Is idiosyncratic risk ignored in asset pricing: Sri Lankan evidence?
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Abstract
The present study focused on one of the important South Asian nations—Sri Lanka—to examine the role of idiosyncratic volatility in asset prices. A four-factor model with idiosyncratic volatility was designed for capturing the market, size, value and idiosyncratic risk yields better than Fama and French’s (J Financ Econ 33:3–56, 1993) three-factor model and performance of the model. Fama–MacBeth’s cross-sectional regression, residual graphs and GRS test all confirm the superiority of four-factor model over 2 three-factor models. For all MC- and IVOL-based portfolios, idiosyncratic volatility is negatively related to the expected returns and positively related for all PB-based portfolios. Finally, study findings confirm that there is a high importance for idiosyncratic volatility risk factor while considering investment decision in Colombo stock exchange. Hence, investor should compensate for holding such risk factors in the portfolio.
Keywords
Asset pricing Idiosyncratic risk Factor models Fama–MacBeth’ cross-sectional regression RiskAbbreviations
- MC
market capitalisation
- Rf
risk-free rate
- SMB
size
- LMH
value
- IVOL
idiosyncratic volatility
JEL Classification
G12Introduction
Risk is broadly classified into two groups: one systematic and another unsystematic. Systematic risk is a risk which cannot be diversified like market risk, whereas unsystematic risk can be diversified, and hence, systematic risk should be priced by the investors. Earlier studies by Sharpe [1], Lintner [2] and Mossin [3] consider only the systematic risk to derive risk return relationship and argued that investor holds well-diversified market portfolio which, in turn, diversified the idiosyncratic volatility. In reality, capital markets are more complex, and simply holding well-diversified portfolios will not automatically reduce the idiosyncratic volatility completely. In such case, if investors are not able to distinguish between systematic and unsystematic risk clearly, investors will observe underperformance in its investment decision. Merton [4] argued that investor who holds undiversified portfolio should not be compensated. Previous studies show mixed results about the importance of the idiosyncratic volatility in stock returns. As a result, it is always a topic of discussion among the researchers whether idiosyncratic volatility should be priced or not by the investors?
Malkiel and Xu [5, 6], Goyal and Santa-Clara [7] and Fu [8] studies find a positive relationship between the idiosyncratic volatility and stock returns, whereas considerable number of studies by Ang et al. [9, 10], Guo and Savickas [11], Frieder and Jiang [12], Chua et al. [13] and Wagner and Winter [14] find a negative relationship between the idiosyncratic volatility and stock returns. One finding which is common in most of the above-mentioned studies is that CAPM neglects idiosyncratic volatility in asset pricing. Presently emerging capital markets are equally important like the other developed markets, and Blackrock [15] reports say that the shares of emerging markets, especially Asian markets, are increasing. Sri Lanka’s Colombo stock exchange is one such important exchange that has seen significant development and foreign investment in the last decade. Colombo stock exchange is one of the important exchanges in South Asia that provides electronic trading. Considering the fact that the effect of idiosyncratic volatility of stock returns is mixed, the present study will be the maiden attempt to study comprehensively on Sri Lanka’s Colombo stock exchange.
The present study will explicitly report how important idiosyncratic volatility is in Sri Lankan context, which is not addressed by any other previous studies. Study by Bali et al. [16] found that stock with small size tends to have more idiosyncratic volatility than big-size stocks. Second, the present study will address the same by following portfolio-based study results. Third study will deploy different designs and methodologies that are different from previous studies. Different researchers follow different frequencies and proxies for idiosyncratic volatility calculation. Daily data were used by Ang et al. [9] study, whereas Frieder and Jiang [12] study used monthly data for calculating idiosyncratic volatility. Many of the studies by Ang et al. [9] and Frieder and Jiang [12] used time series data for fixed time period, whereas Fu [8] study found that idiosyncratic volatility is time-varying. Hence, study findings based on fixed model are questionable and need dynamic check. Ang et al. [9, 10] used lagged realised idiosyncratic volatility as proxy, whereas Fu [8] used expected idiosyncratic volatility as proxy for idiosyncratic volatility. The present study uses Fama and French [17]-based approach in calculating the idiosyncratic volatility proxy. Finally, the study uses both time series and cross-sectional analysis to explore the significance of idiosyncratic volatility in asset pricing. The rest of the paper is divided into the following sections: literature review, data and methodology, empirical results, asset-pricing results, model performance test and conclusions.
