Performance Measurement Models

3.6 Methodology

3.6.3 Performance Measurement Models

This section addresses the second objective of the study, which was, to find out which fund management approach, between style consistent investing and style drifting, produces superior risk adjusted results relative to each other. Therefore, after establishing the style consistent funds and drifting funds using the style drift score, the next mission was to find out which set of funds produce superior performances. When evaluating the risk adjusted performance of a portfolio, the single factor Capital Asset Pricing Model, the Fama and French (1992) 3-factor model and the Carhart (1997) 4-factor models, are some of the most prominent models that are widely used (El Khamlichi et al., 2014a). The alpha from these models determines whether the portfolio outperformed or underperformed the market by being significantly positive or negative. Predominantly, the Fama and French 3- factor model and the Carhart 4- factor model have been used extensively in previous studies both in South Africa and internationally.

The Carhart model is an extension of the Fama and French model, since it has an additional 4^th factor, the momentum term, which adds more explanatory power.

According to studies done on the South African market, the challenge with this model, though, is its inaccuracy in capturing the momentum factor in the JSE with

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precision, since this variable can alter the results of the performances considerably.

Additionally, the South African market fluctuates wildly at times, due to the volatility of the ZAR (South African Rand) currency relative to major world currencies. This could potentially exaggerate the momentum factor of stocks in the markets. Hence, for this analysis, the study will do away with the momentum factor altogether, and employ the widely used Fama and French (1992) 3-factor model to measure fund performances of the South African unit trusts selected.

However, before the Fama-French model is applied, the study firstly engaged the widely used Capital Asset Pricing model in order to compare the changes in alpha when additional factors are included with the Fama-French 3-factor model, as done in most studies of this nature (Eraslan, 2013). For a thorough analysis of performance with all the models used, two sets of regressions were performed for each model across all the funds. The specific sector index was used for the market proxy in the first regressions and then the JSE ALSI index was used as a market proxy in the second set of regressions. This allowed a thorough evaluation of the effect of investing in style indices as compared to the general market. Changes in the models’ resultant R² values and their log likelihood ratios were also be observed.

As alluded previously, performance is measured by examining the amount of alpha and the associated statistical significance. The explanatory power of the models is observed through the adjusted R-squared values.

3.6.3.1 The Capital Asset Pricing Model (CAPM)

Performances of the funds under study will first be evaluated using the CAPM model.

As highlighted in the above section, the study sought to examine whether style models have more explanatory power, relative to general market benchmark models.

Hence, this test was run twice for all the funds, first with the relevant sector index as a market proxy and the second test with the JSE All Share Index, which represents the whole market. The model for the CAPM is expressed as follows;

𝑅_𝑖𝑡 = 𝛼_𝑖 + 𝛽_𝑖(𝑅𝑀_𝑡− 𝑅_𝑓𝑡) + 𝜀_𝑖𝑡 (7)

71 Where;

𝑅_𝑖𝑡 = the return of the fund in excess of the risk free rate 𝛼_𝑖 = Abnormal return of the stock

𝛽_𝑖 = beta of the fund

𝑅𝑀_𝑡 = the return of the market 𝑅_𝑓𝑡 = the risk free rate

𝜀_𝑖𝑡 = the error term.

3.6.3.2 Fama - French 3 Factor Model (FF3F)

The second model used, for performance evaluation, is the Fama-French 3 factor model. Similarly, to the CAPM, regressions under this model were run twice using the same reasoning as above. The FF3F model is expressed as follows:

𝑅_𝑖𝑡 = 𝛼_𝑖 + 𝛽_1𝑖(𝑅𝑀_𝑡− 𝑅_𝑓𝑡) + 𝛽_2𝑖𝑆𝑀𝐵_𝑡 + 𝛽_3𝑖𝐻𝑀𝐿_𝑡 + 𝜀_𝑖𝑡 (8)

Where;

𝑅_𝑖𝑡 = return of fund 𝑖 at time t in excess of the risk free rate 𝛼_𝑖 = abnormal return of the fund

𝛽_1𝑖 = beta of the fund

𝑅𝑀_𝑡 = the return of the market measured by the JSE relevant market index 𝑅_𝑓𝑡 = the risk free rate

𝛽_2𝑖 = sensitivity of the fund’s returns to the size factor

𝑆𝑀𝐵_𝑡 = the small capitalization portfolio less the large capitalization portfolio (size factor)

𝛽_3𝑖 = sensitivity of the fund’s returns to the value factor

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𝐻𝑀𝐿_𝑡 = the high book-to-market funds less the low book-to-market funds (value factor)

𝜀_𝑖𝑡 = the error term or residual term.

3.6.3.3 Sharpe ratio

In addition to the above model, the Sharpe ratio was used to compare performances of the mutual funds against themselves and the market, adjusted for risk. It is expressed as follows;

𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = (𝑅_𝑝− 𝑅_𝑓)

𝜎_𝑝 (9)

Where;

𝑅_𝑝= return of the portfolio 𝑅_𝑓= risk free rate

𝜎_𝑝= standard deviation of portfolio.

3.6.3.4 Market Timing: Treynor- Mazuy model (TM model)

Over and above measuring the performances of these funds, the study also sought to find out whether South African fund managers are able to time the market as they engage in active investing. In other words, the study also sought to examine the funds’ performances when market timing ability was considered. This process remained a quest to measure the funds’ performances, which was part of objective two of the study. Various performance measures try to distinguish security selection, or share-picking ability, from market timing ability, or the ability to predict the market returns.

Although alpha normally measures both, market-timing models were developed to distinguish these two aspects of performance. The Treynor- Mazuy traditional market-timing model assumes the approach that any information, correlated with future market returns, is superior information which makes it unconditional. The

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study utilizes the classic market timing regression of Treynor and Mazuy (1966), which expresses the regression in a quadratic form as below;

𝑅_𝑖𝑡 = 𝛼_𝑖 + 𝛽_1𝑖(𝑅𝑀_𝑡− 𝑅_𝑓𝑡) + Ƴ(𝑅𝑀_𝑡− 𝑅_𝑓𝑡)²+ 𝜀_𝑖𝑡 (10)

Where;

𝑅_𝑖𝑡 = return of fund 𝑖 at time t in excess of the risk free rate 𝛼_𝑖 = abnormal return of the fund

𝛽_1𝑖 = beta of the fund 𝑅𝑀_𝑡 = return of the market 𝑅_𝑓𝑡 = the risk free rate

Ƴ = market timing coefficient 𝜀_𝑖𝑡 = the error term.

The sign on the estimated coefficient Ƴ of the quadratic term, and whether it is statistically different from zero, evaluates market-timing ability. If it is significantly positive, then it represents a convex upward sloping regression line and indicates evidence of successful market timing by the fund manager. Thus, the coefficient will be positive if the manager increases beta when receiving a positive signal about the market. The hypothesis of no timing ability, implies that the coefficient Ƴ on the quadratic term is zero or negative. The market proxy for this model is the funds’

specific equity style benchmarks.