Low-Risk Effect: Evidence, Explanations and Approaches to Enhancing the Performance of Low-Risk Investment Strategies

The authors offer evidence for low-risk effect from the Indian stock market using the top-500 liquid stocks listed on the National Stock Exchange (NSE) of India for the period from January 2004 to December 2018. Finance theory predicts a positive risk-return relationship. However, empirical studies show that low-risk stocks outperform high-risk stocks on a risk-adjusted basis, and it is called low-risk anomaly or low-risk effect. Persistence of such an anomaly is one of the biggest mysteries in modern finance. The authors find strong evidence in favor of a low-risk effect with a flat (negative) risk-return relationship based on the simple average (compounded) returns. It is documented that low-risk effect is independent of size, value, and momentum effects, and it is robust after controlling for variables like liquidity and ticket-size of stocks. It is further documented that low-risk effect is a combination of stock and sector level effects, and it cannot be captured fully by concentrated sector exposure. By integrating the momentum effect with the low-volatility effect, the performance of a low-risk investment strategy can be improved both in absolute and risk-adjusted terms. The paper contributed to the body of knowledge by offering evidence for: a) robustness of low-risk effect for liquidity and ticket-size of stocks and sector exposure, b) how one can benefit from combining momentum and low-volatility effects to create a long-only investment strategy that offers higher risk-adjusted and absolute returns than plain vanilla, long-only, low-risk investment strategy.


INTRODUCTION
Finance theory, pioneered by Modern Portfolio Theory (Markowitz, 1952) and Capital Asset Pricing Model (CAPM) (Sharpe, 1964), advocates a positive relationship between expected return and systematic risk. Capital Asset Pricing Model predicts a positive linear relationship between systematic risk and expected returns of a stock where beta is the measure of risk: a measure of security risk relative to market risk. However, early tests of CAPM (Black, 1972;Fama & MacBeth, 1973) report positive but flatter than expected risk-return relationship. However, these initial studies challenging the foundation of CAPM were simply brushed aside as an exercise of data mining. Foundation of CAPM took a major hit when Fama and French (1992) showed no relationship between beta and return after controlling for size. Black (1993) reported further flattening of the relationship between beta and return in decades since Black (1972)  How strong is the low-risk effect? 3. Is low-risk effect independent of value, size, and momentum effects? 4. Is low-risk effect a macro effect (sector level) or micro effect (stock level)? 5. Is it possible to integrate long-only low-risk strategy with momentum effect to generate superior risk-adjusted performance? 6. What are the characteristics of long-only low-risk portfolio in Indian markets?
To investigate these questions, the authors use Blitz and Vliet (2007) framework and further develop alternative approaches to enhance the performance of long-only, low-risk investment strategy by adding momentum booster to it while retaining low-risk nature of the strategy. They further analyze portfolio characteristics such as monthly portfolio churn requirement and portfolio concentration for the lowrisk portfolio for the practical implementation of long-only, low-risk investment strategy.
The rest of the paper is organized as follows. Section 1 covers the literature review. Section 2 covers data and methodology. Section 3 documents empirical results, Section 4 offers a discussion on empirical results. Final section offers the conclusion. 1 The terms low-risk anomaly, low-risk effect, and low-volatility effect are used interchangeably throughout this paper. The anomaly explains that low-risk stocks earn a higher return, and high-risk stocks earn a lower return than predicted by the Capital Asset Pricing Model (CAPM).

LITERATURE REVIEW
The Capital Asset Pricing Model (CAPM) predicts a linear relationship between systematic risk and expected security returns in which beta is the measure of systematic risk (Sharpe, 1964). However, the early tests of CAPM by Black (1972) and Fama and Macbeth (1973) indicate flatter than expected slope for the security market line. This implies that the risk-return relationship remains positive, but much flatter than expected. Haugen and Heins (1975) were the first to offer evidence for a negative risk-return relationship. Thus, one can trace early evidence of risk-anomaly much before the discovery of return-based anomalies such as size, value, and momentum. At the beginning of the 1990s, Fama and French (1992) report that beta remains unpriced in the cross-section of the stock universe once controlled for size effect. This implies that beta cannot predict the expected return, and there is no relationship between systematic risk and expected return of a stock.
The real impetus for research on low-risk anomaly came about at the beginning of the 21 st century.
