5. There are three risky assets with rates of return r₁, 72, and r3, respectively. The covariance matrix and the expected rates of return are [0.4 0.2 0 Σ 0.2 0.4 0.2 0.2 0.4 0 [0.04] F = 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return Tf = 0.03. (c) Find the tangent portfolio.

5. There are three risky assets with rates of return r₁, 72, and r3, respectively. The covariance matrix and the expected rates of return are [0.4 0.2 0 Σ 0.2 0.4 0.2 0.2 0.4 0 [0.04] F = 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return Tf = 0.03. (c) Find the tangent 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

Risk and return

Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.

Capital Asset Pricing Model

Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.

Question

5. There are three risky assets with rates of return r₁, 12, and r3, respectively. The
covariance matrix and the expected rates of return are
[0.4 0.2 0
=
Σ 0.2 0.4 0.2
0 0.2 0.4
[0.04]
0.08
0.06
(a) Find the global minimum-variance portfolio.
(b) For the required return z = 0.075, find (the weight of) the optimal portfolio
with risky assets.
For (c) and (d) only, assume there is an additional risk-free asset with return
Tf 0.03.
=
(c) Find the tangent portfolio.

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