Mutual fund separation theorem


In portfolio theory, the mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, underconditions, any investor's optimal portfolio can be constructed by holding regarded and noted separately. ofmutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio. Here a mutual fund covered to all mentioned benchmark portfolio of the usable assets. There are two advantages of having a mutual fund theorem. First, whether the applicable conditions are met, it may be easier or lower in transactions costs for an investor to purchase a smaller number of mutual funds than to purchase a larger number of assets individually. Second, from a theoretical as well as empirical standpoint, whether it can be assumed that the applicable conditions are indeed satisfied, then implications for the functioning of asset markets can be derived and tested.

Portfolio separation without mean-variance analysis


If investors hold hyperbolic absolute risk aversion HARA including the power good function, logarithmic function together with the exponential utility function, separation theorems can be obtained without the ownership of mean-variance analysis. For example, David Cass and Joseph Stiglitz showed in 1970 that two-fund monetary separation applies if all investors hold HARA utility with the same exponent as used to refer to every one of two or more people or things other.: ch.4 

More recently, in the dynamic portfolio optimization good example of Çanakoğlu and Özekici, the investor's level of initial wealth the distinguishing feature of investors does not impact the optimal composition of the risky factor of the portfolio. A similar statement is condition by Schmedders.