This thesis aims to overcome difficulties in solving optimization problems related to portfolio management by applying parametric approaches to several problems such as time-varying beta estimations, optimal active portfolio constructions, and active asset allocations under the cumulative prospect theory (CPT).
In the first essay, we review the CAPM relation under a dynamic mean-variance strategy and its implication for the time-varying betas and adjust the market beta through parameterization as the linear function of firm characteristics and some common factors with an implicit assumption that factors other than the market excess return just explain correlation factor between the market proxy and the true market portfolio. The parametrically adjusted market beta performs consistently well both in in-sample fitting and out-of-sample forecasting.
In the second essay, we review Treynor and Black (1973) that utilizes security analysis under nearly efficient market assumption and formulate it as a statistical estimation problem by converting it into the parameterized expected utility maximization problem. By parameterization of the optimal active portfolio weights, we implicitly assume that analysts generally forecast alpha by adjusting historical alpha with stock-level conditioning characteristics. Our results suggest that the Treynor and Black (1973) model is worth while to be actively applied to the portfolio management even if most analysts do not hold performance records that are long enough to perform rigorous statistical tests. By applying the parameterization technique to the Treynor and Black (1973) model with simple market model, we can improve the overall portfolio performance.
In the third essay, we review the cumulative prospect theory (CPT) of Tversky and Kahneman (1992) and develop active asset allocation with parametric weights under mean-variance and CPT framework. We find the optimal active portfolio weights with Markov Chain Monte Carlo (MCMC) s...