What is the beta of:

a. The market portfolio

b. The risk-free asset

c. Portfoho A + B in Example 3.3 and Section 3.7 

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EXAMPLE 3.3 THE PRINCIPLE OF PORTFOLIO DIVERSIFICATION (PART 2) It turns out that Toni would not be rational to accept the above investment- a more attractive investment can be found. It is possible to find another investment decision that has the same expected return but lower risk. This is because of the principle of portfolio diversification. To illustrate, assume that shares of firm B are also traded on the market, with a current market value of $10. These shares also pay a dividend of $1. Assume there is a 0.6750 probability that firm B's shares will increase in mar- ket value to $10.50 at the end of the period, and a 0.3250 probability that they will decrease to $8.50. Now suppose that Toni decides to invest $200 in six shares of firm A at $20 and eight shares of firm B at $10. We must calculate Toni's expected util- ity for the portfolio consisting of six shares of firm A and eight shares of firm B. Notice that the same amount ($200) is invested, but that it is now spread over two different securities. Four possible payoffs now exist from the portfolio: both shares increase in market value, one share increases and the other decreases, or both shares decrease. The amounts of the payoffs and their assumed probabilities are as follows: FABLE 3.4 PAYOFFS AND THEIR PROBABILITIES A B 132 + 132 102 102 ++++ 84 68 84 + 68 ++++ Dividends Total Payoff Probability 14 = $230 0.5742 14 = $214 0.1658 14 $200 0.1008 14 $184 0.1592 1.0000