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Abstract
This paper develops and tests a new multi-attribute, behavioral based measure of mutual fund performance, based at the portfolio decision-making rather than trade level, using the alpha score, hit rate and the win-loss ratio. These measures are then combined to develop a multi-attribute measure of “efficiency”; the author decomposes this into technical, scale, and mix efficiency scores and then separately measure this for overweight and underweight portfolio positions. The author finds that the variations in average technical and mix efficiency scores related to win-loss ratios (hit rates) for relatively overweight (underweight) positions are statistically significant. These findings suggest that the sustainability of investment performance is evidenced from win-to-loss ratios and hit rate in ways that are not exhibited by the alpha performance measure.
Notes
1 This approach was formalized in Carhart (Citation1997) and then developed in Kosowski et al. (Citation2006), Cuthbertson et al. (Citation2004), and Barras et al. (2009) into an analysis based on alpha but implicitly assuming that the separation of skill versus luck is based on persistence observed by outliers.
2 Eeckhoudt et al. (Citation2005) note that this theory has evolved considerably since, including the extension to cumulative representation of uncertainty (Tversky and Kahneman Citation1992); more general criticisms of expected utility theory (Kahneman Citation2003) and in estimating the probability transformation function (Abdellaoui Citation2000).
3 The terms “overweight” and “underweight” refer to the opinion of an investment manager/analyst that a stock will outperform (underperform) the performance benchmark that is being monitored (www.investopedioa.com). This paper uses the generic term “sentiment” to delineate an investment managers opinion towards the stock.
4 There are a wide range of efficiency frontiers, including costs, revenues. In order to separate the pure productivity, scale elements of performance efficiency, this paper utilises the production frontier. Portfolio managers operating on the production frontier are efficient in the sense that they are using the minimal amount of inputs to produce their outputs. Those portfolio managers on the frontier are considered to be efficient in the sense that they are using the minimal amount of input to produce a given level of output. The frontier represents the best performance that can be achieved using the currently available technology.
5 DEA is just one method of estimating efficiency. It is based on linear programming and assumes that the error terms or residuals are modelled as part of the frontier. An alternative method, called stochastic frontier analysis, instead models the efficiency within a formal parametric econometric model which specifies the error term (Aigner, Lovell, and Schmidt Citation1977). The error term arising from the frontier is therefore decomposed into a random factor and a model factor. However, this requires the specification of the error term and can lead to significant issues. In a review paper, Lampe and Higers (Citation2015) find that both DEA and Stochastic Frontier Analysis methods lead to the comparable efficiency scores. In this paper, we follow the main literature by using DEA.
6 An investment mandate is the “allocation of funds to an investment manager to be managed for a specific purpose or style” (www.nasdaq.com/glossary/m/mandate).
7 Skewness and kurtosis statistics were calculated for all portfolios as part of the collection and validation of datasets, but are not reported.
8 Pure productive efficiency assumes constant returns to scale, whereas scale efficiency assumes variable returns to scale (Tung 2013).
9 These results are inconsistent with the t tests reported in Table 6, which indicate significant variation between Q1 and Q4 for the hit rate for both underweight and overweight portfolio positions. This could either be due to distributional assumptions or due to the lack of economies of scale in the data.