The Volatility Effect: Recent Evidence from Indian Markets

We provide evidence of the volatility effect from the Indian markets using the universe of past and present constituents of Nifty 500 index of National Stock Exchange (NSE). The results show that the portfolio consisting of low volatility stocks outperforms the portfolio consists of high volatility stocks and the market portfolio both in absolute and risk-adjusted terms. Further, we report that the volatility effect is a distinct effect. Size, value and momentum factors cannot explain the outperformance of low-volatility stocks. The risk anomaly is robust to the choice of risk measure; however, the volatility effect is stronger than the beta effect and it implies that both systematic risk and idiosyncratic risks contribute to the risk anomaly. The low-volatility portfolio has significant exposure to growth stocks, and it differs from the value tilt observed for low-volatility portfolios in developed markets.


Introduction
Finance theory postulates the positive relationship between risk and return.
Modern portfolio theory [1] offers a model that allows investors to construct a portfolio that optimizes a risk-return trade-off consistent with risk tolerance.
Capital Asset Pricing Model (CAPM) [2] establishes a positive relationship between systematic risk and return with the beta as a measure of systematic risk.
To earn a higher return, one has to invest in the high-beta portfolio and assume a higher risk. The underlying assumption is that rational investor should hold a fully diversified market portfolio that has zero, firm-specific, diversifiable risk.
However, most investors don't hold a perfectly diversified portfolio, especially Theoretical Economics Letters those, who target to outperform the benchmark market portfolio. Therefore, they may keep the unsystematic risk for superior returns. In such cases, investors look at the total risk and may look for a reward for assuming the idiosyncratic risk.
Contrary to the strictly positive relationship postulated by asset pricing theory, empirical evidence is mounting with an inverse risk-return relationship within an asset class such as equity. While the broad positive relationship holds true across asset classes, several studies across global markets report that portfolio constructed of least volatile stocks (or minimum variance portfolio), consistently outperforms the portfolio consisting of high volatility stocks and benchmark universe portfolio on a risk-adjusted basis and most times in absolute return terms over the full market cycle. These results challenged the positive relationship between risk and expected return as proposed by classic asset pricing theories. Several academic studies of the past report flatter or even inverse risk-return relationship, contrary to the positive relationship proposed by CAPM. However, such evidence didn't receive much attention and considered more like data mining exercise. However, over the past two decades, evidence for the low-risk anomaly has been mounting and the debate transcended beyond the existence of an inverse risk-return relationship to economic and behavioural explanations that justify its likely persistence.
Our study contributes to the existing body of literature in several ways. First, the paper offers strong evidence for the low-risk anomaly in Indian equity where the portfolio of low-risk stocks outperforms both high-volatility stocks and equal weight universe portfolio in risk-adjusted and nominal terms. Second, it establishes that the low-risk anomaly is unique and size, value and momentum factors cannot explain it. Third, as per [3], the low-risk stocks have a significant tilt towards value factor and they are a proxy for value stocks but this paper shows that low-risk stocks have actually a growth tilt. The evidence is in line with the fact that while low-risk anomaly is present across global markets, the characteristics of a low-risk portfolio are different in different markets. While the low-risk portfolio has a value tilt in developed markets, it has growth tilt for emerging markets [4]. India being one of the large emerging markets, the growth tilt of low-risk portfolio in the Indian market offers further evidence to more recent work on portfolio characteristics of low (high) risk portfolios. Fourth, we also compare the strength of the volatility effect by using standard deviation and beta as risk measures and also report residual volatility effect after controlling for the beta effect. And fifth, this study offers out of the sample evidence of low-risk anomaly to some earlier studies as it covers the 15-year period starting from January 2004. It also refutes the claim that large part of out-performance of minimum variance strategy is because of the period of 2000 to 2003 and is directly linked to the aftermath of dotcom bubble [5].
We organize the rest of the paper as follows. Section 2 covers the review of the literature, and Section 3 discusses the data and the empirical model. Section 4 discusses the important results and Section 5 offers Conclusion of the study. On the one hand, evidence for risk anomaly is growing and practitioners are busy latching on to the prospect of delivering higher returns without facing higher risks, off late a few studies report the positive relationship between risk and return using different methodologies. The focus of the recent studies is on finding economic and behavioral explanations to explain or explain it away, such puzzling negative relationship between risk and return and more interestingly its persistence.
Bali & Cakici [21] attributes the negative relationship between risk and return shown by Ang A., Hodrick, Xing, & Zhang [13] is because of small and illiquid stocks with lottery-like payoffs. Martellini [22] shows that a positive relationship between risk and return using data consisting of only surviving stocks and therefore may suffer from survivorship bias. Fu [23] shows that the relationship between expected volatility and not the historical volatility expected returns is positive by using EGARCH models to estimate idiosyncratic volatility. Scherer [3] shows that size and value factors explain most of the out-performance of the minimum variance portfolio and low volatility stocks are just a proxy for value stocks. Poullaouec T. [5] shows that out-performance of MSCI MV index MSCI We clearly see the literature gap for there are only a few studies on Indian equity with respect to the low risk anomaly. Equity returns can be attributed to various factors [7] and it is important to see that the volatility effect is independently impacting the returns. This study establishes that the low-risk anomaly in Indian stock market is unique and size, value and momentum factors cannot explain it. Scherer [3] claims that the low-risk stocks have a significant value tilt but this paper shows that low-risk stocks have actually a growth tilt in India. Poullaouec T. [5] claims that large part of out-performance of minimum variance

