Suppose you are a hedge fund. You are trying to form a portfolio out of 2 risky assetsand a risk-free asset. You can take arbitrarily large long or short positions in the risky assets at no cost.You can also take arbitrarily larger long or short positions in the risk-free asset; however, the risk-free ratedepends on whether you are lending or borrowing. You can invest positive amounts in the risk-free assetand make 2% per year. However, if you short the risk-free asset (borrow money), you must pay 9% interesteach year on what you borrow. Formally, let wrf be your portfolio weight on the risk-free asset, and rrf bethe return on the risk-free asset. We have:2% Wrf > 0Prf9% Wrf <0Asset Expected ReturnStandard DeviationA10%12%В17%22%Assume the correlation between assets A and B is 0.4. a)Suppose rrf = 2%. Solve for the tangency portfolio.First, ignore the fact that rrf depends on whether you are long or short the risk-free asset.b)asset. Suppose rrf =Again, ignore the fact that rrf depends on whether you are long or short the risk-free9%. Solve for the tangency portfolio.

The tangency portfolio: The efficiency frontier is a set of portfolios that either yield the highest…

a) First, ignore the fact that r₁f depends on whether you are long or short the risk-free asset. Suppose Trf = 2%. Solve for the tangency portfolio. b) Again, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 9%. Solve for the tangency portfolio.

a) First, ignore the fact that r₁f depends on whether you are long or short the risk-free asset. Suppose Trf = 2%. Solve for the tangency portfolio. b) Again, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 9%. Solve for the tangency portfolio.

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

Problem 1PS

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Concept explainers

Portfolio Management

Portfolio management is the process by which an investor decides that how the person will invest in a variety of assets in order to get a desired return in the future. A portfolio means a pool of assets that includes securities, bonds, and other investment instruments which helps in risk minimization of the money that has been invested. In other words, it can be said that a portfolio means a combination of assets in which an investor decides to invest their money in order to get a lump sum return in the future or even a series of cash flow that the person is expecting at the end of their job life.

Question

Suppose you are a hedge fund. You are trying to form a portfolio out of 2 risky assets
and a risk-free asset. You can take arbitrarily large long or short positions in the risky assets at no cost.
You can also take arbitrarily larger long or short positions in the risk-free asset; however, the risk-free rate
depends on whether you are lending or borrowing. You can invest positive amounts in the risk-free asset
and make 2% per year. However, if you short the risk-free asset (borrow money), you must pay 9% interest
each year on what you borrow. Formally, let wrf be your portfolio weight on the risk-free asset, and rrf be
the return on the risk-free asset. We have:
2% Wrf > 0
Prf
9% Wrf <0
Asset Expected Return
Standard Deviation
A
10%
12%
В
17%
22%
Assume the correlation between assets A and B is 0.4.

a)
Suppose rrf = 2%. Solve for the tangency portfolio.
First, ignore the fact that rrf depends on whether you are long or short the risk-free asset.
b)
asset. Suppose rrf =
Again, ignore the fact that rrf depends on whether you are long or short the risk-free
9%. Solve for the tangency portfolio.

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