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When both borrowing and lending at the risk-free rate are allowed, there is a unique fund F of risky assets that is efficient. All points on the efficient frontier are combinations of F and the risk-free asset. The information concerning the 1-year covaria es of the

When both borrowing and lending at the risk-free rate are allowed, there is a unique fund F of risky assets that is efficient. All points on the efficient frontier are combinations of F and the risk-free asset. The information concerning the 1-year covaria es of the

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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FIGURE 6.14 One-fund theorem. When both borrowing and lending at the risk-free rate are allowed, there is a unique fund F of risky assets that is efficient. All points on the efficient frontier are combinations of F and the risk-free asset. The information concerning the 1-year covariances and mean values of the rates of return on five risky securities (assets) is shown in the table below. Security Covariance V 2.30 93 .62 74 15.1 -23 26 -27 -56 2 56 12.5 93 62 1.40 22 22 56 1.80 .78 -27 78 3.40 -56 14.7 9.02 17.68 4 74 - 23 26 2.60 The mean values in the column labeled F are expressed on a percentage basis, whereas the covariances are expressed in units of (percent)? / 100. For example, the first security has an expected rate of return of 15.1%, or 0.151, and a variance of return of 0.023. And the covariance between security 1 and security 2 is 0.0093, while the covariance between security 1 and security 3 is 0.0062. Assume there is also a risk-free asset with r; = 10%. The one-fund theorem states that there is a single fund F of risky assets such that any efficient portfolio can be constructed as a combination of the fund Fand the risk-free asset. What is the weight w4of security 4 corresponding to the single fund F? Please round your numerical answer to two decimal places. What is the portfolio variance of the single fund F
Transcribed Image Text:FIGURE 6.14 One-fund theorem. When both borrowing and lending at the risk-free rate are allowed, there is a unique fund F of risky assets that is efficient. All points on the efficient frontier are combinations of F and the risk-free asset. The information concerning the 1-year covariances and mean values of the rates of return on five risky securities (assets) is shown in the table below. Security Covariance V 2.30 93 .62 74 15.1 -23 26 -27 -56 2 56 12.5 93 62 1.40 22 22 56 1.80 .78 -27 78 3.40 -56 14.7 9.02 17.68 4 74 - 23 26 2.60 The mean values in the column labeled F are expressed on a percentage basis, whereas the covariances are expressed in units of (percent)? / 100. For example, the first security has an expected rate of return of 15.1%, or 0.151, and a variance of return of 0.023. And the covariance between security 1 and security 2 is 0.0093, while the covariance between security 1 and security 3 is 0.0062. Assume there is also a risk-free asset with r; = 10%. The one-fund theorem states that there is a single fund F of risky assets such that any efficient portfolio can be constructed as a combination of the fund Fand the risk-free asset. What is the weight w4of security 4 corresponding to the single fund F? Please round your numerical answer to two decimal places. What is the portfolio variance of the single fund F
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