There is increasing evidence about the presence of low-risk anomaly across the global markets and asset classes beyond equities.
Finally, global financial crisis of 2008 led to large drawdowns across global equity markets and caused significant damage to equity portfolios of many sovereign wealth funds and pension funds. As a result they switched to low-risk investment strategies, that earn equity returns with smaller drawdowns and lower volatility than market portfolio, which resulted into to an explosion in the launch of long-only variants of indices intending to exploit the benefits of a low-risk anomaly. By the end of the first decade of the 21st century, MSCI launched a minimum variance version of the index, whereas S&P launched an index with a low-volatility version. These facilitated the benchmarking of low-risk investment strategies and the launch of exchange-traded funds (ETF). 25 ETFs are traded in the US markets with asset under management (AUM) worth USD 71 billion (ETF, n.d.). Despite the stellar 10-year bull market in S&P500, the return of S&P500 low-volatility index is comparable to that of S&P500 and is less volatile. This has attracted many individual and institutional money to long-only low-risk investment products. For example, by 2012, UN staff pension fund invested more than USD 500 million in low-volatility equity strategies (P&I, n.d.).
One can classify the studies on low-risk anomaly based on portfolio construction methods, and choice of risk measures, look-back and holding periods, markets and asset classes and portfolio weighting schemes. As the evidence for low-risk anomaly started mounting on, the focus of research shifted to explaining away the risk anomaly. The recent studies focus on the implementation issues of low-risk investment strategies, decomposing the low-risk anomaly into micro and macro effect "micro and macro effects" instead of "micro and macro effect", and understanding the relationship between low-risk effect and other effects such as size, value, and momentum. Market friction and constraints: Black (1993) argues that the leverage constraints push investors expected to tilt their investment towards high-risk stocks rather than leverage to increase returns while investing in low-risk stocks or market portfolios. Frazzini and Pedersen (2014) offer further evidence on the same. The BAB factor returns are stronger when funding constraints are tighter. The short-selling constraints contribute to the flattening of the security market line (Miller, 1977).
Behavioral biases: Bali, Cakici, and Whitelaw (2011) attribute low-risk anomaly to investors' preference for lottery-like payoffs, which makes high-risk stocks overvalued, leading to subsequent lower returns. Barber and Odean (2008) explain that representativeness bias and overconfidence make investors choose more volatile stocks as they expect to meet volatility on the right side. Blitz and Vliet (2007) attribute it to a two-stage investment decision-making process, where investors show conservative behavior at the asset allocation stage but then prefer risky stocks at the second stage of the investment process. This is consistent with rational-thinker, irrational-doer version of prospect theory.
The other research branch pertains to decomposing a low-risk anomaly into macro (sector level) and micro (stock level) components. Baker Blitz and Vliet (2018) report that a simple conservative portfolio construction approach with top-100 liquid stocks with low-volatility, high-payout yield, and strong price momentum outperforms not only market portfolio but also most investment strategies based on size, value, momentum, and quality factors. The conservative formula works in the USA, Europe, Japan, and emerging markets. On the other hand, stocks with high volatility, low payout, and weak momentum deliver poor returns.
In India, NSE launched the NSE Low-Volatility 50 Index in November 2012 with base date of December 31, 2003, and the index has delivered superior returns to all major market-cap weighted benchmark indices, including bellwether Nifty Index both in absolute and risk-adjusted terms. However, low-volatility investing in India is yet to pick up. There is only one ETF tracking this index launched by ICICI prudential mutual fund in India, and its AUM is too small to mention. That said, the scope for low-volatility investment strategies in India is immense. India has very vibrant primary and secondary equity markets, with more than 5,000 stocks listed on major stock exchanges. India is among the top-10 global equity markets ranked by market-cap. According to the Association of Mutual Funds in India (AMFI), the mutual funds' industry in India has grown more than five-fold in the last 10 years, with a total AUM close to USD 350 billion at the end of December 2019. The pension fund industry in India is in a nascent stage, and there is a great potential for low-cost, low-risk equity products.