Literature review
Traditional asset-pricing studies by Sharpe [1], Lintner [2] and Mossin [3] argue that unsystematic risk should not be price the investors as investors hold well-diversified market portfolio. Considerable number of studies in last few decades challenged the basic fundamental idea of not to compensate the unsystematic risk. Black and Scholes [18] and Merton [4] studies argued that increase in the stochastic volatility of the stocks or portfolios leads to increase in the value of the equity, and hence, idiosyncratic risk should be compensated by the investors. Idiosyncratic risk is a firm-specific risk, and considerable number of studies by Banz [19], Reinganum [20], Gibbons [21], Basu [22], Bhandari [23]. Ross [24], Fama and French [17], Balakrishnan and Maiti [25], Balakrishnan et al. [26], Maiti and Balakrishnan [27], Maiti [28, 29, 30], etc., proved that there are several firm-specific risks other than market risk. Campbell et al. [31] found that average total volatility increases over a period of time, whereas market volatility shows no pattern. Further study found that idiosyncratic volatility component of the total volatility factor is very important and time-varying. The study also argued that a well-diversified portfolio must contain over 50 stocks and practically idiosyncratic volatility cannot be diversified completely. A sizeable number of studies related to idiosyncratic risk have been carried out globally, and the results are mixed.
Chua et al. [13] studies found that the expected stock returns are positively related to the idiosyncratic volatility. A sizable number of studies by Jiang and Lee [32], Malkiel and Xu [6], Drew et al. [33], Huang et al. [34] and Zaremba [35] also found positive relationship between expected returns and idiosyncratic volatility. Similarly, other set of studies by Ang et al. [9, 10], Guo and Savickas [11], Frieder and Jiang [12], Chua et al. [13] and Peterson and Smedeman [36] found that idiosyncratic volatility is negatively related to the expect stock returns. Recent study by Liu and Di Iorio [37] in Australian context finds a positive relationship between the expected returns and idiosyncratic volatility. The study also finds that idiosyncratic factor is very much significant in explaining returns in both time series and cross-sectional set-up. Finally, study also finds that big stocks are systematically much riskier than the small stocks. From the above literature review, it is clear that idiosyncratic volatility is important factor in explaining the risk and return relationship. A sizeable number of studies related to idiosyncratic volatility and expected returns have been carried out on the developed markets, and as Sri Lanka is concerned, no study has been done so far related to the idiosyncratic volatility and expected returns.
Data and methodology
Data
Idiosyncratic volatility of the stock is calculated as the standard deviation of the residual obtained from the regression of equation number 1. Then the daily idiosyncratic volatility was converted to monthly idiosyncratic volatility (IVOL) by multiplying the daily value with the square root of number of trading days for that month.
Portfolio construction
Statman [38] argued that a well-diversified portfolio must contain at least 30 stocks, and further Campbell et al. [31] study added that in recent decades to achieve a certain level of diversification in portfolio returns, it must have more than 40 stocks. Our study sample has 251 stocks, and hence, six portfolios are formed to achieve the greater level of diversification. Using single-sorting technique, every year in the month of June (t), six equal-weighted portfolios are constructed based on each MC, P/B, and IVOL variables. The portfolios are names as P11 to P16. Revision of portfolios ranking again done in the month of June^{1} next year (t + 1) following the same procedure and repeated up to year 2016.
Mimicking risk factor construction
Using single-sorting technique every year in the month of June (t), two equal-weighted portfolios are constructed based on MC. Top 50% stocks with high value of MC stocks are named Big (B) and rest 50% names as Small (S). Revision of portfolios ranking again was done in the month of June next year (t + 1) following the same procedure and repeated up to year 2016. Then using single-sorting technique every year in the month of June (t), three value-weighted portfolios ([17] breakpoints of 30:40:30) are constructed based on each P/B and IVOL variables. Top 30% stocks with high value of P/B named as high (H), bottom 30% stocks with less value of P/B named as low (L) and rest 40% named as neutral (N). Similarly, top 30% stocks with high value of IVOL (Hv) named as high IVOL, bottom 30% stocks with less value of IVOL named as low IVOL (Lv) and rest 40% named as neutral (Nv). Revision of portfolios ranking again was done in the month of June next year (t + 1) following the same procedure and repeated up to year 2016.
