详情
MPS Risk Aversion and Continuous Time MV Analysis in Precence of Levy Jumps
This paper studies sequential portfolio choices by MPS-risk-averse investors in a continuous time jump-diffusion framework. It is shown that the optimal trading strategies for MPS risk averse investors, if they exist, must be located on a so-called `temporal efficient frontier' (t.e.f.).
The t.e.f. is found not to coincide with the local instantaneous frontier --- the continuous time analogue of Markowitz's mean-variance frontier. This observation is potentially useful in understanding the existence of documented financial anormally in empirical finance --- MPS risk averse investors may not wish to invest along the local instantaneous Markowitz's mean-variance frontier, but instead hold portfolios on the t.e.f.. The optimal portfolio on the t.e.f. could well fall strictly within the instantaneous local Markowitz's efficient frontier.
Our observations on mutual fund separation are also profound and interesting. In contrast to the classical two-fund separation along the line of Black (1972) and Tobin (1958), our study shows that MPS-risk-averse investors' optimal trading strategy is target rate specific. Precisely, investors with different target rates may end up investing into different managed mutual funds, each involving a specific set of separating portfolios. Our theoretic findings are, nevertheless, much in line with the real world phenomena on the existence of various types of mutual funds offered by different financial institutes, each aiming to attract demand from some specific groups of investors --- a picture that is in sharp contrast to the theoretical prediction made by Black (1972) and Tobin (1958).
Finally, our study sheds light on the difference between expected utility and MPS-risk-averse investors concerning their trading behavior in sequential time frame. Even though these two groups of investors may end up holding a common risky portfolio in each spot market, the differences between their trading behaviors are most reflected through the portfolio weights assigned to each of the separating portfolios within the time frame and across states. Precisely, the portfolio weights corresponding to investors respectively from the two groups are associated with recognizable different time patterns. We showed that such difference in trading behavior would be also reflected from the time patterns of the instantaneous returns and the volatilities of the funds respectively managed by investors from these two groups.