return and beta

a.bp = (0.20)(0.80)+(0.35)(0.95)+(0.30)(1.50)+(0.15)(1.25)

= 0.16 + 0.3325 + 0.45 + 0.1875 = 1.13

b.

c.

d.kA=4% + [0.80 (10% 4%)] = 8.8%

kB=4% + [0.95 (10% 4%)] = 9.7%

kC=4% + [1.50 (10% 4%)] = 13.0%

kD=4% + [1.25 (10% 4%)] = 11.5%

e.Of the four investments, C and D had actual returns that exceeded the CAPM expected return (15% versus 13% and 12.5% versus 11.5%). The under-performance of investments A and B could be due to any unsystematic factor which would have caused the firms not do as well as expected. Another possibility is that the firms characteristics may have changed such that the betas at the time of the purchase overstated the true value of the betas that existed during that year. A third explanation is that beta, as a single measure, may not capture all of the systematic factors that cause the expected return. In other words, there is error in the beta estimates.

5-38LG 6: Security market line SML

Security Market Line

a, b and d.

Required return %

Non-diversifiable risk (beta)

c.kj = RF + [bj (km RF)]

AssetA

kj=0.09 + [0.80 (0.13 0.09)]

kj=0.122

AssetB

kj=0.09 + [1.30 (0.13 0.09)]

kj=0.142

d.Asset A has a smaller required return than Asset B because it is less risky, based on the beta of 0.80 for Asset A versus 1.30 for Asset B. The risk premium for Asset A is 3.2% (12.2% 9%), which is lower than Asset Bs risk premium of 5.2% (14.2% 9%).

5-39LG 6: Shifts in the SML

a, b, c and d.

Security Market Lines

SMLdSMLaSMLcRequired

return (%)

Non-diversifiable risk (beta)

b.kj=RF + [bj (km RF)]

kA = 8% + [1.1 (12% 8%)] = 8% + 4.4% = 12.4%

c.kA=6% + [1.1 (10% 6%)] = 6% + 4.4% = 10.4%

d.kA=8% + [1.1 (13% 8%)] = 8% + 5.5% = 13.5%

e.i.A decrease in inflationary expectations reduces the required return as shown in the parallel downward shift of the SML.

ii.Increased risk aversion results in a steeper slope, since a higher return would be required for each level of risk as measured by beta.

5-40LG 5, 6: Integrated risk, return and CAPM

a.Projectkj=RF + [bj (km RF)]

Akj=9% + [1.5 (14% 9%)]=16.5%

Bkj=9% + [0.75 (14% 9%)]=12.75%

Ckj=9% + [2.0 (14% 9%)]=19.0%

Dkj=9% + [0 (14% 9%)]=9.0%

Ekj=9% + [(-0.5) (14% 9%)]=6.5%

b and d.Security Market Line

SMLdRequired

return (%)

Non-diversifiable risk (beta)

SMLbc.Project A is 150% as responsive as the market.

Project B is 75% as responsive as the market.

Project C is twice as responsive as the market.

Project D is unaffected by market movement.

Project E is only half as responsive as the market, but moves in the opposite direction as the market.

d.kA=9% + [1.5 (12% 9%)]=16.5%

kB=9% + [0.75 (12% 9%)]=11.25%

kC=9% + [2.0 (12% 9%)]=15.0%

kD=9% + [0 (12% 9%)]=9.0%

kE=9% + [(-0.5) (12% 9%)]=7.5%

e.The steeper slope of SMLb indicates a higher risk premium than SMLd for these market conditions. When investor risk aversion declines, investors require lower returns for any given risk level (beta).

5-41LG5, 6: Integrated

Coefficient of variation EP = 1.20; 1C 1.80 (worst); PC = 1.75; PM = 1.00 (preferred)

Required returnEP = 12.4%; 1C = 12.8%; PC = 11.2%; PM= 11.6%

Excess historical returnEP = (2.4%); K = 7.2% (Preferred); PC = (3.2%) worst; PM 3.4%

Portfolio return

Global = 0.95

Portfolio return

Global = 13.4%

Required return

Global = 11.8%

Excess historic return

Global = 1.6%

Each division is earning a positive rate of return. EP and PC are earning a negative excess rate of return and only represent 40 per cent of the total firm. IC has the highest level of risks. On a risk and return basis PM is the best performer and fortunately represents 40 per cent of the total firm. At this stage elimination of the worst decision may not be warranted since they all generate return and contribute to the recovery of globalised overheads.

5-42Ethics problem

One way is to ask how the candidate would handle a hypothetical situation. One may gain insight into the moral/ethical framework within which decisions are made. Another approach is to use a pencil-and-paper honesty test these are surprisingly accurate, despite the obvious notion that the job candidate may attempt to game the exam by giving the right versus the individually accurate responses. Before even administering the situational interview question or the test, ask the candidate to list the preferred attributes of the type of company he or she aspires to work for, and see if character and ethics terms emerge in the description. Some companies do credit history checks, after gaining the candidates approval to do so. Using all four of these techniques allows one to triangulate toward a valid and defensible appraisal of a candidates honesty and integrity.

