3.6 Methodology
3.6.1 Establishing Fund Style
3.6.1.3 Selected Style Factors for the RBSA Model
This sub-section elaborates on the much mentioned twelve style factors. Sharpe’s principle of style analysis differs from the underpinnings of factor analysis models, in that it neglects designating asset classes to specific sectors of the economy such as industrials or resources. Sharpe (1992) purports that if a fund is adequately diversified in industries and economic sectors then the inclusion of sector return factors will not contribute any descriptive power to a model that explains fund returns (Low, 2012).
However, the South African market is heavily influenced by sectors like the Industrials, Financials and the Resources. Van Rensburg (2001), in his study of decomposing style based risk on the JSE, reinforces this notion by using the FINDI (combination of financials and industrials) and Resource 10 (for resources) indices as market proxies in his 2 factor model. Therefore, the classes chosen for this study differs substantially from Sharpe’s original study, since it was done in a different market with dissimilar characteristics from the South African market.
Accordingly, Sharpe (1992) asserts that the applicability of an asset class factor model relies on the asset classes chosen for its implementation. In order for this model to be of any significant power, while not necessary it is desirable that the asset classes are;
1) Mutually exclusive,
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3) Have returns that have low correlations with one another and, if not, then different standard deviations.
These above mentioned 3 conditions mean that the factors must completely describe investable options available to the funds, without any areas of overlap. To achieve this, the study follows the RBSA method as it is set out. The purpose of using the RBSA model is to test, or check, the direction of each fund so that the funds can be separated accordingly, that is, growth stocks, value stocks, low cap, mid cap, large cap, and real estate stocks. Once portfolio managers are certain of which asset class they are going to invest in, it is crucial that they determine the rate of exposure of each component so that they can gauge the movements in their portfolios’ returns.
Since the study is based on domestic general equity unit trusts, the asset classes chosen constitute JSE listed indices only. Some studies on style analysis like Mutooni and Muller (2007) and Du Toit (2012), used balanced funds which employ international equity indices (for example, MSCI World) and bond indices (such as, the STEFI index) to proxy for the diversified holdings. The seminal study of Sharpe (1988) also employs a bond index as one of its factors. However, adjustments in this research were made due to the analysis being of general domestic equity South African funds, unlike mixed asset funds like those studied in the US research on style. As previously mentioned, the unit trusts under consideration should hold a majority of assets whose returns are adequately described by the style factors. This means that a shift of focus from US mutual funds to SA unit trusts warranted a different set of investable asset class factors. Some of style factors have remained the same, with only the relevant indices used to proxy them having changed in relation to Sharpe’s style analysis.
Twelve factors or style indices are therefore selected for the right side of equation (4) that is,
(𝐹
1,…..…,𝐹
𝑛)
as per Sharpe (1992) model and their monthly returns were regressed against past monthly returns of the unit trusts on the left side of the equation, that is,𝑅𝑖
. The style indices or factors are selected from the FTSE/JSE indices list according to the exposure of most unit trusts to them. Keeping in mind that the study’s sample is purely South African domestic equity funds and not balanced funds or funds of funds which Sharpe (1992) used in his original study,63
bond indices were not used in this study. The equity indices used in this study and their justifications are as follows:
1. Short term treasury bills (SA Govt. 91-day T-bill, R203): with maturities of less than 3 months: The study uses the South African 91-day Treasury Bill rates obtained from the South African Reserve Bank. Whilst an index of this style factor is recommended, the study justifies its deviation from Sharpe’s recommendation by citing the fact that the unit trusts are South African and their investments are largely purported to comprise of SA assets (Viviers et al., 2009). Furthermore, this factor is often given weight when the funds under analysis hold cash on reserve to meet regulatory requirements and liquidity needs, and hence they invest in money market instruments (Van Heerden, 2014). The most accurate weighting will thus be obtained when limiting this factor to characteristics inherent to South African Bills, as movements in international interest rates are only likely to convolute the calculation of weightings (Saini et al., 2011). This data was obtained from the Reserve Bank of South Africa.
Consequently, a portfolio’s composition in relation to what type of stocks it includes is pivotal to any analysis on returns (Lau, 2007). The study continues to follow Sharpe’s guidelines, recognising that domestic stocks can fall into one of four categories. Initially, stocks are divided into three groups by market capitalisation – creating three distinct categories: large capitalization (cap), medium cap and small cap stocks.
