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CHAPTER 8 AN INTRODUCTION TO ASSET PRICING MODELS Answers to Questions 1. It can be shown that the expected return function is a weighted average of the individual returns. In addition, it is shown that combining any portfolio with the risk-free asset, that the standard deviation of the combination is only a function of the weight for the risky asset portfolio. Therefore, since both the expected return and the variance are simple weighted averages, the combination will lie along a straight line. 2. Expected Rate of Return * F M * P * * B RFR *A E Expected Risk ( σ of return) The existence of a risk-free asset excludes the E-A segment of the efficient frontier because any point below A is dominated by the RFR. In fact, the entire efficient frontier below M is dominated by points on the RFR-M Line (combinations obtained by investing a part of the portfolio in the risk-free asset and the remainder in M), e.g., the point P dominates the previously efficient B because it has lower risk for the same level of return. As shown, M is at the point where the ray from RFR is tangent to the efficient frontier. The new efficient frontier thus becomes RFR-M-F. 3. Expected Rate of Return M C B RFR A E Expected Risk ( σ of return) 8 - 1
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This figure indicates what happens as a risk-free asset is combined with risky portfolios higher and higher on the efficient frontier. In each case, as you combine with the higher return portfolio, the new line will dominate all portfolios below this line. This program continues until you combine with the portfolio at the point of tangency and this line becomes dominant over all prior lines. It is not possible to do any better because there are no further risky asset portfolios at a higher point. 4. The “M” or “market” portfolio contains all risky assets available. If a risky asset, be it an obscure bond or a rare stamp, was not included in the market portfolio, then there would be no demand for this asset, and consequently, its price would fall. Notably, the price decline would continue to the point where the return would make the asset desirable such that it would be part of the M portfolio - e.g., if the bonds of ABC Corporation were selling for 100 and had a coupon of 8 percent, the investor’s return would be 8 percent; however, if there was no demand for ABC bonds the price would fall, say to 80, at which point the 10 percent (80/800) return might make it a desirable investment. Conversely, if the demand for ABC bonds was greater than supply, prices would be bid up to the point where the return would be in equilibrium. In either case, ABC bonds would be included in the market portfolio. 5. Leverage indicates the ability to borrow funds and invest these added funds in the market portfolio of risky assets. The idea is to increase the risk of the portfolio (because of the leverage), and also the expected return from the portfolio. It is shown that if you can borrow at the RFR then the set of leveraged portfolios is simply a linear extension of the
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This note was uploaded on 05/20/2010 for the course FIN 5DLS taught by Professor Leejohn during the One '10 term at La Trobe University.

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