61 months of total return for a sample of asset classes are contained in the Project.xlsx spreadsheet available on Moodle. The asset classes are:

Asset Class Name

Asset Class Description

ASX300

S&P/ASX300 Index - Australian Equity Index

AUBD

Bloomberg Australian Investment Grade Corporate Bond Index

CASH

Australian Bank Bill Index - Cash

USBD

Barclays US Corporate Bond Index

S&P500

S&P500 - US Equity Index

NKY

Nikkei 225 - Japanese Equity Index

EMEQ

MSCI Emerging Markets Equity Index

EMBD

Bloomberg Emerging Markets Bond Index

Assume that utility functions are of the form: U = E(R) - A2. There are three different types of investors that correspond to the investment options offered by superannuation funds. The Conservative investor has a risk aversion coefficient (A) of 12. The Balanced investor has a risk aversion coefficient of 7 and the High Growth investor has a risk-aversion coefficient of 2. Investors are unable to short-sell the asset classes and are not allowed to borrow or lend at a risk- free rate. They can invest in the Australian Bank Bill Index (CASH), which is a close substitute for the risk-free rate, but it is not a risk-free asset.

The expected return of each asset class is given in the table below (do not estimate them from the historical data). You are required to use all of the historical data provided to estimate the covariance matrix so that you can construct portfolios using the Markowitz approach.

Asset Class

ASX300

AUBD

CASH

USBD

S&P500

NKY

EMEQ

EMBD

Expected Returns

0.47%

0.35%

0.35%

0.48%

0.50%

0.35%

0.50%

0.40%

Domestic Portfolio

Initially each of the three investor portfolios can only include Australian assets: ASX300, AUBD and CASH.

What are the weights in the optimal risky portfolio for each of the three investors?

How do each of the three investors benefit from the shift to an optimal risky portfolio from a portfolio that has 50% invested in the ASX300 index and 50% invested in the AUBD index?

Discuss the differences in the asset class weights within each of three investor portfolios as well as the differences between each investor's portfolios. Why do these differences exist? Do these differences make sense?

International Portfolio

Now the three investor portfolios are allowed to contain investments in any of the eight asset classes.

What are the weights in the optimal risky portfolio for each of the three investors?

Discuss the differences in the asset class weights within each of three investor portfolios as well as the differences between each investor's portfolios. Why do these differences exist? Do these differences make sense?

What is the benefit to each of three investor types from allowing overseas investments? Which investor type benefitted the most? Why?

Minimum Variance Portfolio

What are the weights in the minimum variance portfolio? Discuss the differences in the weights for this portfolio. Which investor is most adversely affected by having to hold the minimum variance portfolio compared to their optimal risky portfolio?

Your report should conclude with your recommendation on the portfolio that each three investor types should hold.