The large cap stocks are further deconstructed into one of two categories, based on their book to market ratio. High book to market ratio stocks are deemed Value stocks, whilst stocks with lower book to market ratios are growth stocks. Any positive holding of all four categories of domestic stock falls into the area of Sharpe’s triangle:
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FIGURE 3-1: Sharpe’s triangle
SOURCE: Sharpe (1988) pp27.
2. Large Cap stocks: J200 Top 40 index - the Top 40 stocks in the JSE by market capitalization
3. Value stocks: J330 index - Large capitalisation stocks from the JSE Top 40 with high book to market ratios are grouped into the value index, J330.
4. Growth Stocks: J331 index - Large capitalisation stocks from the JSE Top 40 with low book to market ratios are grouped into the growth index, J331.
5. Mid Cap Stocks: J201 index - The J201, is a Mid Cap Index that consists of the next 60 largest stocks by market capitalization which are not in the JSE Top 40, but are in the All Share Index.
6. Small Cap Stocks: J202 index - The J202, is an index of equity stocks that forms part of the ALSI, but with market capitalisation values smaller than that of the mid and large capitalization stocks.
In order to fulfil the requirements of creating an exhaustive list of potential investment options available to the unit trusts, the study considered the dominant sector indices on the JSE in which most stocks are invested. These included:
7. Resources stocks: J210 Resource 10 index - JSE index that benchmarks the top 10 resources stocks.
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8. Industrials stocks: J211 Industrial 25 index - benchmark index for the top 25 industrial stocks in the JSE.
9. Financials stocks: J212 Financials 15 index - index that benchmarks the top 15 financial stocks in the JSE.
10. Property stocks: J253 SA Listed Property index - index of property based unit trust returns, it proxies the returns earned from property investments.
11. Consumables stocks: J530 Consumer Goods index - JSE index for consumer goods.
12. Technology stocks: J590 Technology index - The index comprising technology stocks listed in the JSE.
The R2 values, obtained from the regression, measures the part of the variance of returns explained by the style factors, or the extent of accuracy with which the Sharpe model replicates return exposures. The statistical significance of the coefficients contributes in explaining the probable style to which those returns can be attributed (Cuthbertson et al., 2010).
The returns across these twelve style factors selected above, were compiled and the returns for each fund for the 120-month period sorted into tables. This served as the data input for the study’s regressions. The regression’s independent variable was the monthly return of a single unit trust, whilst there are twelve dependent variables which are the returns of each style factor for the monthly period. The study illustrates the Sharpe RBSA factor model again from equation 4 (repeated for ease of reference).
𝑅𝑖 = [𝑏𝑖1𝐹1 + 𝑏𝑖2𝐹2+ ⋯ + 𝑏𝑖𝑛𝐹𝑛] + 𝑒𝑖 (4)
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Where 𝑅𝑖 represents the monthly return on the
𝑖
𝑡ℎ unit trust; 𝐹𝑛 represents the return of the 𝑛𝑡ℎ style factor and 𝑏𝑖𝑛, which is the coefficient to the 𝑛𝑡ℎ style factor, indicates the weighting/exposure of the unit trust to this factor. The error term (𝑒
𝑖) is used to denote the tracking error of the funds. If the study assumes that this error term is uncorrelated with the factors, then a claim can be made that this term denotes the portion of return due to selection (or skill), whilst the sum of the factor weightings is the return attributable to style (Kurniawan et al., 2012).A more implicit characteristic that can be seen in this regression is the omission of an intercept term (Dickson, 2016). This ensures that the portfolio weightings are fully accounted for by the style weightings from the regressions. This is equivalent to controlling for non-style factors, in the sense that now only the weightings can be varied to represent a unit trust’s composition – subject to the restrictions imposed on the model (Eddy, 2014).
The initial regression is termed the unconstrained regression, as the weights of the factors do not sum to one and some of these weights are negative (Froot and Teo, 2008). Negative weightings indicate that the fund has taken a short position to these asset factors – which is often prohibited in terms of their mandates. Consequently, the study must constrain these regressions in excel with the use of the solver function, which was done. In order to derive feasible weightings to the twelve asset classes that provide significant results with out-of-sample data, the study must impose the following constraints which have already been highlighted earlier:
• The first is that the individual weightings must fall into the range of zero and one;
• The second constraint is that the sum of all twelve weightings must equal one;
• A further, more implicit, constraint is the minimisation of the residual sum of squares, which is not automatically done by an Excel regression. This is achieved by using the solver function on a cell that has summed up the squared residuals, in order for it to be manually minimised.
The results of the constrained regression will be grouped by their return and risk profiles, and discussed in the next chapter.
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