In this paper, we suggest a technology process assuming that a stock mutual fund, as an usual firm, can be seen as a decision-making unit, so that we can measure the effect of its decisions regarding allocation of resources for administrative and non-administrative expenses on its own levels of gain and risk. Theoretically, this approach enables us to take into account some of the critiques reported in the fund’s performance literature. In practice, we can test it by applying nonparametric linear mathematical programming methods. Here, we perform an empirical exercise based on bootstrapped Directional Distance Function in order to analyze the management efficiency of stock mutual funds in Brazil. We are able to evidence a high level of persistence in terms of efficiency over years. We can identify that the most efficient funds have higher values of net assets and that they allocate more weighted resources to administrative expenses than do the inefficient ones. Therefore, we get a high correlation of average weighted expenses on administrative expenses and average bootstrapped efficiency, about 0.7. We claim that investors should also perceive this kind of efficiency measure proposed here—relevant under the point of view of the fund managers—as a signal of performance in a short run.
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A highly cited application of this arithmetic is Fama and French (2010). They use traditional asset pricing frameworks to infer about whether the performance of investment funds is random—good or bad luck—or systematic, signaling management skill.
See Kerstens et al. (2012).
The problem of choosing a direction vector is as old as the definition of DDF. Recently, an effort has been devoted to reaching a modeling allow choosing the direction vector with some criterion. In Fare et al. (2013) for example, the authors proposes use the optimization problem that define the directional distance function for choose the direction vector on unit simplex. It is worth to notice that this approach have problems as well. With three or more DMUs and one efficient the direction vector remains undefined.
Brazilian practice draws a distinction between administration and portfolio management of investment funds. In the case of funds administered by banks, the portfolio manager is generally a part of the same financial conglomerate, so here we use the expressions administer and manage as synonyms.
The standard deviation does not yet satisfy the characteristics in the sense of Artzner et al. (1999).
For the sake of compatibility with the frequency of the accounting variables, we annualize the financial data in the exercise, in order to measure the inefficiency. The average return was annualized from the average daily return and the number of business days in the year, while the semivariance, as a particular case of the standard deviation, was annualized by the product of the latter (obtained from daily data) and the square root of the number of business days. These relations are easily derived if the daily returns are assumed to be i.i.d.
See Andrews and Pregibon (1978).
There is no rule for the number of DMUs that must be deleted, but the computational cost for six or more deletion is huge vis-à-vis a low benefit.
See Avkiran (1999) for details.
Except for the GWI LEVERAGE fund (F35), which was excluded from the sample in 2008 because its annualized return was negative.
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This paper has greatly benefited from comments and suggestions by participants at 2013 First International Workshop in Financial Econometrics.
See Table 8 below.
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Matos, P., Padilha, G. & Benegas, M. On the management efficiency of Brazilian stock mutual funds. Oper Res Int J 16, 365–399 (2016). https://doi.org/10.1007/s12351-015-0204-y
- Operational research in finance
- Management efficiency
- Brazilian stock mutual funds
- Directional distance function with bootstrap