Classical Mean Variance Model Revisited : Pseudo Efficiency

Since Markowitz published his seminal work on mean-variance portfolio selection in 1952, almost all literature in the past half century adhere their investigation to a binding budget spending assumption on this classical investment issue. In the mean-variance world for a market of all risky assets, however, the common belief of monotonicity does not hold, i.e., not the larger amount you invest, the larger expected future wealth you can expect for a given risk (variance) level. We introduce in this paper the concept of pseudo efficiency to remove from the candidates such efficient mean-variance policies which can be achieved by less initial investment level. By relaxing the binding budget spending restriction in investment, we derive an optimal scheme in managing initial wealth which dominates the traditional mean-variance efficient frontier