Case Analysis & Recommendations
This paper attempts to address the dilemma, which was faced by the treasurer of South Carolina in the year 1998. Till the previous year, the state had barred the pension fund to invest in any kind of equities however; in 1998 the constitution for investing in the equities had been amended. Therefore, the treasurer was thinking to invest in the international stocks. A number of international stocks are available for the company in which the company could allocate its investment of the current pension fund value of $ 17.5 billion.
Mean Returns and Standard Deviations
Beginning with the analysis, the mean annual returns and the standard deviations have been calculated for the basic US assets. The basic US assets include treasury bonds, corporate bonds. Common stocks and the T-bills are issued by the US government. The mean returns and the standard deviations of these asset classes have been computed using exhibit 1. It could be seen that the highest average return is for the common stocks because of the recent rise in the stock market. However, it should also be seen that the high return is also accompanied by the high risk as seen by the volatility of the stock returns. The return for the treasury bonds and the corporate bonds is 5.57% and 5.825% and the return for t-bills is 4.03%. The coefficient of variation, which is the risk per unit of return, is approximately same for common stocks and the corporate bonds. The Sharpe ratios have also been calculated for all the asset classes assuming a risk free rate of 2%. The highest Sharpe ratio has been seen for the treasury bills whereas; the lowest is for the treasury bonds. These statistics show that investments in t-bills and common stock are more likely to optimize the returns of the portfolio.
International Diversification & Correlations
If the pension funds go for to invest in the most successful international stocks, then the pension fund can formulate a portfolio and create diversification benefits. The correlation matrix has been created between the asset classes. If we look at the correlation matrix then it could be seen that the correlation between t-bills and other three classes of assets then it has a negative correlation which is beneficial for creating an international diversified portfolio. On the other hand,the correlation between the corporate bonds and the other classes of the assets specially the treasury bonds is positive and high.
If the investment in corporate bonds is high, then this might increase the risks for the pension fund portfolio and minimize the returns in the long term. The correlation between corporate bonds and treasury bonds is 92.72%, which is high. Therefore, the optimal weights for investment in each asset classes should be in those classes that have lower positive or negative correlation between them in order to create international diversification benefits.
Optimization of Pension Fund Portfolio
By using the excel solver, the optimal weights for the investment in the four basic asset classes have been determined. The investment in the most successful international stocks based upon their average returns has been made. It is suggested for the treasurer to invest in five common stocks of international corporations. These include the stocks of Coca Cola Company, McDonalds Corp, United Technologies, Procter and Gamble and general Motors Corp. The highest performing stock is the stock of P&G with the lowest coefficient of variation from all the five internationals stocks that have been chosen.
The optimization of the portfolio and the calculation of the optimal weights for each asset class have been calculated on the basis of the Sharpe ratio for the portfolio. The constraints have been incorporated in the excel solver. The first constraint is that the weights of all the four asset classes should be equal to or greater than 0. The next constraint, which has been set, is that the standard deviation for the entire portfolio should be less than or equal to 10% and the target has been set as the Sharpe ratio for the portfolio.
Based upon this, the optimal weights for the investment in each of the four asset classes including the equity asset class comprised of four major international stocks are 30% in treasury bills, 32% in treasury bonds, 23% in corporate bonds and the remaining 15% in common stocks of international companies. This gives a total portfolio return of 4.62% and a standard deviation of the portfolio of 6.98%, which is the optimal risk and return for the pension fund portfolio of South Carolina. The volatility of this portfolio is the minimum volatility, which would be experienced by the investors investing in this portfolio.The treasury fund manager of South Carolina state fund needs to use these mix of weights in order to create the most diversified international portfolio fund......................
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