ch 7 finance

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Chapter 7

Risk and Return

Learning Objectives

1. Explain the relation between risk and return.

2. escribe the two co!ponents o" a total holding period return# and calculate this return "or

an asset.

$. Explain what an expected return is# and calculate the expected return "or an asset.

%. Explain what the standard deviation o" returns is# explain wh& it is especiall& use"ul in

"inance# and be able to calculate it.

'. Explain the concept o" diversi"ication.

(. iscuss which t&pe o" risk !atters to investors and wh&.

7. escribe what the Capital )sset *ricing +odel ,C)*+- tells us and how to use it to evaluate

whether the expected return o" an asset is su""icient to co!pensate an investor "or the risks

associated with that asset.

. Chapter Outline

7.1 Risk and Return

The greater the risk, the larger the return investors require as compensation for bearing that

risk.

Higher risk means you are less certain about the ex post level of compensation.

Which stock would you invest in?

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7.2 /uantitative +easures Return

A. Holding Period Returns

The total holding period return consists of two components$ %#& capital appreciation

and %'& income.

The capital appreciation component of a return, ()*$

# +)*

+ +

)apital *ppreciation ( -

nitial rice

= =

The income component of a return ($#

+

)/)ash /low( -

nitial rice =

The total holding period return is simply # #T )* + + +

)/ 0)/( - ( 0( - .

+ =

1uppose a stock had an initial price of 234 per share, paid a dividend of 2#.'5 per share duringthe year, and had an ending share price of 243. )ompute the percentage total return.

6#7.#8#8#7.234

2#+.'5

234

2#.'5&234,%243

234

2#.'5

234

342243(eturnercentageTotal ===

+=+

=

What was the dividend yield? The capital gains yield?

69+.#+#9+8.234

'5.#2

:yield:ividend

t

#t====

+

657.####584.234

;2

234

&342%243

yieldgains)apital

t

t#t===

=

=

+

Total holding period return - #8.#76 - #.9+6 0 ##.576

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B. Expected Returns


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A. Calculating the Variance and Standard Deviation

The variance , 2-squares the difference between each possible occurrence and the

mean %squaring the differences makes all the numbers positive& and multiplies each

difference by its associated probability before summing them up$

( )( )''

( i i#

Ear %(& ( < ( n

i

p=

= =

Eariance measures the dispersion of points around the mean of a distribution. n this

context, we are attempting to characteri=e the variability of possible future security

returns around the expected return. n other words, we are trying to quantify risk and

return. Eariance measures the total risk of the possible returns.

f all of the possible outcomes are equally likely, then the formula becomes$

Eariance -[ ]

'

i' #(

(


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/rom our previous calculations,


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C. Historical Maret Per!or"ance

The key point is that, on average, annual returns have been higher for riskier securities. /or

instance,


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The average %or mean& rate of return is simply the arithmetic average, total returns divided by the numberof observations. The average return is the best guess of what returns will be in any given year in thefuture.

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7.% Risk and iversi"ication

By investing in two or more assets whose values do not always move in the same direction

at the same time, an investor can reduce the risk of his or her investments, or portfolio.

This is the idea behind the concept of diversification.

A. Single#Asset Port!olios

(eturns for individual stocks from one day to the next have been found to be largely

independent of each other and approximately normally distributed.

* first pass at comparing risk and return for individual stocks is the coefficient of

variation, )E,

.%( &

iR

i

i

CVE

=

The coefficient of variation is a measure of the risk associated with an investment for

each one percent of expected return.

* lower value for the )E is what we are looking for.

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B. Port!olios $ith More %han &ne Asset

The coefficient of variation has a critical shortcoming that is not quite evident when

we are only considering a single asset.

The expected return of a portfolio is made up of two assets$

# # ' '%( & %( & %( &PortfolioE x E x E= +

The expected return of a portfolio is made up of multiple assets$

( ) ( )

( ) ( ) ( )

ortfolio i i#

# # ' '

< (


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*s a result, the level of risk for a portfolio of the two stocks is less than the average of

the risks associated with the individual shares.