Using double-sorting technique, every year in the month of June (t), six value-weighted portfolios are constructed from the cross of two MC and three P/B portfolios obtained from single sort. Six portfolios are named as S/L, S/N, S/G, B/L, B/N and B/G, where S/L portfolio contains ‘small size and low value stocks’ and B/G portfolio contains ‘big size and high value stocks’. Revision of portfolios ranking again was done in the month of June next year (t + 1) following the same procedure and repeated up to year 2016. Then using double-sorting technique, every year in the month of June (t), six value-weighted portfolios are constructed from the cross of two MC and three IVOL portfolios obtained from single sort. Six portfolios are named as S/Lv, S/Nv, S/Gv, B/Lv, B/Nv and B/Gv, where S/Lv portfolio contains ‘small size and low idiosyncratic volatility stocks’ and B/G portfolio contains ‘big size and high idiosyncratic volatility stocks’. Revision of portfolios ranking again was done in the month of June next year (t + 1) following the same procedure and repeated up to year 2016.
The present study uses four regressions as explained below:
Fama–French three-factor model
Three factor model with idiosyncratic volatility
Four-factor model with market, size, value, and idiosyncratic volatility
Fama–MacBeth’s cross-sectional regression
It is a step regression as explained below
Explanatory variables
Descriptive statistics for the independent variables
Rm | SMB | LMH | LvMHv | |
---|---|---|---|---|
Mean returns | 0.006 | 0.003 | 0.001 | 0.001 |
SD | 0.053 | 0.011 | 0.011 | 0.009 |
Year-wise monthly IVOL
Average monthly IVOL | ||||||||
---|---|---|---|---|---|---|---|---|
2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 |
0.295 | 0.245 | 0.443 | 0.365 | 0.250 | 0.189 | 0.166 | 0.166 | 0.180 |
Correlation matrix for explanatory variables
Rm | SMB | LMH | LvMHv | |
---|---|---|---|---|
Rm | 1 | |||
SMB | − 0.056 | 1 | ||
LMH | − 0.147 | − 0.092 | 1 | |
LvMHv | 0.013 | − 0.196 | 0.269 | 1 |
Empirical results
Summary statistics of six portfolios formed on MC, PB and IVOL
Portfolio | MC | PB | IVOL | ||||||
---|---|---|---|---|---|---|---|---|---|
Mean excess returns | SD | T-statistics | Mean excess returns | SD | T-statistics | Mean excess returns | SD | T-statistics | |
P11 | 0.017 | 0.109 | 1.566 | 0.017 | 0.106 | 1.559 | 0.014 | 0.107 | 1.310 |
P12 | 0.017 | 0.108 | 1.518 | 0.015 | 0.106 | 1.333 | 0.015 | 0.108 | 1.369 |
P13 | 0.017 | 0.106 | 1.611 | 0.016 | 0.107 | 1.476 | 0.016 | 0.108 | 1.490 |
P14 | 0.014 | 0.108 | 1.281 | 0.016 | 0.105 | 1.502 | 0.016 | 0.105 | 1.436 |
P15 | 0.015 | 0.105 | 1.351 | 0.015 | 0.108 | 1.373 | 0.015 | 0.105 | 1.349 |
P16 | 0.014 | 0.107 | 1.316 | 0.015 | 0.109 | 1.363 | 0.017 | 0.109 | 1.515 |
Results and discussion
Asset-pricing results
Fama–French’s Three-factor regressions (market, size and value)
Regression results of Fama–French’s three-factor model for six portfolios \(R_{Pt} {-} \, R_{Ft} = \, a \, + \, b \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, s \, \;{\text{SMB}}_{t} + \, l\,{\text{ LMH}}_{t} + \, e_{t}\)
