β
0.60
$100,000 (0.35)
20
i
2
$100,000
β
i
$2,000,000
20
i
2
$100,000
β
i
1,165,000
β
$100,000 (1.12)
20
i
2
$100,000
β
i
$2,000,000
β
0.6385
Question and Problem Answers
page 1
Chapter 5  Modern Portfolio Theory
±
5  1:
Shares
Price
Market Value
β
100,000 Alliance Gaming
4.000
$400,000.
2.00
$400,000 * 2.00 =
800,000.00
25,000 Burlington Northern
35.000
$875,000.
0.92
$875,000 * 0.92 =
805,000.00
25,000 Ameren Corp
25.000
$625,000.
0.71
$625,000 * 0.71 =
443,750.00
Cash
$100,000.
0.00
$100,000 * 0.00 =
0.00
TOTAL PORTFOLIO
$2,000,000.
2,048,750.00
$2,048,750. / $2,000,000. =
1.024375
A.
Cash has a
β
= 0.00. The return on cash, if any, is independent of conditions in the equity market.
B.
β
= 1.024
C.
The portfolio
β
characterizes this portfolio as fairly close to the market. On average we would expect this portfolio
to move with the market. We expect that when the market declines by 1% this portfolio would decline by 1.024%,
but if the market advances 1% this portfolio would advance by 1.024%.
±
5  2:
The first thing to do is to write down the information you are given: The weighted average of the 20 stocks in the portfolio
is 0.60. One of the twenty stocks has a
β
= 0.35. We do not know any of the other
β
s but we do know
that each of the
twenty stocks has a market value of $100,000. Thus
Simple algebra gives us
and we can put Caterpillar's
β
of 1.12 into the portfolio
β
calculation.
We could accomplish the same thing by calculating:
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INANCIAL MARKETS .
.. AND THE INSTRUMENTS THAT TRADE IN THEM
β
0.60
0.35
20
1.12
20
0.6385
±
5  3:
The SML shows us how much investors require in compensation for the systematic risk they bear. Investors require some
return for postponing consumption. This return is the intercept of the SML and represents investments with no systematic
risk. In other words, all investments must earn at least this minimum return, otherwise investors will consume their income
rather than investing it.
Stocks with an "average" amount of systematic risk (
β
=1; the market risk) should provide a return equal to the average of
all investments. Thus the SML must pass through both the risk free rate of return (
β
=0) and the market rate of return (
β
=1).
The SML has a positive slope. This reflects the premise that investors are risk averse: the more risky an investment is, the
greater the return an investor will demand for investing in it. The slope of the line is known as the risk premium; this is
the premium that investors demand by taking on an additional unit of systematic risk as measured by
β
.
Note that the SML and CAPM deal solely in systematic risk. Unsystematic risk is assumed eliminated through
diversification.
@ Finance 254 [G. McIntire]
±
5  4:
A.
The Tbill return does not depend on the state of the economy because the Treasury must and will redeem the bills
at par regardless. The TBills are risk free in the nominal sense because the 8% return will be realized in all possible
states. However, this 8% return is composed of the real risk free rate (say 3%) plus an inflation premium (5%). If
inflation averaged 9% over the year rather than the expected 5% then the real returns realized on the Tbills would
be 1%. Thus, in real terms, Tbills are not riskless.
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 Spring '07
 Jackson
 Capital Asset Pricing Model, Financial Markets, Modern portfolio theory, Risk in finance

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