' # ' #'

' ' ' ' '

( # ( ' ( # ' ( 'Asset Portfolio x x x x = + +

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(#,'is the covariancebetween stocks # and '. The covariance is a measure of how the

returns on two assets covary, or move together$

( )#'# ' ( #, # ', '

#

)ov%( ,( & %(


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C. %he 'i"its o! Diversi!ication

f the returns on the individual stocks added to our portfolio do not all change in the

same way, then increasing the number of stocks in the portfolio will reduce the

standard deviation of the portfolio returns even further.

However, the decrease in the standard deviation for the portfolio gets smaller and

smaller as more assets are added.

*s the number of assets becomes very large, the portfolio standard deviation does not

approach =ero. t only decreases up to a point.

That is because investors can diversify away risk that is unique to the individual assets

but they cannot diversify away risk that is common to all assets.

The risk that can be diversified away is called diversi"iable# uns&ste!atic# or uni5ue

risk#and the risk that cannot be diversified away is called nondiversi"iable#

s&ste!atic risk# or !arket risk.

Nost of the riskreduction benefits from diversification can be achieved in a portfolio

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7.' &ste!atic Risk

With complete diversification, all of the unique risk is eliminated from the portfolio,

but the investor still faces systematic risk.

A. (h) S)ste"atic Ris Is All %hat Matters

:iversified investors face only systematic risk, whereas investors whose portfolios are

not well diversified face systematic risk plus unsystematic risk.

Because diversified investors face less risk, they will be willing to pay higher prices

for individual assets than other investors.

Therefore, expected returns on individual assets will be lower than the total risk

%systematic plus unsystematic risk& of those assets suggests they should be.

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The bottom line is that only systematic risk is rewarded in asset markets, and this is

why we are only concerned about systematic risk when we think about the relation

between risk and return in finance.

B. Measuring S)ste"atic Ris

f systematic risk is all that matters when we think about expected returns, then we

cannot use the standard deviation as a measure of risk since the standard deviation is a

measure of total risk.

1ince systematic risk is, by definition, risk that cannot be diversified away, the

systematic risk %or !arket risk& of an individual asset is really Oust a measure of the

relation between the returns on the individual asset and the returns on the market.

We quantify the relation between the returns on a stock and the general market by

finding the slope of the line of best fitbetween the returns of the stock and the general

market.



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We call the slope of the line of best fit beta.



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f the beta of an asset is$


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The Capital )sset *ricing +odel ,C)*+- is a model that describes the relation

between risk and expected return$


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A. %he Securit) Maret 'ine

ecurit& +arket Line ,+L- is the line described by$


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asset$#

T

+

0)/( -

. f an assetRs price implies that the expected return is greater

than that predicted by the )*N, that asset will plot above the 1NI.

B. %he Capital Asset Pricing Model and Port!olio Returns

The expected return for a portfolio$


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6eta# 6eta# 8ho9s :ot the 6eta;

Based on what weSve studied so far, you can see that beta is a pretty important topic. Mou might wonderthen, are all published betas created equal? (ead on for a partial answer to this question.

We did some checking on betas and found some interesting results. The Ealue IineInvestment !rve"isone of the bestknown sources for information on publicly traded companies. However, with theexplosion of online investing, there has been a corresponding increase in the amount of investmentinformation available online. We decided to compare the betas presented by Ealue Iine to those reported

by Mahoo /inance %finance.yahoo.com& and )LL Noney %money.cnn.com&. What we found leads to animportant note of caution.

)onsider *ma=on.com, the big online retailer. ts beta reported on the nternet was 8.35, which is muchlarger than Ealue IineSs beta of #.'5. *ma=on.comwasnSt the only stock that showed a divergence inbetas from different sources. n fact, for most of the technology companies we looked at, Ealue Iinereported betas that were significantly lower than their online cousins. /or example, the online beta for:ell was #.89, but Ealue Iine reported +.;5. The online beta for computer antivirus company Nc*feewas '.44 versus a Ealue Iine beta of #.9+. Ealue IineSs betas are not always lower. /or example, theonline beta for Mahoo was +.94, compared to Ealue IineSs #.55.