MC | PB | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.003 | 0.003 | 0.004 | 0.003 | 0.003 | 0.003 | 0.004 | 0.002 | 0.004 | 0.004 | 0.003 | 0.002 |
Rm | 2.001 | 2.005 | 1.958 | 1.991 | 1.944 | 1.991 | 1.991 | 1.981 | 1.971 | 1.936 | 1.995 | 1.993 |
SMB | 0.619 | 0.578 | 0.490 | − 0.268 | − 0.218 | − 0.214 | 0.544 | 0.263 | 0.049 | 0.018 | − 0.120 | 0.099 |
LMH | − 0.380 | 0.063 | − 0.079 | − 0.153 | − 0.265 | − 0.068 | 0.650 | 0.061 | − 0.168 | − 0.253 | − 0.327 | − 0.754 |
tc | 1.535 | 1.463 | 1.963 | 1.304 | 1.600 | 1.527 | 1.786 | 0.850 | 1.878 | 2.055* | 1.470 | 1.298 |
tr | 5.664* | 5.412* | 5.756* | 5.047* | 5.837* | 6.194* | 5.836* | 5.142* | 5.378* | 5.283* | 5.552* | 6.872* |
ts | 3.228* | 3.291* | 2.665* | − 1.554 | − 1.263 | − 1.335 | 3.085* | 1.505 | 0.274 | 0.104 | − 0.626 | 0.620 |
tl | − 2.072* | 0.376 | − 0.449 | − 0.925 | − 1.610 | − 0.441 | 3.849* | 0.363 | − 0.979 | − 1.500 | − 1.781 | − 4.957 |
R^{2} | 0.967 | 0.972 | 0.968 | 0.973 | 0.972 | 0.976 | 0.971 | 0.972 | 0.970 | 0.970 | 0.967 | 0.977 |
IVOL | ||||||
---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.002 | 0.003 | 0.004 | 0.003 | 0.001 | 0.004 |
Rm | 1.997 | 1.996 | 1.997 | 1.951 | 1.950 | 2.008 |
SMB | − 0.159 | 0.097 | − 0.013 | 0.371 | 0.393 | 0.223 |
LMH | − 0.063 | 0.123 | − 0.122 | 0.124 | − 0.171 | − 0.281 |
tc | 1.453 | 1.207 | 2.018* | 1.141 | 0.729 | 1.835 |
tr | 6.885* | 5.827* | 5.658* | 4.996* | 5.585* | 5.768* |
ts | − 1.030 | 0.508 | − 0.069 | 1.878 | 2.307* | 1.210 |
tl | − 0.424 | 0.676 | − 0.693 | 0.654 | − 1.049 | − 1.586 |
R^{2} | 0.978 | 0.967 | 0.969 | 0.963 | 0.972 | 0.969 |
Three factor regressions (market, size and idiosyncratic volatility)
Portfolio P11 (first portfolio) is well captured by the model for MC-, P/B- and IVOL-based portfolios. Further result shows that one portfolio of PB (P14) and one portfolio of IVOL (P16) are significant at 5% level. It implies that high idiosyncratic volatility stocks portfolio is not captured by the model. Market (Rm) coefficients of all portfolios based on MC, P/B and IVOL are highly positive and significant. Size (SMB) coefficients are positive for small-size portfolios and become negative towards big-size portfolios in case of MC-based portfolios, whereas SMB coefficients are mostly positive in case of P/B- and IVOL-based portfolios. Value (LMH) coefficients are mostly negative for MC-, P/B- and IVOL-based portfolios. SMB coefficients of 3 MC-based (P11, P12 and P13) and 1 PB-based (P11) portfolios found to be significant. In most of the cases, IVOL coefficient is found to be positive and is significant for 4 IVOL (P11, P12, P13 and P16), 1 MC (P12) and 1 PB (P11) portfolios, respectively. First four portfolios of IVOL-based portfolios have positive IVOL coefficient, and IVOL coefficient changes its sign towards high IVOL portfolios. Average alpha value and R-square values are 0.003 and 97% for three-factor regressions with idiosyncratic volatility.