The research on low-risk effect in India is at a nascent stage. M. Joshipura and N. Joshipura (2016) report strong evidence for a low-risk effect. Peswani and Joshipura (2019) report evidence of low-risk effect in stocks belongs to different size buckets. However, research on the attractiveness of long-only factor investment strategies, implementation challenges, and integrating size, value, and momentum effects with low-risk effect to enhance the performance of low-risk investment strategies is as at nascent stages in developed markets and a yet-to-start stage in emerging markets like India. The focus is on several under-investigated aspects of low-risk effect in the Indian markets, including testing robustness of low-risk anomaly after controlling for liquidity, ticket-size, and sector exposure; testing practical aspects of long-only, low-risk investment strategy like sector concentration, turnover requirement, sensitivity to alternative weighting scheme, and enhancing the performance of low-risk investment strategy by adding the benefit of momentum effect using alternative approaches.

METHODOLOGY
At the end of every month, the data on Adjusted monthly closing price, Market capitalization, Price-to-book ratio, Monthly trading turnover, Global Industry Classification Standards (GICS) sector, are collected from Centre for Monitoring Indian Economy's (CMIE) Prowess Database for all the listed stocks on National Stock Exchange (NSE) of India starting from January 2004 to December 2018. Then the authors sort the stocks based on size measured by market capitalization at the end of every month and then pick the top 500 stocks with available returns for at least 12 months out of the previous 36 months and next 1 month. The adjusted closing price at the end of the month is a proxy for ticket-size and monthly trading turnover as a proxy for liquidity. Momentum for each stock at the end of the month is calculated using the previous 12-month minus 1-month total return. Besides, the authors collect the data for size, value, and momentum factor returns and well as risk-free monthly returns (based on 91-days treasury bills) for the Indian markets from the Indian Institute of Management, Ahmedabad online data library (CMIE, n.d.).
At the end of every month, the authors sort the universe of largest 500 stocks based on the volatility of monthly excess returns (over risk-free returns) of the past three years and construct equalweight risk quintile portfolios. For each quintile portfolio, the excess return for the month following the portfolio construction period is calculated. For the resultant time series, simple annualized average excess return, annualized standard deviation, compounded excess returns (CAGR), Sharpe ratios, ex-ante and ex-post betas, CAPM style one-factor alpha over equal-weight universe portfolio (a proxy for market portfolio) and corresponding t-statistics are calculated. Also, tracking errors and skewness for quintile portfolios are calculated.
To test the significance of the difference between the Shape ratio of each risk-quintile portfolio over the market portfolio, Jobson and Korkie (1981) test with Memmel's (2003) correction is used.
The authors calculate CAPM style alpha using the following one-factor regression model: ,,, , where R p,t is the return on portfolio p in period R f,t is the risk-free return in the period t.〈 p is the alpha of portfolio p. R m,t is market portfolio return in the period t. β p,m is the beta of portfolio p, and ε p,t is the idiosyncratic return of portfolio p in the period t.
Equal weight universe is used as proxy for market portfolio.
Fama-French (FF) and Fama-French-Carhart (FFC) models are further deployed to evaluate whether size, value, and momentum factors explain the low-risk anomaly. Small-Minus-Big (SMB), Value-Minus-Growth (VMG), and Winner-Minus-Loser (WML) are the proxies for size, value, and momentum factors (Fama & French, 1992;Carhart, 1997). IIMA online data library is used for monthly factor returns.
where R SMB , R VMG , and R WML represent the size, value, and momentum factor premiums, respectively, and β p,SMB , β p,VMG , and β p,WML represent factor loadings of portfolio p on size, value, and momentum factors, respectively.
The study applies bivariate analysis, a strong non-parametric technique using a double sorting approach, to separate low-risk effect from other effects. It is a robust technique and does not get impacted by time-varying exposure of low-risk and high-risk portfolios in three-and four-factor regressions. It allows us to control for the effect of one factor at a time to check the robustness of the low-risk effect. First, one ranks stocks on one of the control factors (size, value, momentum, ticket-size, liquidity) to create quintile portfolios, then one sorts the stocks based on volatility within each control factor quintile portfolio and constructs risk quintile portfolio to represent each quintile of control factor. For example, to control for the size effect, one first sorts stocks based on size to create size quintile portfolios. Next, the stocks are sorted based on volatility within each size quintile portfolios and then 20% least volatile stocks from every size bucket are combined to construct a lowrisk portfolio representing each size quintile and, hence, controlled for any size exposure. To con-trol for any concentrated sector exposure, low-risk and high-risk portfolios are created to represent each sector and, hence, capture only micro (stock level) low-risk effect while controlling for macro (sector level) effect. The study also reports median sector exposure for low-risk portfolios over the entire period, and the graphically illustrates the time-varying sector exposures to GICS sectors.
