Russian mutual funds: skill versus luck - Дипломная работа

SMB represents a portfolio with long position on small and short on big capitalization companies, HML - portfolio with long on companies with high book-to-market value and short on low B/M. By adding these two factors to CAPM they create three-factor model. From this idea come another well-known model: four-factor model by M.Carhart. In 1997 was published “On persistence in mutual fund performance”. In this paper was introduced new model based on Fama-French three-factor model. The model includes new factor WML, meaning winners minus losers or a portfolio with long on best companies in the last period (usually a year) and short on worst in terms of returns. M.Carhart concluded that most mutual funds cannot have returns above benchmark for a long period of time, very few can provide stable returns above market. He proposed to analyze top alphas of mutual funds during a long period of time. No fund was able to hold top positions for the whole period. Since Fama-French three-factor and Cathart four-factor models are not used in this paper there will be not much said about these two papers. In this research Jensen alpha is used but not as a single criteria of fund`s performance but as a part of a process that is necessary to distinguish luck from skill. At first, it was thought that alpha shows manager`s skills. The higher alpha - the better fund is operated. But it is not always true. By observing it is clear that the funds with big alphas are not always with high returns. If a fund has top alpha every year for many years then it can be said that it is managed skillfully. But there is either no such funds or there are few of them. Most funds do not have stable alphas for a long period of time. Jensen alpha by itself cannot separate luck from skill, which makes alpha unstable in time and cannot predict future abnormal returns. As it was mentioned earlier it were assumed that managers have no timing skills since beta is constant and average from the whole retrospective period. In 1989 M.Grinblatt and S.Titman in “Portfolio performance evaluation: old issues and new insights” showed that a manager with positive expectations will increase his portfolio`s beta with the market and his reaction function depends on his risk appetite. Also, authors found evidence that simple passive strategies can be beaten. [M.Grinblatt and S.Titman, 1989]. Later in 1992 in their paper “The persistence of mutual fund performance” they found out that the difference in different mutual funds` returns are stable in time and have connections with abilities to provide abnormal returns. In this paper only picking skills are tested, so there is no need to discuss timing further. The core papers for this research with which the last share similar methodology and main ideas are: “Luck versus Skill in the Cross Section of Mutual Fund Returns” by E.Fama and K.French, Can Mutual Fund “Stars” Really Pick Stocks? New Evidence from a Bootstrap Analysis” by R.KosowskiI, A.Timmermann, R.Wermers, and H.White. As it can be noticed from the titles: the topic and the question authors raised are similar to this paper`s. The last is based on the ideas and methods described in core papers. These papers are concentrated on American market, meaning mutual funds in USA. Authors determine the skill contribution to funds alphas in USA. Thus the main goal of current research is to analyze and use their ideas on Russian market as it was done by D.Muravyev in 2006 and then go further with more models and recent data with changes in some assumptions. More detailed information about approaches that were used in these papers can be found in chapter “Methodology”. The main results and research process of core papers are described in short below. All the core papers are based on bootstrap approach. Authors use different assumptions but general idea is the same. The approach is based on idea of zero skill contribution. It can be achieved through random returns created with zero-alpha model and random errors. The basic form of bootstrap approach with Jensen alpha as a parameter to measure skill is presented below: a) Estimate real alphas for each fund in the sample using one model. Below is presented an example with CAPM. These real alphas are Jensen alphas. In the equation beta is covariance of funds returns and benchmark returns divided by variation of benchmark returns: , where: - means returns above risk-free rate, - is from regression or Jensen alpha, - is beta with the market, - is risk market premium or benchmark returns minus risk-free rate, - represents errors of the model. b) Store beta and residuals from the regression for each fund; c) Use residuals to create new series of pseudo residuals by resampling observations in random order with possibility to replace. It means not only to change order of observations but some of them will be duplicated and some excluded. An example of series of pseudo errors: , where: - is series of pseudo returns, - is t observation o