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Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%. An individual asset i has an estimate of βi = 1.1 and σ2 ei = 0.0225 using the single index model Ri = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi.  (b) Calculate the optimal weight of combining asset i and the index portfolio M .  (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combining asset i and the index portfolio M .

Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%. An individual asset i has an estimate of βi = 1.1 and σ2 ei = 0.0225 using the single index model Ri = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi.  (b) Calculate the optimal weight of combining asset i and the index portfolio M .  (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combining asset i and the index portfolio M .

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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Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.
An individual asset i has an estimate of βi = 1.1 and σ2
ei = 0.0225 using the single index model
Ri = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%.

a) According to asset i’s return forecast, calculate αi. 

(b) Calculate the optimal weight of combining asset i and the index portfolio M . 


(c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combining
asset i and the index portfolio M .

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