We also found some unusual, and even hard to believe, estimates for beta. 1tarwood Hotels had a verylow online beta of +.++, while Ealue Iine reported #.85. The online estimate for Hormel /oods, thefamous maker of 1pam %the lunch meat, not Ounk email&, was +.+9, compared to Ealue IineSs +.35.erhaps the most outrageous reported betas were the online betas for the nternational /ight Ieague andLano !et )orp., with betas of 33.7 and @97.+9 %notice the minus sign&, respectively. Ealue Iine did notreport a beta for these companies. How do you suppose we should interpret a beta of @97.+9?

There are a few lessons to be learned from all of this. /irst, not all betas are created equal. 1ome arecomputed using weekly returns and some using daily returns. 1ome are computed using 9+ months ofstock returnsU some consider more or less. 1ome betas are computed by comparing the stock to the 1J5++ index, while others use alternative indices. /inally, some reporting firms %including Ealue Iine& make

adOustments to raw betas to reflect information other than Oust the fluctuation in stock prices.

The second lesson is perhaps more subtle. We are interested in knowing what the betas of the stocks willbe in the future, but betas have to be estimated using historical data. *nytime we use the past to predictthe future, there is the danger of a poor estimate. The moral of the story is that, as with any financial tool,beta is not a black box that should be taken without question.

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http://finance.yahoo.com/http://money.cnn.com/http://amazon.com/http://amazon.com/http://finance.yahoo.com/http://money.cnn.com/http://amazon.com/http://amazon.com/


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#. n a game of chance, the probability of winning a 25+ pri=e is 7+ percent, and the probability of winninga 2#++ pri=e is 9+ percent. What is the expected value of a pri=e in the game?a. 25+b. 235c. 24+d. 2#++

'. Kse the following table to calculate the expected return for the asset.

(eturn robability

+.# +.'5+.' +.5

+.'5 +.'5

a. #5.++6b. #3.5+6c. #4.356d. '+.++6

8. The expected return for the asset below is #4.35 percent. f the return distribution for the asset isdescribed as in the following table, what is the variance for the assetSs returns?

(eturn robability

+.# +.'5+.' +.5

+.'5 +.'5

a. +.++';9;b. +.+++9#8

c. +.+#5#;5d. +.+57749

7. *hmet purchased a stock for 275 one year ago. The stock is now worth 295. :uring the year, the stockpaid a dividend of 2'.5+. What is the total return to *hmet from owning the stock? %(ound your answerto the nearest whole percent.&a. 56b. 776c. 856d. 5+6

5. Babs purchased a piece of real estate last year for 245,+++. The real estate is now worth 2#+',+++. f

Babs needs to have a total return of '5 percent during the year, then what is the dollar amount of incomethat she needed to have to reach her obOective?a. 28,35+b. 27,'5+c. 27,35+d. 25,'5+

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9. Tommie has made an investment that will generate returns that are subOect to the state of the economyduring the year. Kse the following information to calculate the standard deviation of the returndistribution for TommieSs investment.

1tate (eturn robabilityWeak +.#8 +.8" +.' +.7Areat +.'5 +.8

a. +.+758b. +.+793c. +.+74#d. +.+7;5

3. Mou invested 28,+++ in a portfolio with an expected return of #+ percent and 2',+++ in a portfolio with anexpected return of #9 percent. What is the expected return of the combined portfolio?a. 9.'6b. #'.76c. #8.+6

d. #8.96

4. The beta of


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Chapter 7 a!ple /uestions

)nswer ection

+


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/eedback$

3. *L1$ B

Iearning bOective$ I 5

Ievel of :ifficulty$ Nedium/eedback$

4. *L1$ B

Iearning bOective$ I 9Ievel of :ifficulty$ Hard

/eedback$

;. *L1$ B

Iearning bOective$ I 9Ievel of :ifficulty$ Hard

/eedback$

#+. *L1$ B

Iearning bOective$ I 9Ievel of :ifficulty$ Hard/eedback$

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