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Posted on March 8th, 2013, by

Limitations to the traditional methods

In actuality, traditional methods reveal the controversy of the dependency of the performance of mutual funds on both skills of fund managers and luck. However, it is necessary to take into consideration some limitations of the traditional methods. To put it more precisely, traditional methods focus on the analysis of the work of fund managers and on the marketing development. However, existing studies and traditional methods often fail to define accurately luck and, therefore, it is even more difficult to measure luck in terms of traditional methods, especially using quantitative methods of analysis. As the matter of fact, it is unclear what the luck actually is and how to measure luck in regard to the work of fund managers. In actuality, luck should be measure accurately and it is important to distinguish luck from the results of the work of fund managers and the use of their professional skills. Therefore, traditional methods have a vague boundary between luck and results of the work of fund managers.

On the other hand, traditional methods provide researchers with the possibility to conduct accurate analysis and to obtain reliable data because the information obtained in the result of the use of traditional methods is valid and reliable because these methods have the high degree of reliability.

Nevertheless, traditional methods have some more limitations, such as certain rigidity of methods. What is meant here is the fact that the business environment is changing and the tasks of researchers change too. Therefore, methods should also change respectively to new challenges and tasks, which they should solve. In such a situation, traditional methods should be backed up with new methods that can enhance the findings of the research.

2.3 Skill vs. luck in the performance of mutual funds’ managers

In such a context, existing studies and methods contribute to the better understanding of the correlation between professional skills of fund managers and luck and their contribution to the successful performance of mutual funds. At this point, it is important to distinguish luck from professional skills as the major factors of mutual funds’ success. What is meant here is the fact that existing studies and traditional methods reveal the fact that both professionals skills of fund managers and luck contribute to the overall success of mutual funds. On the other hand, traditional methods fail to distinguish clearly professional skills’ impact and luck’s impact on the performance of mutual funds.

In such a way, traditional methods still fail to provide the definite answer to the question whether professional skills are prior to luck.

Therefore, it is necessary to conduct the further analysis and use new methods of studies to reveal the priority of either professional skills or luck in regard to the successful performance of mutual funds.

3. The Capital Asset Pricing Model as a framework to performance measures

3.1 The CAPM logic

Along with traditional methods of the quantitative, statistical analysis that could be applied to mutual funds and the impact of professional skills and luck of fund managers on their performance, it is possible to use the Capital Asset Pricing Model (CAPM), which is another effective quantitative method that can help to reveal the extent to which professional skills and luck are important for fund managers and effectiveness of their work. The CAPM contributes to the revelation of the correlation between risk assessment and expected returns, which investors are likely to obtain in the result of their investments. In regard to mutual funds, the CAPM can reveal the effectiveness of mutual funds performance and the effectiveness of fund managers’ performance through the revelation of the risk assessment associated with mutual funds and the work of fund managers based on their professional skills and expected returns. At the same time, it is important to study risks and expected returns in case of the prevalence of luck over professional skills of fund managers. In fact, the higher returns and lower risks are the more successful the performance of mutual funds is. If mutual funds are driven by professional skills of managers and reach a tremendous success than professional skills are prior to luck, if the contrary occurs, i.e. mutual funds are driven by luck, regardless of professional skills of their fund managers, than luck is prior to professional skills.

3.2 The testing approach of the CAPM

In order to understand how CAPM works in relation to mutual funds, it is possible to develop an abstract case, where investors expect to receive certain benefits from their investments in the mutual fund M and they need to assess risks and expected returns using the CAPM.

First, all investors will choose the market portfolio, M, as their optimal portfolio. M includes all assets in the economy, with each asset weighted in the portfolio in proportion to its weight in the economy. Since all investors have the same expectations and use the same input list, they will each choose an identical risky portfolio, which is the portfolio on the efficient frontier that lies on the tangency line drawn from the risk free asset (Fletcher, 1995). If any asset were left out of that portfolio its demand would be zero and therefore its price would approach zero. Seeing this, all investors would adjust their portfolio to include this asset until it had a price that would reflect its amount of risk. Thus we can see that all assets will be included in M. (Fama & French, 2004)

Second, the market portfolio, M, lies on the efficient frontier and is the tangent asset to the risk-free asset. Since investors all have identical input lists and all hold M, all information about assets in the market is incorporated into M, resulting in an efficient portfolio (Fama & French, 2004). Each individual investor will then choose to allocate his wealth between M and the risk free asset, or in other words the Capital Allocation Line runs between the risk free asset and the portfolio M (Fama & French, 2004).

