Therefore, the Markowitz Efficient portfolio was also called the

mean-variance efficient portfolio. Whereas in the modern portfolio theory approach to investment, it started with the assumption that investors have spent a certain amount of money on investment these days.

"The Sampling Error in Estimates of

Mean-Variance Efficient Portfolio Weights." The Journal of Finance, vol.

Hence, without knowing his exact utility function in terms of Von Neumann and Morgenstern (1944), an investor is likely to maximize the true expected utility when selecting his preferred

mean-variance efficient portfolio.

In addition, the object of Equation (3) is the optimal

mean-variance efficient portfolio for n securities rather than the market equilibrium.

Furthermore, in Section 4, we employ the results in Section 3 and the Lagrange multiplier method to obtain the

mean-variance efficient portfolio and efficient frontier.

In the model, when commissions are tied to returns and the reference portfolio is a

mean-variance efficient portfolio, optimal decisions by the funds would lead them closer to the efficient frontier with the ensuing benefits to the funds' affiliates.

For example, the investor could use the Markowitz

mean-variance efficient portfolio approach; the Bayes-Stein shrinkage portfolio approach; or any of the 'data-and-model' approaches.

Thus, our simulation creates a situation where the market is indeed a

mean-variance efficient portfolio and all securities earn true returns in accordance with their betas.

[10] Britten-Jones, Mark, 1999, The sampling error in estimates of

mean-variance efficient portfolio weights, Journal of Finance 54, 655-671.

If so, you still want to solve the mean-variance problem of figure 1, and you still want a

mean-variance efficient portfolio. The important implication of a multifactor world is that you, the mean-variance investor, should no longer hold the market portfolio.

(2) The term `market' here refers to the set of assets in the

mean-variance efficient portfolio. If this set of assets coincided with the entire range of assets available in the market, then our tests would be a test of the CAPM hypothesis.

This means that every

mean-variance efficient portfolio [[??].sup.[sigma]] consists of a fraction ([mu]([[??].sup.[sigma]] - r/[mu]([[??].sup.(t)] - r), invested in the risky-assets-only portfolio [[??].sup.(t)] and a fraction (1 - [mu]([[??].sup.[sigma]] - r/[mu]([[??].sup.(t)] - r) invested in the riskfree asset.