Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations

This paper discusses a portfolio adjusting problem with additional risk assets and a riskless asset in the situation where security returns are given by experts' evaluations rather than historical data. Uncertain variables are employed to describe the security returns. Using expected value and risk index as measurements of portfolio return and risk respectively, we propose two portfolio optimization models for an existing portfolio in two cases, taking minimum transaction lot, transaction cost, and lower and upper bound constraints into account. In one case the riskless asset can be both borrowed and lent freely, and in another case the riskless asset can only be lent and the borrowing of riskless asset is not allowed. The adjusting models are converted into their crisp equivalents, enabling the users to solve them with currently available programming solvers. For the sake of illustration, numerical examples in two cases are also provided. The results show that under the same predetermined maximum tolerable risk level the expected return of the optimal portfolio is smaller when the riskless asset can only be lent than when the riskless asset can be both borrowed and lent freely.