Third, the risk premium on the market portfolio will be proportional to its own risk and the degree of risk aversion of the average investor (Fama & French, 2004). Each investor chooses a proportion b to invest in the market portfolio M and a proportion 1-b to invest in the risk free asset such that

b = [E(rMarket) rfree] / [AsMarket^2]
where E(rMarket) is the expected return to the market portfolio, rf is the risk free return, A is a measure of risk aversion, and sMarket^2 is the market portfolio’s risk. Since any borrowing is offset by lending, b for the average investor is equal to 1. From this we can show that
E(rMarket) rfree = AsMarket^2

Fourth, the risk premium on individual assets [E(ri) rf] will be proportional to the risk premium on the market portfolio and the beta coefficient of the asset relative to the market portfolio where beta is defined as
Я = [Cov(ri, rMarket)] / sMarket^2

The correct risk premium of an asset must be determined by the contribution of the asset to the risk of the portfolio. As the number of assets in the market portfolio gets very large, a given asset’s contribution to the risk of the portfolio depends almost entirely on its covariance with other assets in the portfolio and its weight in the portfolio, while the contribution of its own risk (or the asset’s variance) to the risk of the portfolio approaches zero. Thus, as the number of assets in the portfolio gets very large,
Cov(ri, rMarket) = Cov(ri, SUM:wkrk)
Consequently for specific assets in the market portfolio the correct measure of risk is their covariance with the market portfolio. An asset’s reward-to-risk ratio would be
wi[E(ri) ri] / wiCov(ri, rmarket) = [E(ri) ri] / Cov(ri, rmarket)

Because we are in equilibrium, all assets must offer equivalent reward-to-risk ratios, otherwise investors would choose assets with superior ratios to invest in. This means that the reward-to-risk ratio of all assets must be equal to the reward-to-risk ratio of the market portfolio, that is,
[E(ri) rfree] / Cov(ri, rMarket) = [E(rMarket) rfree] / sMarket^2
or E(ri) = rfree + Яi[E(rMarket) rfree] (Fama & French, 2004)

This equation is the most common form of the CAPM. Яi is an appropriate measure of risk for an asset since it measures the asset’s contribution to the risk of the market portfolio. Яi is proportional to the premium of the assetan asset’s premium depends on its contribution to the risk of the market portfolio (Fama & French, 2004).
represent the return-beta relationship through the security market line, or the SML. At Я = 0 the line will intersect the y-axis at the risk free rate. At Я = 1 the line will be at E(rM) on the y-axis since Cov(rM, rM) / s2M = 1. Also, it can be shown that the slope of the SML is equal to the expected excess returns to the market (E(rM) rf) (Fama & French, 2004).

In equilibrium, all assets will lie on the SML because they will have an appropriate return-beta relationship. However, if we depart from equilibrium some assets will not be correctly priced. If an asset is overpriced it will lie below the SML since it will provide an expected return less than what is determined by the SML given its risk (beta). If an asset is underpriced it will lie above the SML since its return will be greater than what the SML determines (Scholz, 2006).

The CAPM gives investors a tool for determining their investment decisions. By estimating a SML and plotting an asset, the investor can determine whether the asset is over or underpriced and make investment decisions based on that knowledge (Scholz, 2006). In such a way, the CAPM contributes to the revelation of the importance of the detailed analysis, while taking decision in regard to investments. At this point, it is important to place emphasis on the fact that the analysis of risks and expected returns is possible only on the condition of well-developed professional skills of fund managers. In contrast, luck makes the risk assessment and forecast of expected returns pointless. At the same time, the empirical data prove that the risk assessment and evaluation of expected returns allows investors to define mutual funds or target project to invest their money to. They do not trust in mutual funds that rely on luck solely and have no portfolio or whose portfolio fails to provide adequate analysis of risk assessment and expected returns.

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