A version of the Herfindahl index for low-risk portfolios is used to come up with stock and sector concentration. The Herfindahl index is calculated as the sum of squared weights. Its inverse, N ranges from 1 for a portfolio with only one stock (sector) and N for a portfolio of N equally weighted stocks (sectors). Higher N shows lower concentration risk and vice versa.
Alternative approaches are developed to enhance the performance of low-risk investment strategy by plugging in the benefits of momentum investing to our pure low-risk portfolio. A 2×5 portfolio construction approach is used. At the end of each month, the stocks to high-momentum or low-momentum sub-universe are first assigned based on their past 12-month minus 1-month returns. Stocks above median momentum returns are assigned to high-momentum universe, and stocks below median momentum are assigned to low-momentum universe. Then risk-quintile portfolios from high-momentum stocks and separately from low-momentum stocks are constructed. The idea is to evaluate whether one can improve the performance of long-only, low-risk portfolio by adding momentum filter.
A scaled volatility measure is further proposed, which scales down the volatility for positive momentum stocks and scales up the volatility for negative momentum stocks. Such scaling helps systematically prefer low-volatility positive momentum stocks, and avoid low-volatility negative momentum stocks. This approach allows us to combine the benefits of risk anomaly and momentum effect while avoiding the stocks with the worst combination of high-risk and negative momentum: where momentum return is lesser of momentum return and 100%. The horse race is run between three different lowrisk portfolios: 1) pure low-risk portfolio; 2) low-risk portfolio constructed from the high momentum universe; and 3) low-risk portfolio constructed using scaled volatility sorting to compare performance and portfolio characteristics of alternative low-risk investment strategies. Table 1 reports the results of univariate analysis for resultant time-series of risk quintile portfolios constructed by sorting stocks on a 36-month look-back period and 1-month holding period. The time-series covers 144 monthly-rebalancing iterations on a rolling forward basis from January 2007 to December 2018. Panel A, reports the annualized simple excess returns, standard deviations, compounded returns, Sharpe ratios, Memmel's statistics for the difference of Sharpe ratio of risk-quintile portfolios over universe portfolio, ex-ante, and ex-post betas, and alphas for risk quintile portfolios sorted on volatility and beta with their corresponding t-statistics. Panel B

RESULTS
reports the performance of risk quintile portfolios in up and down markets over universe portfolio, maximum drawdown of risk-quintile and universe portfolio, tracking error, and the skewness of risk-quintile portfolios.
Panel A of Table 1 reports the main results of volatility sorted quintile portfolios. Portfolio P1 is the low-risk portfolio and Portfolio P5 is the high-risk portfolio. The simple average annualized excess return for low-risk portfolio (P1), high-risk portfolio (P5), and the equal-weight universe portfolio (EWI) are 13.28%, 11.8%, and 13.63%, respectively. While the low-risk portfolio has a higher return than the high-risk portfolio, the return increases as one moves from portfolio P1 to P3 with portfolio P3 return of 15.06% and portfolio P4 return of 14.73%. The compounded return for a lowrisk portfolio, high-risk portfolio and universe are 11.57%, 3.02%, and 9.66%, respectively. The long-short portfolio of the long low-risk stocks and short high-risk stocks (L-H) delivers 8.55% compounded annualized return. The third row of Panel A reports the annualized standard deviation of risk quintile portfolios. The annualized standard deviation of excess returns drops consistently as one moves from P1 to P5. The returns of low-risk portfolio (P1) are 40% less volatile than market portfolio. The Sharpe ratios of the lowrisk portfolio, high-risk portfolio, and market are Panel A of Table 2 reports three-factor and four-factor alphas for risk quintile portfolios constructed based on volatility sorting with their corresponding t-statistics. Panel B reports the regression coefficients of market size, value, and momentum factors for low-risk and high-risk portfolios. Together they report the strength of risk effect after controlling for size, value, and momentum effects. Table 2 reports the results for the three-factor Fama-French (3F) and four-factor Fama-French-Carhart (4F) regressions for risk quintile portfolios. Panel A reports 3F and 4F alphas of risk-quintile portfolios. 3F and 4F alphas for low-risk portfolio (P1) are 5.3% (t = 3.23) and 3.19% (t = 2.00), respectively, and are economically and statically significant; the same is true for high-risk portfolio (P5). 3F and 4F alphas for high-risk portfolio (P5) are -7.11% (t = -3.02) and -4.39% (t = -1.9), respectively, and are economically and statistically significant.
