lecture2012 - Lecture 12 Risk & Return Theories II I....

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Lecture 12 I. The link between the Two Fund Theorem and “price of risk”. Recall the Two Fund Theorem from Risk and Return I. The investor’s problem of choosing an optimal portfolio given Given N assets with respective expected returns r 1 ; r 2 ;:::;r N , variances ¾ 2 1 ; ¾ 2 2 ;:::;¾ 2 N , ¾ 2 n > 0 for all n; and covariances ¾ j;n . Markowitz portfolio theory implies that any risk-averse investor will choose a portfolio of these assets that lies on the upward slopping portion of the e¢cient frontier. The optimal choice for each investor will depend on their preferences over risk and return. A) Risk-Free Asset If we introduce a risk-free asset ( ¾ 2 = 0 ) to the investors choice set, the variance of any portfolio formed from a combination of w F invested in the risk-free asset and w M invested in a risky portfolio will be w 2 M ¾ 2 M . Where ¾ 2 M is the variance of the risky portfolio. Thus, as the investor alters w M ; the proportion of wealth invested in the risky portfolio, the trade-o¤ between return and standard deviation is linear. This has a remarkable e¤ect on investors’ optimal choices. Given a set of risky assets and a risk-free asset, each risk-averse investor will choose to hold the same risky portfolio, regardless of their preferences over risk and return. The investor’s optimal portfolio choice will be a linear combination of the risk-free asset and the “market
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lecture2012 - Lecture 12 Risk & Return Theories II I....

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