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(rf '
)
F
(rf F)("/o)
r f p('10)
Return ( r f )(%) Probability ( p f )
5 0.2 1 24 576 115.2
20 0.6 12 1 0.6
1
441
 
40 0.2 8 21 88.2
P=  19 d=204

Knowing 2 = 204, we proceed with Step 4 and
6 14.28%
U= =
For stock B:
Step 1 Step 2 Step 3
V2P,("/o)
Return ( r f )("/O) ripf(%) (r, F)("/o)
Probability ( p f ) (r, (rf
10 0.2 2 5 25 5
15 9 0
0.6 0 0

20 0.2 5
4 5
25
d = 10
15
P= 
173
RISK, RETURN, AND VALUATION
CHAP. 71
Knowing d = 10, we take Step 4 and
a= 3.16%
U=
Statistically,if the probability distribution is normal, 68 percent of the returns will lie in t1standard deviation,
95 percent of all observations will lie between 2 2 standard deviations, and 99 percent of all observations will lie
between 2 3 standard deviations of the expected value.
EXAMPLE 7.4 Using the results from Example 7.3,
1 1
1 Stock B
Stock A
19% 15%
Expected return ( t )
14.28% 3.16%
Standard deviation (U)
For stock A, there is a 68 percent probability that the actual return will be in the range of 19 percent plus
or minus 14.28 percent or from 4.72 percent to 33.28 percent. Since the range is so great, stock A is risky; it is
likely to either fall far below its expected rate of return or far exceed the expected return. For stock B, the 68
percent range is 15 percent plus or minus 3.16 percent or from 11.84 percent to 18.16 percent. With such a small
U, there is only a small probability that stock B's return will be far less or greater than expected; hence, stock B
is not very risky.
Measure of Relative Risk Coefficient of Variation
One must be careful when using the standard deviation to compare risk since it is only an absolute
measure of dispersion (risk) and does not consider the dispersion of outcomes in relationship to an
expected value (return). Therefore, when comparing securities that have different expected returns, use
the coefficient of variation. The coefficient of variation is computed simply by dividing the standard
deviation for a security by expected value: U/?. The higher the coefficient, the more risky the
security.
EXAMPLE 7.5 Again, using the results from Example 7.3:
I I I
Stock B
Stock A
19% 15%
14.28% 3.16%
0.21Yo
Although stock A is expected to produce a considerably higher return than stock B, stock A is overall more
risky than stock B, based on the computed coefficient variation.
"jpes of Risk
The various risks that must be considered when making financial and investment decisions are as
follows:
1. Business risk is caused by fluctuations of earnings before interest and taxes (operating income).
Business risk depends on variability in demand, sales price, input prices, and amount of
operating leverage.
2. Liquidity risk represents the possibility that an asset may not be sold on short notice for its
market value. If an asset must be sold at a high discount, then it is said to have a substantial
amount of liquidity risk.
RISK,RETURN, AND VALUATION [CHAP. 7
174
Default risk is the risk that a borrower will be unable to make interest payments or principal
repayments on debt. For example, there is a great amount of default risk inherent in the bonds
of a company experiencing financial difficulty.
Market risk is the risk that a stockâ€™s price will change due to changes in the stock market
atmosphere as a whole since prices of all stocks are correlated to some degree with broad swings
in the stock market.
Interest rate risk is the risk resulting from fluctuations in the value of an asset as interest rates
change. For example, if interest rates rise (fall), bond prices fall (rise).
Purchasing power risk is the risk that a rise in price will reduce the quantity of goods that can
be purchased with a fixed sum of money.
PORTFOLIO RISK AND CAPITAL ASSET PRICING MODEL (CAPM)
7.2
Most financial assets are not held in isolation; rather, they are held as parts of portfolios. Therefore,
riskreturn analysis (discussed in Section 7.1) should not be confined to single assets only. It is important
to look at portfolios and the gains from diversification. What is important is the return on the portfolio,
not just the return on one asset, and the portfolioâ€™s risk.
Portfolio Return
The expected return on a portfolio ( r p )is simply the weighted average return of the individual assets
in the portfolio, the weights being the fraction of the total funds invested in each asset:
n
j= 1
ri = expected return on each individual asset
where
wj = fraction for each respective asset investment
n = number of assets in the portfolio
cwj
n
= 1.0
j= 1
EXAMPLE 7.6 A portfolio consists of assets A and B. Asset A makes up onethird of the portfolio and has an
expected return of 18 percent. Asset B makes up the other twothirds of the portfolio and is expected to earn 9
percent. What is the expected return on the portfolio?
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