Short Question (SQ2) The market index model can be formulated as: Rea+B Rt + Et, (15%) where R denote the annual excess returns of the risky asset and, RM,t is the excess annual return on the market index, S&P 500. There are two risky funds, A and B, and their returns follow the above market index model. The estimations of annual means, annual standard deviations, and the parameters of the index model for Funds A and B and the S&P 500 index are in the table below. Assets Fund A Fund B S&P 500 (M) Risk premium 13% 7% 10% Standard deviation of Market beta (B) returns 40% 20% 20% 1.0 0.5 1.0 An investor wants to invest $10 thousands into funds A and B, and he plans to allocate 70% of his capital into A and the remaining into B. (A) What would be the alpha, beta, and R-squared for his portfolio (the combination of Funds A and B) under the market index model? (6%) (B) If this investor would like to short sell a hedging portfolio, constructed with S&P 500 index portfolio and the risk-free asset, to make his overall position market neutral, what is the dollar amount of the hedging portfolio should they short sell? (3%) (C) Please calculate the variance and Sharpe ratio of the overall position constructed in part (B). (6%) * Terminology: . • • A hedging portfolio here describes a position to be shorted to make the overall portfolio market neutral Overall position describes the overall position combining the buy position and the short-sell position Market-neutral in the market index model indicates having zero beta on the market index

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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Short Question (SQ2)
The market index model can be formulated as:
Rea+B Rt + Et,
(15%)
where R denote the annual excess returns of the risky asset and, RM,t is the excess annual return on
the market index, S&P 500. There are two risky funds, A and B, and their returns follow the above
market index model. The estimations of annual means, annual standard deviations, and the parameters
of the index model for Funds A and B and the S&P 500 index are in the table below.
Assets
Fund A
Fund B
S&P 500 (M)
Risk premium
13%
7%
10%
Standard deviation of
Market beta (B)
returns
40%
20%
20%
1.0
0.5
1.0
An investor wants to invest $10 thousands into funds A and B, and he plans to allocate 70% of his
capital into A and the remaining into B.
(A) What would be the alpha, beta, and R-squared for his portfolio (the combination of Funds
A and B) under the market index model? (6%)
(B) If this investor would like to short sell a hedging portfolio, constructed with S&P 500 index
portfolio and the risk-free asset, to make his overall position market neutral, what is the dollar
amount of the hedging portfolio should they short sell? (3%)
(C) Please calculate the variance and Sharpe ratio of the overall position constructed in part (B).
(6%)
* Terminology:
.
•
•
A hedging portfolio here describes a position to be shorted to make the overall
portfolio market neutral
Overall position describes the overall position combining the buy position and the
short-sell position
Market-neutral in the market index model indicates having zero beta on the market
index
Transcribed Image Text:Short Question (SQ2) The market index model can be formulated as: Rea+B Rt + Et, (15%) where R denote the annual excess returns of the risky asset and, RM,t is the excess annual return on the market index, S&P 500. There are two risky funds, A and B, and their returns follow the above market index model. The estimations of annual means, annual standard deviations, and the parameters of the index model for Funds A and B and the S&P 500 index are in the table below. Assets Fund A Fund B S&P 500 (M) Risk premium 13% 7% 10% Standard deviation of Market beta (B) returns 40% 20% 20% 1.0 0.5 1.0 An investor wants to invest $10 thousands into funds A and B, and he plans to allocate 70% of his capital into A and the remaining into B. (A) What would be the alpha, beta, and R-squared for his portfolio (the combination of Funds A and B) under the market index model? (6%) (B) If this investor would like to short sell a hedging portfolio, constructed with S&P 500 index portfolio and the risk-free asset, to make his overall position market neutral, what is the dollar amount of the hedging portfolio should they short sell? (3%) (C) Please calculate the variance and Sharpe ratio of the overall position constructed in part (B). (6%) * Terminology: . • • A hedging portfolio here describes a position to be shorted to make the overall portfolio market neutral Overall position describes the overall position combining the buy position and the short-sell position Market-neutral in the market index model indicates having zero beta on the market index
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