### Data

Present study uses both daily and monthly data of 251 stocks listed in Colombo stock exchange for the period July 2008 to December 2016 of the following variables. Market capitalisation (MC) was used as proxy for size, *P*/*B* ratio was used as proxy for value, Standard and Poor’s Sri Lanka 20 index return were used as the proxy for market (Rm), and 91-day T-Bill was used as the proxy for risk-free rate (Rf). Similar to Ang et al. [9, 10] study, standard deviation of Fama and French’s [17] three-factor regression residuals was used as the proxy for idiosyncratic volatility. For the same period, daily excess returns are regressed with the daily excess market (Rm–Rf), size (SMB) and value (LMH) factor for the whole sample period to obtain the regression residuals.

$$R_{Pt} {-}R_{Ft} = aa + bb\left( {R_{Mt} - R_{Ft} } \right) + ss\;{\text{ SMB}}_{t} + \, ll\;{\text{ LMH}}_{t} + e_{t}$$

(1)

where *R*_{Pt}–*R*_{Ft} is the daily excess return of the stocks, *R*_{Mt}–*R*_{Ft} is the daily excess return of the market, SMB is the daily excess return of the size risk factor, LMH is the daily excess return of the value risk factor, *ss* and *ll* are the portfolio’s responsiveness to (sensitivity coefficients) SMB and LMH factors, respectively.

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^{Footnote 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.

Present study uses three risk-mimicking portfolios SMB (size), LMH (value) and LvMHv (idiosyncratic volatility), and they are estimated as described below:^{Footnote 2}

$${\text{SMB}} = \left( {S/L + S/M + S/H} \right)/3 - \left( {B/L \, + \, B/M \, + \, B/H} \right)/3$$

(2)

$${\text{LMH}} = \left( {S/L \, + \, B/L} \right)/2 \, {-} \, \left( {S/H \, + \, B/H} \right)/2$$

(3)

$${\text{LvMHv}} = \, \left( {S / {\text{Lv }} + \, B / {\text{Lv}}} \right)/2 \, {-} \, \left( {S / {\text{Hv }} + \, B / {\text{Hv}}} \right)/2$$

(4)

The present study uses four regressions as explained below:

### Fama–French three-factor model

$$R_{Pt} {-}R_{Ft} = a + b\left( {R_{Mt} - R_{Ft} } \right) + s\;{\text{ SMB}}_{t} + \, l\,{\text{ LMH}}_{t} + \, e_{t}$$

(5)

where SMB mimics size risk factor, LMH mimics value risk factor, *s* and *l* are the sensitivity coefficients of SMB and LMH factors.

### Three factor model with idiosyncratic volatility

$$R_{Pt} {-} \, R_{Ft} = \, a \, + \, b \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, s \, \,{\text{SMB}}_{t} + \, v\,{\text{ LvMHv}}_{t} + \, e_{t}$$

(6)

where SMB mimics size risk factor, LMH mimics idiosyncratic volatility risk factor, *s* and *v* are the sensitivity coefficients of SMB and LvMHv factors.

### Four-factor model with market, size, value, and idiosyncratic volatility

$$R_{Pt} {-} \, R_{Ft} = \, a \, + \, b \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, s\,{\text{ SMB}}_{t} + \, l\,{\text{ LMH}}_{t} + \, v\,{\text{ LvMHv}}_{t} + \, e_{t}$$

(7)

### Fama–MacBeth’s cross-sectional regression

*It is a step regression as explained below*

*Step 1*

$$\begin{aligned} & \left( {R_{Pt} {-} \, R_{Ft} } \right)_{1,t} = \, a \, + \, b_{{1,{\text{beta}}}} \left( {R_{Mt} - R_{Ft} } \right)_{1,t} + \, s_{{ 1 , {\text{smb}}}} {\text{SMB}}_{1,t} + \, l_{1,t} {\text{LMH}}_{1,t} + \, v_{1,t} {\text{LvMHv}}_{1,t} + e_{1,t} \\ & \left( {R_{Pt} {-} \, R_{Ft} } \right)_{2,t} = \, a \, + \, b_{{ 2 , {\text{beta}}}} \left( {R_{Mt} - R_{Ft} } \right)_{2,t} + \, s_{{ 2 , {\text{smb}}}} {\text{SMB}}_{2,t} + \, l_{2,t} {\text{LMH}}_{2,t} + \, v_{2,t} {\text{LvMHv}}_{2,t} + e_{2,t} \\ & : \\ & : \\ & \left( {R_{Pt} {-} \, R_{Ft} } \right)_{n,t} = \, a \, + \, b_{{n,{\text{beta}}}} \left( {R_{Mt} - R_{Ft} } \right)_{n,t} + \, s_{{{\text{smb}},t}} {\text{SMB}}_{n,t} + \, l_{{{\text{lmh}},t}} {\text{LMH}}_{n,t} + \, v_{n,t} {\text{LvMHv}}_{n,t} + e_{n,t} \\ \end{aligned}$$

(8)

*Step 2*

$$R_{Pt} {-} \, R_{Ft} = \lambda_{0} \, + \, \lambda_{\text{rm}} \, \left( {R_{Mt} - R_{Ft} } \right) \, + \, \lambda_{\text{smb}} \, \;{\text{SMB}}_{t} + \, \lambda_{\text{lmh}} {\text{ LMH}}_{t} + \, \lambda_{\text{ivol}} {\text{ LvMHv}}_{t} + \, e_{t}$$

(9)