Suppose a portfolio manager is considering asset allocation for her four clients using the following seven asset classes:

1. US stock market, with the S&P 500 index as benchmark
2. UK stock market, with the FTSE 100 index as benchmark
3. European stock market, with the Swiss Market Index (SMI) as benchmark
4. Southeast Asian market, with the Straits Times Index (STI) as benchmark
5. East Asian market, with the Hang Seng Index (HSI) as benchmark
6. Japanese market, with the NIKKEI 225 index as benchmark
7. Risk free assets, with an annual return of 4.1%

A. Capital Market Expectation: Expected Returns and Standard Deviations Asset Class Expected Ret Std Dev. S&P 500 9.57% 13.90% FTSE 100 6.75% 14.01% SMI 11.48% 17.07% STI 8.76% 24.09% HSI 15.98% 26.25% NIKKEI 225 7.91% 32.20% B. Capital Market Expectation: Correlations S&P 500 FTSE 100 SMI STI HSI NIKKEI 225 S&P 500 1.0000 0.7431 0.6643 0.5692 0.5561 0.3747 FTSE 100 0.7431 1.0000 0.7434 0.5570 0.5559 0.4302 SMI 0.6643 0.7434 1.0000 0.4832 0.4666 0.3301 STI 0.5692 0.5570 0.4832 1.0000 0.7518 0.4236 HSI 0.5561 0.5559 0.4666 0.7518 1.0000 0.3731 NIKKEI 225 0.3747 0.4302 0.3301 0.4236 0.3731 1.0000

Expected std. dev.	Expected correlation
	S&P 500	FTSE 100	SMI	STI	HIS	NIKKEI 225
S&P 500	0.0957	0.1390	1.0000
FTSE 100	0.0675	0.1401	0.7431	1.0000
SMI	0.1148	0.1707	0.6643	0.7434	1.0000
STI	0.0876	0.2409	0.5692	0.5570	0.4832	1.0000
HSI	0.1598	0.2625	0.5561	0.5559	0.4666	0.7518	1.0000
NIKKEI 225	0.0791	0.3220	0.3747	0.4302	0.3301	0.4236	0.3731	1.0000

The clients requirements are as follows.

Client 1: 10% expected return with risk not exceeding 10.5%, no short sale restrictions

Client 2: 10% expected return with risk not exceeding 10.5%, short sales are prohibited

Client 3: maximize the expected utility of E(U) = E(r) - A*Var(r) (where A=1.8), no short sale restrictions

Client 4: maximize the expected utility of E(U) = E(r) - A*Var(r) (where A=1.8), short sales are prohibited

How should the portfolio manager make asset allocation for the four clients, respectively?