Question 1

Jim Shechan is the portfolio manager for the $200million Brent Industries defined Benefit pension Fund. Jim is planning on making a presentation to the trustees of the pension plan. His firm has come up with the long-term capital market expectations shown in figure 4.

Figure 4

ASSET CLASS	EXPECTED RETURN	EXPECTED STD. DEV.	CORRELATIONS
			1	2	3	4	5
U.S EQUITY	12%	16%	1.00
US BONDS	8.25%	6.50%	0.32	1.00
INTL EQUITIES	14%	18%	0.46	0.22	1.00
INTL BONDS	9.25%	12.25%	0.23	0.56	0.32	1.00
ALTERNATIVE INV.	11.50%	21%	0.25	0.11	0.08	0.06	1.00

Based on the above capital market expectations, Jim identifies an efficient frontier with the 6 corner portfolios with the characteristics shown in figure 5. He risk free is assumed to be equal to the T-bill rate of 2.50%

Figure 5

Corner portfolio	EXPECTED RETURN	EXPECTED STD. DEV.	Sharpe ratio	CORRELATIONS
				Us equity	Us bonds	Intl equities	Intl bonds	Alternat. Inv.
1	14.00%	18.00%		0%	0%	100%	0%	0%
2	13.66%	16.03%		0%	0%	86.36%	0%	14%
3	13.02%	13.58%		21.69%	0%	56.56%	0%	21.76%
4	12.79%	13.00%		21.48%	0%	52.01%	5.24%	21.27%
5	10.54%	8.14%		9.40%	51.30%	26.55%	0%	12.76%
6	8.70%	6.32%		0%	89..65%	4.67%	0%	5.68%

The Trustees have established a spending rate of 8.50%. Inflation is expected to be 2% per year, and the cost of managing the fund is expected to be 0.40%

The trustees would like to limit risk (as defined by std. deviation) to no more than 10% per year

a) What are the Sharpe ratios for the corner portfolio?

b) What is the required rate of return?

c) Which Corner portfolios are ideal for the efficient portfolio?

d) What are the weights for the assets classes for the efficient portfolio?

e) What is the Standard deviation of this portfolio?