Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Question 2 (20 marks) You are working for a fund that invests actively in different investment sectors. Analysts at your firm have produced the following

image text in transcribed

Question 2 (20 marks) You are working for a fund that invests actively in different investment sectors. Analysts at your firm have produced the following estimates of sector portfolio (annualized) return variance-covariance matrix from historical data: Consumer sector Industrial sector Technology sector Services sector 0.3 0.2 0.3 0.1 0.2 0.4 0.3 0.2 Consumer sector Industrial sector Technology sector Services sector 0.3 0.3 0.6 0.4 0.1 0.2 0.4 0.3 Assume that the risk-free rate is 2% per annum and that your firm can short-sell as well as buy any sector portfolios and the risk-free asset. Your firm does not trust numerical optimizers such as Excel Solver and demands analytical solutions. a) Analysts at your firm have also estimated the following annualized historical average returns: Consumer sector 10% Industrial sector 10% Technology sector 10% Services sector 10% Average return p.a. John believes that the historical estimates above are representative of the forward- looking estimates of return covariances and expected returns. John wishes to get an expected return of 8% by forming a portfolio of the four sectors and the risk-free asset. What is the minimum return standard deviation that John must bear given his beliefs? Show your workings. (6 marks) b) Another fund manager, Paul, after reviewing John's portfolio, expresses concern that the portfolio involves short-selling certain sectors and putting large weights on other sectors. He suggests that modifying the variance-covariance matrix by reducing the magnitude of the off-diagonal terms from the historical estimates would result in a less extreme portfolio than John's portfolio in part a). Do you agree? Why or why not? Explain in words without any calculation. (2 marks) Question 2 (20 marks) You are working for a fund that invests actively in different investment sectors. Analysts at your firm have produced the following estimates of sector portfolio (annualized) return variance-covariance matrix from historical data: Consumer sector Industrial sector Technology sector Services sector 0.3 0.2 0.3 0.1 0.2 0.4 0.3 0.2 Consumer sector Industrial sector Technology sector Services sector 0.3 0.3 0.6 0.4 0.1 0.2 0.4 0.3 Assume that the risk-free rate is 2% per annum and that your firm can short-sell as well as buy any sector portfolios and the risk-free asset. Your firm does not trust numerical optimizers such as Excel Solver and demands analytical solutions. a) Analysts at your firm have also estimated the following annualized historical average returns: Consumer sector 10% Industrial sector 10% Technology sector 10% Services sector 10% Average return p.a. John believes that the historical estimates above are representative of the forward- looking estimates of return covariances and expected returns. John wishes to get an expected return of 8% by forming a portfolio of the four sectors and the risk-free asset. What is the minimum return standard deviation that John must bear given his beliefs? Show your workings. (6 marks) b) Another fund manager, Paul, after reviewing John's portfolio, expresses concern that the portfolio involves short-selling certain sectors and putting large weights on other sectors. He suggests that modifying the variance-covariance matrix by reducing the magnitude of the off-diagonal terms from the historical estimates would result in a less extreme portfolio than John's portfolio in part a). Do you agree? Why or why not? Explain in words without any calculation. (2 marks)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Guidelines For Auditing Process Safety Management Systems

Authors: CCPS (Center For Chemical Process Safety)

2nd Edition

0470282355, 978-0470282359

More Books

Students also viewed these Accounting questions

Question

8. Explain the contact hypothesis.

Answered: 1 week ago

Question

2. Define the grand narrative.

Answered: 1 week ago