05 - Question and Problem Answers Chapter 5 - Modern...

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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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2F 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 T-bill return does not depend on the state of the economy because the Treasury must and will redeem the bills at par regardless. The T-Bills 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 T-bills would be -1%. Thus, in real terms, T-bills are not riskless.
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This note was uploaded on 08/25/2009 for the course FIN 300 taught by Professor Jackson during the Spring '07 term at University of Illinois at Urbana–Champaign.

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05 - Question and Problem Answers Chapter 5 - Modern...

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