Data and Empirical Model
Our universe consists of past and present constituents of NSE 500 index. We collect the data of adjusted monthly closing price, market capitalization and Here i SR is the Sharpe ratio of portfolio i, , i j ρ is the correlation between portfolios i and j and T is the number of observations.
The CAPM alpha is calculated using EWI return as proxy for market by using following one-factor regression.
( ) where , p t R return on portfolio p is in period t. , p m β is the beta of portfolio p with respect to market portfolio and , p t ε is the idiosyncratic return of portfolio p in period t. We use equally weighted universe as proxy for market portfolio in this study unless otherwise specified.
The three-factor alpha is calculated by adding SMB (size) and VMG (value) proxies to the regression. We add WML (momentum) proxy in addition to size and value to the regression to calculate four-factor alpha. , where SMB R , VMG R and WML R represents the return on size, value and momentum factors in our universe and  We can see that the annualized excess return for the LV portfolio is 10.62%

Empirical Results and Discussion
and it declines as we move towards the HV portfolio. The return for the HV excess return for the HV portfolio is −17.35%. This shows that the returns decline as we move from a low-volatility portfolio to a high-volatility portfolio. The annualized standard deviation declines monotonically as we move from LV to HV portfolio with LV portfolio having the standard deviation of 19.52% vs. HV portfolio having the standard deviation of 46.28%. The standard deviation of the These results show that the LV portfolio has a large and positive alpha, whereas the HV portfolio has a large but negative alpha. Both are highly significant, both economic and statistical terms but with the negative sign. The last raw reports maximum drawdown, a measure of peak-to-trough percentage fall in a portfolio.
The maximum drawdown for LV portfolio is −48.2% whereas the corresponding numbers for both HV and universe portfolio are 81.11% and 72.45 respectively.
The difference in drawdown explains the out-performance of LV portfolio and underperformance of the HV portfolio over time. The portfolio that loses 50% of its value in a period needs 100% returns in the next period to breakeven, whereas, the portfolio that loses 75% of its value in a period needs 300% return to breakeven. The base effect plays a very important role in long term compounded returns and LV portfolio has a clear advantage here and that results in eventual out-performance. shows that the volatility effect is stronger than the beta effect and it implies that both systematic risk and idiosyncratic risk contribute to the out-performance of LV portfolio and underperformance of HV portfolio in absolute and risk-adjusted terms.
Panel A of Table 3 reports the three-factor and four-factor alpha for LV and HV portfolios. Three-factor annualized alpha for LV portfolio is 12% (t = 5.3) which is economically and statistically significant. The four-factor alpha for the   Table 3. Three-factor (Fama-French) and four-factor (Fama-French-Carhart) style regression analysis for volatility decile portfolios.
This table reports annualized alpha and regression coefficients for the three-factor and four-factor regressions for low-volatility and high-volatility portfolios. the results show that the positive (negative) alpha for low-volatility (high-volatility) portfolio remain high and significant and the volatility effect is a distinct effect and size, value and momentum factors cannot subsume it. LV portfolio is 10.37% (t = 4.9). Both three and four-factor alphas remain and that establishes that the volatility effect is a distinct size, value, and momentum factors cannot explain it. Likewise, both three-factor and four-factor alphas remain large and negative for HV portfolio at −21.2% (t = −6.22) and −19.09% (t = −6.22) respectively. Again, large-negative alphas for HV portfolio establishes that size, value and momentum factors cannot explain the volatility effect.