Four-factor regression results (market, size, value and idiosyncratic volatility)
Portfolio P11 (first portfolio) is well captured by the model for MC-, P/B- and IVOL-based portfolios. Further result shows that one portfolio of PB (P14) and one portfolio of IVOL (P16) are significant at 5% level. It implies that high idiosyncratic volatility stock portfolio is not captured by the model. Market (Rm) coefficients of all portfolios based on MC, P/B and IVOL are highly positive and significant. Size (SMB) coefficients are positive for small-size portfolios and become negative towards big-size portfolios in case of MC-based portfolios, whereas SMB coefficients are mostly positive in case of P/B- and IVOL-based portfolios. Value (LMH) coefficients are mostly negative for MC-, P/B- and IVOL-based portfolios. First portfolio of IVOL portfolios SMB coefficient is negative that implies that among low idiosyncratic volatility stocks big stocks have less idiosyncratic risk. SMB coefficients of 3 MC-based (P11, P12 and P13), 1 PB-based (P11) and 1 IVOL-based (P15) portfolios found to be significant. In most of the cases, IVOL coefficient found to be positive and is significant for 4 IVOL (P11, P12, P13 and P16) and 1 MC (P12) portfolios, respectively. First four portfolios of IVOL-based portfolios have positive IVOL coefficient and IVOL coefficient changes its sign towards high IVOL portfolios. Average alpha value and R^{2} values are 0.003 and 97% for four-factor regressions.
Regression results of three-factor model with idiosyncratic volatility for six portfolios \(R_{Pt} {-} \, R_{Ft} = \, a \, + \, b \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, s\,{\text{ SMB}}_{t} + \, v\,{\text{ LvMHv}}_{t} + \, e_{t}\)
MC | PB | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.003 | 0.003 | 0.004 | 0.002 | 0.003 | 0.003 | 0.003 | 0.002 | 0.004 | 0.004 | 0.003 | 0.002 |
Rm | 2.014 | 2.003 | 1.961 | 1.996 | 1.953 | 1.993 | 1.970 | 1.979 | 1.977 | 1.944 | 2.006 | 2.017 |
SMB | 0.642 | 0.648 | 0.527 | − 0.240 | − 0.177 | − 0.166 | 0.548 | 0.280 | 0.068 | 0.044 | − 0.063 | 0.180 |
LvMHv | − 0.112 | 0.476 | 0.180 | 0.075 | 0.076 | 0.258 | 0.458 | 0.147 | 0.004 | − 0.006 | 0.142 | 0.008 |
tc | 1.512 | 1.376 | 1.917 | 1.272 | 1.547 | 1.461 | 1.600 | 0.814 | 1.859 | 2.019* | 1.402 | 1.121 |
tr | 5.469* | 5.490* | 5.560* | 5.626* | 5.994* | 6.476* | 5.988* | 5.840* | 5.879* | 5.488* | 5.647* | 5.334* |
ts | 3.227* | 3.730* | 2.834* | − 1.365 | − 1.001 | − 1.026 | 2.902* | 1.583 | 0.370 | 0.245 | − 0.317 | 0.991 |
tv | − 0.459 | 2.244* | 0.794 | 0.349 | 0.350 | 1.307 | 1.983* | 0.681 | 0.019 | − 0.027 | 0.590 | 0.035 |
R^{2} | 0.966 | 0.973 | 0.968 | 0.973 | 0.971 | 0.977 | 0.967 | 0.972 | 0.970 | 0.969 | 0.966 | 0.971 |
IVOL | ||||||
---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.002 | 0.002 | 0.004 | 0.002 | 0.001 | 0.004 |
Rm | 1.998 | 1.992 | 2.001 | 1.947 | 1.955 | 2.017 |
SMB | − 0.078 | 0.200 | 0.073 | 0.384 | 0.394 | 0.161 |
LvMHv | 0.462 | 0.727 | 0.456 | 0.167 | − 0.110 | − 0.576 |
tc | 1.355 | 1.093 | 1.936 | 1.105 | 0.747 | 2.006* |
tr | 6.767* | 5.061* | 5.446* | 4.472* | 5.152* | 5.802* |
ts | − 0.517 | 1.089 | 0.400 | 1.919 | 2.267* | 0.879 |
tv | 2.494* | 3.240* | 2.038* | 0.681 | − 0.520 | − 2.569* |
R^{2} | 0.980 | 0.970 | 0.970 | 0.963 | 0.972 | 0.971 |