Panel B of Table 2 reports regression coefficients for 3F and 4F regressions on extreme risk quintile portfolios. The regression coefficients for 3F regression for low-risk portfolio (P1) shows that the size factor loading is 0.02 (t = 0.59) and value factor loading is -0.04 (t = -1.7), and similar factor loading for 4F regression shows that low-risk portfolio (P1) has insignificant size exposure and significant exposure   to value factor but with a negative sign. The factor loading of the low-risk portfolio on momentum factor is 0.11 (t = 4.62). The analysis of regression coefficients of 3F regression for high-risk portfolio (P5) shows that the size factor loading is -0.06 (t = -1.14) and value factor loading is 0.12 (t = 3.15). The momentum factor loading in the 4F regression for the high-risk portfolio is -0.14 (t = -4.17). Table 3 reports the annualized alpha and corresponding t-statistics of risk-quintile portfolios after controlling for size, value, and momentum, as well as ticket-size and liquidity. First, quintile portfolios are created by sorting stocks on the control variable and then by sorting on volatility within each quintile portfolio. The risk quintile portfolios are constructed to represent each quintile of control variable. It enables us to separate the alpha of risk-effect after controlling for the effect of other factors, one at a time. Table 3 reports the results of the double sorting approach to disentangle the low-risk effect from other known effects and factors. The double sort is a robust non-parametric technique that allows testing the robustness of low-risk effect after controlling for other factors, one at a time. It also captures any time-varying exposure of low-risk effect to size, value, and momentum factors, which are assumed to be constant in Fama-French and Fama-French-Carhart regressions.

Fama-French-Carhart style regression coefficient for low-risk (LV) and high-risk (HV) portfolios LV portfolio Coefficient t-value HV portfolio Coefficient t-value
Panel A of Table 3 reports CAPM style 1-factor alphas for risk-quintile portfolios with their statistical significance. This ensures that each risk-quintile portfolio has stocks representing all size buckets. Such portfolios are controlled for size exposure. One follows the same process to control for value and momentum effects and other variables such as liquidity and unit stock price (ticket size).
The alpha for low-risk portfolio after controlling for size effect is 5.63% (t = 3.34), where the corresponding alpha for high-risk portfolio is -7.53% (t = -3.18). The alpha for the low-risk portfolio is large, positive, and statistically significant, whereas the alpha for high-risk portfolio remains large, negative and statistically significant after controlling for size effect. Panels B and C report alphas for risk quintile portfolios controlled for value and momentum factors, respectively, and results are similar. Alphas for low-risk portfolio are large and positive, whereas for high-risk portfolios are large and negative. All are economically and statistically significant. Table 3 report alphas for risk quintile portfolios after controlling for liquidity (measured by monthly turnover) and ticket size (measured by unit stock price). The results show large positive alphas for low-risk portfolios and large negative alphas for high-risk portfolios.  Table 4 reports the performance of sector-neutral low-risk and high-risk portfolios. The stocks are first assigned to one of the GICS sectors, and then stocks within a sector are sorted based on volatility. The low-risk (high-risk) portfolio is constructed from all the stocks with below median (above median) volatility from each sector. The table further reports the ex-post beta, annualized alpha and corresponding t-statistics, simple and compounded returns, standard deviation, Sharpe ratio, and skewness for low-risk and highrisk portfolios. Table 4 reports the results for sector controlled low-risk and high-risk portfolios. The stocks are first assigned to one of eleven GICS sectors, and then within each sector, stocks are assigned to either low or high-risk bucket with median volatility breakpoint. One then creates a low-risk (high-risk) portfolio by pulling together low-risk (high-risk) stocks from each sector to create sector-neutral low-risk (high-risk) portfolios, and controls for sector concentration risk of lowrisk portfolio in this manner. The sector-controlled low-risk portfolio delivers a positive alpha of 3.01% (t = 2.41), whereas high-risk portfolio delivers a negative alpha of -2.86% (t = -2.18); both are economically and statistically significant, albeit with opposite signs. The simple annualized average returns for low-risk, high-risk, and market portfolios are 13.68%, 13.62%, and 13.63%, with corresponding standard deviations of 23.8%, 33.33%, and 29.84%, respectively. There is not much difference in simple returns of sector-neutral low-risk and high-risk portfolios. The difference is large between their compounded returns. CAGR for low-risk and high-risk portfolios is 10.85% and 7.41%, respectively. The Sharpe ratio of the low-risk portfolio is higher than that of both high-risk portfolio and market portfolio because of its less volatile returns.

