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f X 18% = 6%
$x 9 % = 6 3
rp = 12%

Portfolio Risk
Unlike returns, the risk of a portfolio (a,)is not simply the weighted average of the standard
deviations of the individual assets in the contribution, for a portfolioвЂ™s risk is also dependent on the
correlation coefficients of its assets. The correlation coefficient ( p ) is a measure of the degree to which
two variables вЂњmoveвЂќ together. It has a numerical value that ranges from 1.0 to 1.0. In a twoasset (A
and B) portfolio, the portfolio risk is defined as:
+ WвЂ™B&
up= V w i u : +2WAWgвЂ™pABcT*q3
175
RISK, RETURN, AND VALUATION
CHAP. 71
and uB = standard deviations of assets A and B, respectively
where uA
wA and wB = weights, or fractions, of total funds invested in assets A and B
pAB = the correlation coefficient between assets A and B
Portfolio risk can be minimized by diversification, or by combining assets in an appropriate manner.
The degree to which risk is minimized depends on the correlation between the assets being combined.
For example, by combining two perfectly negative correlated assets ( p = l), the overall portfolio risk
can be completely eliminated. Combining two perfectly positive correlated assets ( p = +1)does nothing
to help reduce risk. (See Example 7.7.)An example of the latter might be ownership of two automobile
stocks or two housing stocks.
EXAMPLE 7.7 Assume the following:
a w
Asset
f
A 20%
5
B 10%
The portfolio risk then is:
+ 0.0089pAB
= v0.0089
( a ) Now assume that the correlation coefficient between A and B is +1(a perfectly positive correlation). This
means that when the value of asset A increases in response to market conditions, so does the value of
asset B, and it does so at exactly the same rate as A. The portfolio risk when p = +1then becomes:
+
+ 0.0089p˜˜˜ 0 . 0 0 8 9 0.0089(1)
q0.0089 = 0.1334 = 13.34%
Up = = =
(6) If p = 0, the assets lack correlation and the portfolio risk is simply the risk of the expected returns on
the assets, i.e., the weighted average of the standard deviations of the individual assets in the portfolio.
Therefore, when PAB = 0, the portfolio risk for this example is:
VEGG = 0.0943 = 9.43%
+ 0.089p˜B= t/0.0089 + 0.0089(0)
up= d0.0089 =
If p = 1 (a perfectly negative correlation coefficient), then as the price of A rises, the price of B declines
(c)
at the very same rate. In such a case, risk would be completely eliminated. Therefore, when PAB = 1,
the portfolio risk is
 0.0089 = fi= 0
+ 0.0089p˜˜d0.0089 + 0.0089( 1)
V0.0089 = d0.0089
=
U ,=
,
When we compare the results of (a); (b); and (c), we see that a positive correlation between assets increases
a portfolioвЂ™s risk above the level found at zero correlation, while a perfectly negative correlation eliminates
that risk.
EXAMPLE 7.8 To illustrate the point of diversification, assume the data on the following three securities are as
follows:
Security X (%) Security Y (%)
Year security 2 (%)
19x1 50
10 10
19x2 20 40 20
19x3 30 30 30
19x4 40 20 40

19x5 50
 10 50

30 30 30
вЂ˜1
14.14 14.14 14.14
RISK, RETURN, AND VALUATION [CHAR 7
176
Note here that securities X and Y have a perfectly negative correlation, and securities X and 2 have a perfectly
positive correlation. Notice what happens to the portfolio risk when X and Y, and X and Z are combined. Assume
that funds are split equally between the two securities in each portfolio.
Portfolio xz
Portfolio XY
(50%50%)
Year (SOo/oSOo/o)
10
30
19x1
20
30
19x2
30
30
19x3
40
30
19x4
30 50
19x5 
30
30
rP
14.14
0
*P
Again, see that the two perfectly negative correlated securities (XY) result in a zero overall risk.
Capital Asset Pricing Model (CAPM)
A security risk consists of two components diversifiable risk and nondiversifiable risk. Diversifi
able risk, some times called controllable risk or unsystematic risk, represents the portion of a securityвЂ™s
risk that can be controlled through diversification. This type of risk is unique to a given security. Business,
liquidity, and default risks fall into this category. Nondiversifiable risk, sometimes referred to as
noncontroflubferisk or systematic risk, results from forces outside of the firmвЂ™s control and is therefore
not unique to the given security. Purchasing power, interest rate, and market risks fall into this category.
Nondiversifiable risk is assessed relative to the risk of a diversified portfolio of securities, or the market
portfolio. This type of risk is measured by the beta coefficient.
The capital asset pricing model (CAPM) relates the risk measured by beta to the level of expected
or required rate of return on a security. The model, also called the security market line (SML), is given
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