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Questions Suppose a portfolio manager is considering asset allocation for her four clients using the following seven asset classes: US stock market, with the S&P

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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%

Capital market expectation: anticipated returns, standard deviations and correlations (all annualized)

Expected ret.

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?

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