Regression results of four-factor model for six portfolios \(R_{Pt} {-} \, R_{Ft} = \, a \, + \, b \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, s \, \,{\text{SMB}}_{t} + \, l\;{\text{ LMH}}_{t} + \, v\;{\text{ LvMHv}}_{t} + \, e_{t}\)
MC | PB | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.003 | 0.003 | 0.004 | 0.002 | 0.003 | 0.003 | 0.003 | 0.002 | 0.004 | 0.004 | 0.003 | 0.002 |
Rm | 2.001 | 2.002 | 1.957 | 1.990 | 1.943 | 1.989 | 1.989 | 1.980 | 1.971 | 1.935 | 1.993 | 1.991 |
SMB | 0.622 | 0.646 | 0.520 | − 0.249 | − 0.193 | − 0.173 | 0.579 | 0.281 | 0.058 | 0.030 | − 0.083 | 0.137 |
LMH | − 0.384 | − 0.035 | − 0.124 | − 0.180 | − 0.301 | − 0.128 | 0.598 | 0.033 | − 0.181 | − 0.271 | − 0.381 | − 0.811 |
LvMHv | 0.018 | 0.488 | 0.222 | 0.136 | 0.177 | 0.301 | 0.256 | 0.136 | 0.065 | 0.085 | 0.271 | 0.281 |
tc | 1.520 | 1.366 | 1.906 | 1.263 | 1.549 | 1.451 | 1.722 | 0.811 | 1.850 | 2.021* | 1.407 | 1.224 |
tr | 5.336* | 5.432* | 5.635* | 5.775* | 5.643* | 6.457* | 5.821* | 5.872* | 5.046* | 5.964* | 5.516* | 6.061* |
ts | 3.173* | 3.695* | 2.787* | − 1.418 | − 1.101 | − 1.065 | 3.240* | 1.583 | 0.318 | 0.167 | − 0.424 | 0.856 |
tl | − 2.008* | − 0.203 | − 0.678 | − 1.049 | − 1.760 | − 0.811 | 3.427* | 0.192 | − 1.014 | − 1.539 | − 2.009* | − 5.171 |
tv | 0.072 | 2.208* | 0.941 | 0.610 | 0.799 | 1.471 | 1.133 | 0.604 | 0.282 | 0.374 | 1.102 | 1.384 |
R^{2} | 0.967 | 0.973 | 0.968 | 0.973 | 0.972 | 0.977 | 0.971 | 0.972 | 0.970 | 0.970 | 0.967 | 0.978 |
IVOL | ||||||
---|---|---|---|---|---|---|
P11 | P12 | P13 | P14 | P15 | P16 | |
c | 0.002 | 0.002 | 0.004 | 0.002 | 0.001 | 0.004 |
Rm | 1.993 | 1.991 | 1.993 | 1.950 | 1.950 | 2.011 |
SMB | − 0.087 | 0.199 | 0.061 | 0.389 | 0.385 | 0.152 |
LMH | − 0.167 | − 0.024 | − 0.229 | 0.097 | − 0.160 | − 0.177 |
LvMHv | 0.518 | 0.736 | 0.534 | 0.134 | − 0.057 | − 0.517 |
tc | 1.347 | 1.085 | 1.932 | 1.104 | 0.739 | 1.997* |
tr | 6.854* | 5.068* | 5.747* | 4.738* | 5.258* | 5.945* |
ts | − 0.575 | 1.075 | 0.335 | 1.934 | 2.214* | 0.827 |
tl | − 1.127 | − 0.135 | − 1.286 | 0.491 | − 0.940 | − 0.986 |
tv | 2.705* | 3.146* | 2.310* | 0.527 | − 0.257 | − 2.224* |
R^{2} | 0.980 | 0.970 | 0.971 | 0.963 | 0.972 | 0.971 |
Fama–MacBeth’s cross-sectional regression results
Fama–Macbeth’s cross-sectional regression result
Parameters | λ_{0} | λ_{rm} | λ_{lvmhv} | Adjusted R^{2} | F-statistics(P value) | ||
---|---|---|---|---|---|---|---|
Two factors with market and idiosyncratic volatility | |||||||
MC | Mean | 0.025 | − 0.005 | − 0.004 | 23.8 | 0.468 | 0.665 |
SD | 0.314 | 0.166 | 0.024 | ||||
T-statistics | 0.787 | − 0.269 | − 1.475 | ||||
PB | Mean | 0.049 | − 0.017 | 0.002 | 44.2 | 1.187 | 0.417 |
SD | 0.316 | 0.168 | 0.042 | ||||
T-statistics | 1.498 | − 0.966 | 0.530 | ||||
IVOL | Mean | − 0.019 | 0.018 | − 0.001 | 42.1 | 1.091 | 0.441 |
SD | 0.345 | 0.181 | 0.010 | ||||
T-statistics | − 0.540 | 0.941 | − 0.839 |
Parameters | λ_{0} | λ_{rm} | λ_{smb} | λ_{lmh} | Adjusted R^{2} | F-statistics (P value) | ||
---|---|---|---|---|---|---|---|---|
Fama–French three factor | ||||||||
MC | Mean | 0.028 | − 0.006 | 0.005 | 0.005 | 41.1 | 0.466 | 0.736 |
SD | 0.323 | 0.170 | 0.043 | 0.032 | ||||
T-statistics | 0.838 | − 0.365 | 1.214 | 1.516 | ||||
PB | Mean | 0.062 | − 0.023 | 0.001 | 0.001 | 66 | 1.292 | 0.464 |
SD | 0.396 | 0.207 | 0.009 | 0.012 | ||||
T-statistics | 1.526 | − 1.108 | 0.966 | 0.519 | ||||
IVOL | Mean | 0.008 | 0.004 | − 0.004 | − 0.001 | 44.2 | 0.527 | 0.706 |
