FINC3017 Asset Allocation and Portfolio Construction

The correlation matrix is presented below as the Matrix B

The variance-covariance matrix is obtained by A*B*A. The variance-Covariance Matrix obtained from the above operation is given below.

To calculate the portfolio allocation to each asset EFTs using Markowitz theory we will use the excel solver and maximize the Sharpe ratio which on the hand maximizes the utility of each investor.

Kendall Optimum Portfolio

To create this portfolio the following assumption were made.

• The initial weights of the EFTs are all assumed to be equal
• The sum of the weights is 1
• All the weights of the portfolio formed sought to have all the EFTs included with the lowest range [0.05,0.4]

Under the above conditions the optimal portfolio for Kendall has the following weights.

The variance-covariance matrix as calculated before is given

The weights are calculated using solver as given below

From the above table the portfolio consists of 40% ,5%,40%,10%,5% for ALARGE,ASMALL,US100,ASIA100 and EM500 respectively. This portfolio is the one that will optimize the Sharpe ratio which also means that the utility of Kendall is maximized. The portfolio mean and standard deviation are calculated using the weight matrix and the EFT expected return matrix.

For the weights to be determined, the Sharpe ratio is maximized

For the case of Morgan, the conditions for constructing the optimum portfolio was under the following conditions.

• The initial weights of the EFTs are all assumed to be equal
• The sum of the weights is 1
• All the weights of the portfolio formed sought to have all the EFTs included with the lowest range [0.1,0.5]

Morgan optimum portfolio is determined below

Morgan optimum portfolio weights are 20%, 10%, 50%, 10% and 10% for the EFTs ALARGE, ASMALL, US100, ASIA100 and EM500 respectively. The portfolio mean, standard deviation and the Sharpe ratio as well as the expected utility of the constructed portfolio are presented below

The recommended portfolio does not necessarily require shot selling. Short selling is a strategy used by traders and portfolio managers to speculate portfolio and investment so as to decide whether to sell or hold a portfolio. Short selling helps to hedge downside risks resulting from holding an asset or portfolio for a long period of time. In the case of the above portfolio and in line with the Kendall’s investment experience, it is not advisable to short sell since it is an optimal portfolio.

The 5-ETF portfolio that recommendable to invest in the case of Morgan is.

The net sector and geography exposure in the optimal portfolio identified for Kendall inQ2

The Geographical exposure of Kendall’s optimal portfolio identified in Question 2

If the investors allocates part of the portfolio to cash and Assuming the cash investment is the risk free rate and earn 3.75% p.a and there is no limit to borrowing and lending of the cash.

1.3 Conclusion

After the calculating the expected utility the two investors would choose only one ETF. This will be based on the optimal utility. The choice of one ETF will pose serious risk to any investor. Choice of one ETL exposes the investor to loss in case of future uncertainties. Moreover, if an ETF is chosen and it performs poorly, it will drain the capital of the investor. To reduce these risks, diversification is called for. To come up with an optimal risk portfolio the Markowitz Portfolio Theory was applied. Diversification of a portfolio implied that the portfolio created was spread through various sectors and a number of geographical areas. The geographical and sector concentration exposure of the portfolio shows the portions of the assets in different sectors and countries. In case of any sector or geography attached risk, it will not affect the whole portfolio. This reduces losses and retains the capital of the investors.

Bibliography

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