Panels D and E of
Panels A, B, and C of Table 5 report performance statistics including annualized simple return, standard deviation, CAGR, Sharpe ratio, ex-ante, and ex-post betas, and CAPM style alpha for risk-quintile portfolios constructed from high-momentum and low-momentum universe, as well as based on scaled volatility measure. Table 5 reports the results of risk quintile portfolios constructed from universe of high-momentum and the low-momentum stocks. Panel A of Table  5 reports the results for risk-quintile portfolios from the universe of high-momentum stocks. The high-momentum universe portfolio itself has an alpha of 5.97% over the market portfolio and a Sharpe ratio of 0.67 compared to 0.46 for the market portfolio. The CAGR, Sharpe ratio and annualized CAPM style alphas for low-risk portfolios are 16.16%, 0.99%, and 10.6%, respectively. The corresponding statistics for high-risk portfolios are 8.97%, 0.43%, and -0.04%. Table 5 reports results for the risk-quintile portfolios constructed from the low-momentum universe. The low-momentum universe portfolio itself has a negative alpha of -5.97%, and a CAGR of just 3.54% and Sharpe ratio of 0.28, all performance statistics are poor in comparison to market portfolio. All risk-quintile portfolios report negative alphas and lower Sharpe ratios with respect to market portfolio. The worst performing portfolio is the high-risk and low-momentum portfolio. The CAGR, Sharpe ratio, and annualized CAPM style alphas for high-risk portfolio are -3.69%, 0.15%, and -13.13%, respectively.

Panel B of
Panel C of Table 5 reports the results of low-risk portfolio (P1) and high-risk portfolio (P5) constructed based on volatility scaled by momentum (as explained in the methodology section). The results are very similar to Panel A. Low-risk port- folio results in a higher CAGR of 17.64% comparable to 16.16% in the low-risk, high-momentum portfolio in Panel A. However, with little higher volatility and, hence, lower Sharpe ratio. The alpha of the scaled volatility based low-risk portfolio is 10.87%, similar to 10.6% of low-risk portfolio filtered for high-momentum. The erosion in the performance of high-risk portfolios is comparable in both approaches. Table 6 reports sector concentration N score, maximum weight, and the corresponding sector in a given month during the sample period. The table further reports one-way annual churn required to implement the investment strategy like volatility-sorted, beta-sorted, high-momentum, and scaled volatility-sorted low-risk investment portfolios, as well as a broad-based value-weighted market index, NSE 500. 2 In addition to results presented here, long-only, low-risk portfolios have been constructed using downside volatility as risk-measure, and inverse-volatility and inverse-beta as portfolio weighting schemes and the results show that low-risk effect is robust to the choice of riskmeasure and portfolio weighting scheme. Table 6 and Figures 1a, 1b, 1c, and 1d report the portfolio characteristics of pure and enhanced low-risk strategies discussing sector concentration and the one-way turnover required for these strategies 2 .
The major worry surrounding low-risk investment strategy is that it exposes the portfolio to concentrated exposure to a few sectors such as utility and real estate. Hence, it can create undesirable idiosyncratic sector concentration risk that can lead to sharp portfolio decline. Figure 1 provides the graphical representation of time-varying sector exposure for volatility sorted, beta sorted, scaled volatility sorted, and volatility sorted high-momentum universe, long-only, low-risk portfolios. It is evident from the results of table 6 that the sector N score for all versions of volatility strategies is approximately 7, whereas the N score for NSE 500  index, The N score for the most broad-based value-weighted market index is 5.5. The N score of 11 means the portfolio represents all the eleven sectors equally, and the N score of 1 means the portfolio represents only one sector, as explained in the methodology section. For example, the latest weight of the financial sector in the NSE 500 index is 37%, whereas, at no point in the entire study period, any of the low-volatility strategies has sector exposure over 31%.