Panel-B of Table 3 reports the regression coefficients for the three-factor and four-factor regressions for the LV and HV portfolios. While the beta of an LV portfolio for three and four-factor regressions are comparable to ex-post beta reported in Table 1, we observe that the regression coefficients for size (SMB) factor are about 0.03 for both three-factor and four-factor model is statistically insignificant and it shows that LV portfolio has no exposure to the size factor.  Finally, we control for the beta to see the robustness of the volatility effect and measure the implied relationship between idiosyncratic risk and expected returns. Since the volatility is the measure to total risk, systematic risk as well as idiosyncratic risk and beta measures the systematic risk, the volatility effect controlled for beta captures the relationship between the idiosyncratic risk and expected returns. In addition, it captures the relative strength of volatility and beta effect. Panel D reports that alpha volatility decile portfolios after controlling for the beta. The alpha for LV portfolio is 3.74% (t = 0.62) which is economically significant but statistically insignificant. However, alpha for HV portfolio is −12.88% (t = −1.7), it is economically significant and statically significant at 10% significance level. This shows that the volatility effect is still present after controlling for the beta, but it is much weaker and more dominant for the HV portfolio than the LV portfolio. Our results are in line with Blitz, Pang, & Vliet [24] who report stronger volatility effect than beta effect. Our result also supports Bali & Cakici [21] who argued that the volatility effect associated with idiosyncratic risk is because of high idiosyncratic risk stocks with lottery-like payoffs.
The dominant inverse relationship between idiosyncratic risk and expected returns on the HV leg of the portfolio than the LV portfolio supports this argument.

Conclusion
Our study offers a piece of strong evidence for the volatility effect in Indian markets. The inverse relationship between risk and returns is clear as the portfolio consisting of low-volatility stocks outperforms the market portfolio and the portfolio consisting of high-volatility stocks. The out-performance of the LV portfolio and underperformance of the HV portfolio both contribute to the volatility effect. Such an inverse risk-return relationship is present notwithstanding the choice of risk measures. However, the effect is stronger for standard deviation rather than beta as a risk measure. Both systematic risk and idiosyncratic risk contribute to the volatility effect. The portfolio of LV stocks not only outperforms in risk-adjusted terms but also in absolute returns terms. The volatility effect is a distinct effect, exposure to size, value, and momentum factors cannot explain it. Also, the low volatility portfolio has a systematic tilt towards growth and winners' stocks, whereas the high volatility portfolio has a tilt towards value and loser stocks. Both LV and HV portfolios don't show any tilt towards large or small stocks. The growth tilt of the LV portfolio differs from the value tilt observed in developed markets. Thus, while the volatility effect is universal, the characteristics of a low volatility portfolio are different for developed and emerging markets.