CHAPTER 5

Case 1

Analysing risk and return on Chargers Products investment

This case requires students to review and apply the concept of the risk-return trade-off by analysing two possible asset investments using standard deviation, coefficient of variation and CAPM.

1.Expected rate of return:

Asset X:

CashEndingBeginningGain/Annual Rate

YearFlow (Ct)Value (Pt)Value (Pt-1)Lossof Return

2001$1,000$22,000$20,000$2,00015.00%

20071,50021,00022,000-1,0002.27

20031,40024,00021,0003,00020.95

20041,70022,00024,000-2,000-1.25

20051,90023,00022,0001,00013.18

20061,60026,00023,0003,00020.00

20071,70025,00026,000-1,0002.69

20082,00024,00025,000-1,0004.00

20092,10027,00024,0003,00021.25

20102,20030,00027,0003,00019.26

Average expected return for Asset X = 11.74%

Asset Y:

CashEndingBeginningGain/Annual Rate

YearFlow (Ct)Value (Pt)Value (Pt-1)Lossof Return

2001$1,500$20,000$20,000$07.50%

20071,60020,00020,00008.00

20031,70021,00020,0001,00013.50

20041,80021,00021,00008.57

20051,90022,00021,0001,00013.81

20062,00023,00022,0001,00013.64

20072,10023,00023,00009.13

20082,20024,00023,0001,00013.91

20092,30025,00024,0001,00013.75

20102,40025,00025,00009.60

Average expected return for Asset Y = 11.14%

2.(k=

Asset X:

ReturnAverage

YearkiReturn, k

2200115.00%11.74%3.26%10.63

20072.2711.74-9.4789.68

200320.9511.749.2184.82

2004-1.2511.74-12.99168.74

200513.1811.741.442.07

200620.0011.748.2668.23

20072.6911.74-9.0581.90

20084.0011.74-7.7459.91

200921.2511.749.5190.44

201019.2611.747.52

56.55

712.97

Asset Y:

ReturnAverage

YearkiReturn, k

2

20017.50%11.14%-3.64%13.25

20078.0011.14-3.149.86

200313.5011.142.365.57

20048.5711.14-2.576.60

200513.8111.142.677.13

200613.6411.142.506.25

20079.1311.14-2.014.04

200813.9111.142.777.67

200913.7511.142.616.81

20109.6011.14-1.54

2.37

69.55a.

b.

3.Summary statistics:

Asset XAsset YExpected return11.74%11.14%

Standard deviation8.90%2.78%

Coefficient of variation0.760.25

Comparing the expected returns calculated in 1, Asset X provides a return of 11.74%, only slightly above the return of 11.14% expected from Asset Y. The higher standard deviation and coefficient of variation of Investment X indicates greater risk. With just this information, it is difficult to determine whether the 0.60% difference in return is adequate compensation for the difference in risk. Based on this information, however, Asset Y is likely to be the better choice if the investor has a reasonable level of risk-aversion.

4.Using the capital asset pricing model, the required return on each asset is as follows:

Capital asset pricing model: kj = RF + [bj (km RF)]

AssetRF + [bj (km RF)]=kj

X7% + [1.6 (10% 7%)]=11.8%

Y7% + [1.1 (10% 7%)]=10.3%

From the calculations in 1, the expected return for Asset X is 11.74%, compared to its required return of 11.8%. On the other hand, Asset Y has an expected return of 11.14% and a required return of only 10.8%. This makes Asset Y the better choice.

5.In 3, we concluded that it would be difficult to make a choice between X and Y because the additional return on X may or may not provide the needed compensation for the extra risk. In 4, by calculating a required rate of return, it was easy to reject X and select Y. The required return on Asset X is 11.8%, but its expected return (11.74%) is lower; therefore Asset X is unattractive. For Asset Y the reverse is true, and it is a good investment vehicle.

Clearly, Charger Products is better off using the standard deviation and coefficient of variation, rather than a strictly subjective approach, to assess investment risk. Beta and CAPM, however, provide a link between risk and return. They quantify risk and convert it into a required return that can be compared to the expected return to draw a definitive conclusion about investment acceptability. Contrasting the conclusions in the responses to 3 and 4 above should clearly demonstrate why Stanley is better off using beta to assess risk.

6.(a) Increase in risk-free rate to 8 % and market return to 11 %:

AssetRF + [bj (km RF)]=kj

X8% + [1.6 (11% 8%)]=12.8%

Y8% + [1.1 (11% 8%)]=11.3%

(b) Decrease in market return to 9 %:

AssetRF + [bj (km RF)]=kj

X7% + [1.6 (9% 7%)]=10.2%

Y7% + [1.1 (9% 7%)]=9.2%

In situation (a), the required return rises for both assets, and neither has an expected return above the firms required return.

With situation (b), the drop in market rate causes the required return to decrease so that the expected returns of both assets are above the required return. However, Asset Y provides a larger return compared to its required return (11.14 9.20 = 1.94), and it does so with less risk than Asset X.

Spreadsheet Exercise - Janes Portfolio

The answer to this exercise is located at http://www.pearson.com.au/9781442518193.

Risk

premium (A)

Risk

premium (B)

Market risk

premium

PAGE 39Copyright 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd)

9781442518193 / Gitman et al / Principles of Managerial Finance / 6th edition

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Asset B

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