Note: Figures 1a, 1b, 1c, and 1d report time-varying sector profile of low-risk portfolio constructed using volatility sorting, beta sorting, volatility sorting from high-momentum bucket, and scaled-volatility sorting.  It is evident from the results in Panel A of Table 1 that there is no clear relationship between risk and return. The simple annualized excess returns for risk-quantile portfolios initially increase and then decrease. However, the expected positive risk-return relationship turns on its head for compounded returns. The CAGR increases (exception: 2 nd to 3 rd quintile) as one moves from low-risk portfolio to high-risk portfolio. The standard deviation of risk quintile portfolios increases monotonically as one moves from low-risk to high-risk portfolio, and the volatility of a high-risk portfolio is more than double that of low-risk portfolios. The volatility drag has a large negative impact on high-risk portfolios and leads to negative risk-return relationship on a CAGR 3 basis. Both higher return and lower volatility contribute to the highest Sharpe ratio for low-risk portfolio than other risk quantile portfolios and market portfolio. Ex-post beta too monotonically increases as one moves from low-risk to high-risk portfolio, and the same trend is visible for ex-ante beta. This implies that risk is sticky and low-risk portfolios continue to remain low-risk and high-risk portfolios continue to remain high-risk portfolios. The CAPM style alpha for volatility sorted low-risk portfolio is large and positive, whereas it is large and negative for high-risk portfolios. Both are economically and statistically significant and imply a negative risk-return relationship. The CAPM alphas for beta sorted risk-quintile portfolios show similar trends, except alpha for a low-risk portfolio for beta sorted, is not as large and significant as volatility sorted low-risk portfolio.
Low-risk (high-risk) portfolio tends to underperform (outperforms) during rising markets and outperforms (underperforms) during falling markets. However, the low-risk portfolio outperformance in falling markets is much stronger, resulting in a lowrisk portfolio's superior performance. Maximum drawdown is the real measure of risk for any investor and low-risk portfolio has much lower drawdown than both high-risk portfolio and market portfolio and, hence, the success of low-volatility investment 3 CAGR = Simple return -0.5 × variance of returns, hence given the level of simple return, higher the variance of returns, lower the CAGR. 4 An investment losing 50% in a given period needs to gain 100% in the following period to breakeven. In contrast, an investment losing 80% in a given period needs to gain 400% in the following period to breakeven. strategy lies in winning by losing less 4 . As Baker, Bradley, and Wurgler (2011) reported, the fund managers with relative performance mandate cannot afford large tracking errors, resulting in flattened risk-return relationship. Both low-risk and high-risk portfolios have large tracking errors. It explains low preference for low-risk yet high-tracking error portfolio by fund managers with relative performance mandate. However, such investors should also avoid high-risk portfolio as that too has large tracking error. Perhaps fund managers with call option like compensation structure and investors with a preference for lottery-like payoffs look for high-risk stocks for their positive skewness and avoid low-risk stocks for their negative skewness in return distributions.

Is the low-risk effect distinct?
As reported in Panel A of Table 2, three-factor and four-factor alphas for low-risk (high-risk) portfolios are positive (negative) and economically and statistically significant. This implies that size, value, and momentum cannot explain large positive (negative) residual alpha for low-risk (high-risk) portfolio and, hence, low-risk effect is a distinct effect. Analyzing factor loadings of three-factor and four-factor models reveals that low-risk portfolio has a clear tilt towards growth and winner stocks, whereas high-risk portfolio has a tilt towards value and loser stocks. The growth tilt of low-volatility portfolios is different from the value tilt of low-risk portfolios seen in the developed markets. However, Chow, Hsu, Kuo, and Li (2014) report the growth tilt of low-risk portfolios in the emerging markets. Both low-risk and highrisk portfolios do not show any tilt on size factor, which is due to the selection of the largest 500 listed stocks on NSE.

Is low-risk effect robust
to time-varying exposure to classic factors, liquidity, and ticket-size exposure?
The double sorting is a strong non-parametric approach to detangle the low-risk effect from other effects, one at a time. The three-factor and four-fac-tor regressions do not capture any time-varying exposure to size, value, and momentum factors; double sorting tides over that potential limitation as well. The results in Panels A, B, and C of Table  3 establish that large-positive (small-negative) alpha of low-risk (high-risk) portfolio persist after controlling for size, value, and momentum effects. The results in Panels D and E of Table 3 suggest that large-positive (large-negative) alpha of lowrisk (high-risk) portfolio persists after controlling for liquidity and ticket size exposure and, hence, the low-risk effect is truly distinctб and one cannot fully explain it by systematic exposure of extreme risk-quintile portfolio to liquidity and ticket-size.