SD | 0.504 | 0.259 | 0.035 | 0.042 | ||||
T-statistics | 0.155 | 0.164 | − 1.001 | − 0.124 |
Parameters | λ_{0} | λ_{rm} | λ_{smb} | λ_{lvmhv} | Adjusted R^{2} | F-statistics (P value) | ||
---|---|---|---|---|---|---|---|---|
Three factors with idiosyncratic volatility | ||||||||
MC | Mean | 0.035 | − 0.011 | 0.010 | − 0.003 | 80.8 | 2.809 | 0.273 |
SD | 0.315 | 0.167 | 0.037 | 0.024 | ||||
T-statistics | 1.091 | − 0.617 | 2.573* | − 1.357 | ||||
PB | Mean | 0.047 | − 0.016 | 0.001 | 0.002 | 62.5 | 1.110 | 0.506 |
SD | 0.316 | 0.168 | 0.008 | 0.062 | ||||
T-statistics | 1.461 | − 0.926 | 0.966 | 0.242 | ||||
IVOL | Mean | 0.003 | 0.007 | − 0.002 | − 0.001 | 43.9 | 0.521 | 0.709 |
SD | 0.693 | 0.346 | 0.069 | 0.012 | ||||
T-statistics | 0.038 | 0.192 | − 0.345 | − 0.585 |
Parameters | λ_{0} | λ_{rm} | λ_{smb} | λ_{lmh} | λ_{lvmhv} | Adjusted R^{2} | F-statistics (P value) | ||
---|---|---|---|---|---|---|---|---|---|
Four factors | |||||||||
MC | Mean | 0.041 | − 0.012 | 0.003 | 0.008 | − 0.005 | 98.9 | 22.012 | 0.158 |
SD | 0.319 | 0.168 | 0.041 | 0.033 | 0.025 | ||||
T-statistics | 1.252 | − 0.712 | 0.811 | 2.264* | − 2.017 | ||||
PB | Mean | 0.065 | − 0.025 | 0.001 | 0.001 | 0.001 | 66.2 | 0.490 | 0.774 |
SD | 0.458 | 0.239 | 0.008 | 0.012 | 0.083 | ||||
T-statistics | 1.393 | − 1.033 | 0.965 | 0.511 | 0.106 | ||||
IVOL | Mean | − 0.005 | 0.011 | − 0.002 | 0.000 | − 0.001 | 44.8 | 0.203 | 0.910 |
SD | 0.842 | 0.423 | 0.070 | 0.048 | 0.012 | ||||
T-statistics | − 0.053 | 0.243 | − 0.330 | − 0.042 | − 0.585 |
Residual graphs
Model performance test
Summary of GRS test results for all the factor models
GRS F-statistics | P value | Theta/thetas, proportion of the potential efficiency | Average absolute alpha value | Average R^{2} (%) | |
---|---|---|---|---|---|
Fama–French three factor | |||||
MC | 0.746 | 0.614 | 0.826 | 0.003 | 97.1 |
PB* | 2.371 | 0.036 | 0.635 | 0.003 | 97.1 |
IVOL | 1.153 | 0.339 | 0.762 | 0.003 | 97.0 |
Three factors with idiosyncratic volatility | |||||
MC | 0.710 | 0.642 | 0.839 | 0.003 | 97.1 |
PB* | 2.617 | 0.022 | 0.626 | 0.003 | 96.9 |
IVOL | 1.095 | 0.372 | 0.779 | 0.003 | 97.1 |
Four factors | |||||
MC | 0.732 | 0.625 | 0.835 | 0.003 | 97.2 |
PB* | 2.627 | 0.022 | 0.625 | 0.003 | 97.1 |
IVOL | 1.144 | 0.344 | 0.772 | 0.003 | 97.1 |
Conclusion
Due to high transaction cost and incomplete information, investors generally does not hold well-diversified portfolio, and as a result, idiosyncratic volatility associated with the investment does not diversify completely. This signifies the importance of idiosyncratic volatility in investment decision, and investors should compensate for holding idiosyncratic risk. The present study in Sri Lankan contest evaluates the role of idiosyncratic volatility in pricing Colombo stock exchange in both time series and cross-sectional set-up for a period of July 2008 to December 2016. The study result shows that IVOL-based investment strategy will yield comparatively less average returns than market-, size- and value-based investment strategies. Idiosyncratic volatility risk factor is positively weakly correlated with the market risk and size risk factors, whereas negatively weakly correlated with the value risk factor. Average portfolio means excess return pattern based on MC, PB and IVOL that shows weak size, value and idiosyncratic volatility effects in Colombo stock exchange portfolios.
Asset-pricing results show that both Fama–French’s three-factor model and three-factor model with idiosyncratic volatility factor yield similar results. Hence, investors may align their investment decision based on market and size along with value or idiosyncratic volatility factor as both will yield similar results. However, four-factor model yields comparatively better results than 2 three-factor models as some of the information which is omitted by the three-factor models is captured by the four-factor model. Times series regressions with different factor model yield almost similar results, but cross-sectional set-up estimates give more vivid view of the risk variables. For all MC- and IVOL-based portfolios idiosyncratic volatility is negatively related to the expected returns, whereas it is positively related to all PB-based portfolios. This implies that high idiosyncratic risk prevails in the small size, big P/B value and low IVOL stocks of the Colombo stock exchanges stocks. Further Fama–MacBeth cross-sectional regression confirms that idiosyncratic volatility captures information omitted by the Fama–French three-factor model, and study findings are similar to Liu and Di Iorio [37] findings in Australian context. Further Fama–MacBeth’s cross-sectional regression, residual graphs and GRS test all confirm the superiority of four-factor model over 2 three-factor models. Except PB-based portfolios, all other portfolios based on MC and IVOL passes GRS model performance test for all the factor models used in the study.
The study findings imply that there is a high importance for considering idiosyncratic volatility risk factor while considering investment decision in the Colombo stock exchange. Idiosyncratic volatility relationship to the portfolio expected returns is highly dependent on the portfolio construction factor variables. It is advisable not to form portfolios completely based on the P/B ratio of the stocks as it may leads to higher risk. Further study results imply that investment decision on Colombo stock exchange should not be solemnly based on the time series analysis, but one must also consider cross-sectional analysis or both for high precisions. Finally, study concludes that idiosyncratic volatility is an equally important factor similar to market, size and value factors in pricing Colombo stock exchange for the study sample period. The study findings are in line with Liu and Di Iorio [37] findings in Australian context. Hence, investor should compensate for holding idiosyncratic risk stocks in the portfolio.
Footnotes
- 1.
Three months lag period given, generally in Sri Lanka the financial year ends in the month of March of every year.
- 2.
Fama and French [17] estimate HML, which stands for high minus low, and mimics the risk factor associated with company value. They form HML using BE/ME while this study estimates LMH (See [25]) using P/B ratio which is inversely related to BE/ME as BE/ME ratios for the sample companies are not directly available in the data source. Hence, our interpretations of the results of value factor are mirror image to those of FFTF model [17].
Notes
Acknowledgements
Not applicable.
Authors’ contributions
Complete work. The author read and approved the final manuscript.
Funding
Not applicable.
Competing interests
The author declares that he has no competing interests.
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