Is low-risk effect a concentrated macro (sector-level) or micro (stock-level) bet?
The results from Table 4 give interesting insights. As Baker, Bradley, and Wurgler (2011) reported, low-risk anomaly is a combination of macro (sector level) and micro (stock level) effect, and, hence, portfolio of low-cost sector exchange-traded funds (ETFs) cannot fully capture it. The approach of constructing sector-neutral low (high) risk portfolios controls the volatility effect of the macro (sector level). It captures pure micro (stock level) effect, and significant positive (negative) alpha for sector-neutral low-risk (high-risk) portfolio implies that the low-risk effect is strong and significant after controlling for macro effect, albeit of smaller magnitude.

4.5.
Can one enhance the performance of low-risk investment strategy by adding momentum booster to it?
The power of adding momentum filter while constructing low-risk investment strategy is visible in results presented in Panels A and B of Table 5. All risk quantile portfolios constructed from universe of high-momentum stocks deliver superior absolute and risk-adjusted performance over corresponding pure risk-quintile portfolios (see Table  1). The high-momentum universe portfolio outperforms low-momentum universe portfolio by a huge margin. The combined benefit of high-momentum and low-risk is visible in the performance of low-risk, high-momentum portfolio. The lowrisk, high-momentum portfolio (Panel A, Table 5) delivers close to 5% higher CAGR than pure lowrisk portfolio (Panel A, Table 1) without any increase in volatility. A momentum booster is added to pure low-risk investment strategy. On the other hand, the CAGR of low-risk portfolio constructed from low-momentum universe is close to 4% lower than pure low-risk portfolio and is more volatile. It is observed that the performance of highrisk portfolio further deteriorates when combined with low-momentum. The CAGR for high-risk, low-momentum stocks is negative in about 7% lower than pure high-risk portfolio. It implies that low-risk, high-momentum stocks are ideal for long only investors, high-risk, low-momentum stocks are the perfect candidates for shorting. The results are similar using alternative approach to add momentum booster to low-risk investment strategy. Low-risk (high-risk) portfolio constructed based on scaled volatility measure delivers superior (inferior) absolute, as well as risk-adjusted returns over pure low-risk (high-risk) portfolio. In sum, notwithstanding the approach, combining momentum effect with low-risk effect results in enhancing performance of low-risk investment strategy.
4.6. Portfolio characteristics of pure and enhanced low-risk investment strategies Table 6 and Figure 1 show that low-risk portfolio is not a concentrated portfolio and the sector concentration of low-risk portfolio is actually lower than the most broad-based value-weighted market index in India, NSE 500. Hence, low-risk portfolio does not lead to any undesirable sector concentration and a resulting tail risk associated with such concentration. Contrary to developed markets where the utilities and real estate dominate minimum variance portfolios, Indian markets have hardly any exposure to utilities and real estate sectors. It is spread across health care, financials, consumer staples, industrials, and materials and has small exposure to real estate and utility sectors.
Turning attention to the monthly portfolio churn requirement, the average one-way monthly portfolio churn required for pure low-risk strategies is about 5%, which means close to 100% of two-way churn for the year. The monthly churn needed for enhanced strategies is close to 10% and the annual two-way churn of close to 200%. However, as reported by Chow, Hsu, Kuo, and Li (2014) and implemented by MSCI minimum volatility index, independently imposing an explicit limit on annual turnover does not dilute exposure to low-risk effect. Besides, in the case of Indian markets, there are several discount brokerage houses now offering genuine zero brokerage services. The transac-tion costs have come down to a maximum of 0.2% per transaction, including regulatory charges, security transaction tax, and impact cost. So, even 200% of an annual churn causes a performance drag of only 0.4% per annum.
In sum, low-risk investment strategy requires little churning and remains robust after implementing turnover constraints. It is easily implementable with little cost.

CONCLUSION
In conclusion, strong evidence for low-risk effect with low-risk stocks outperforms high-risk stocks both on an absolute and risk-adjusted basis is found. The effect is more pronounced for compounded returns than simple returns. The low-risk portfolio delivers high-positive alpha, whereas high-risk portfolio delivers high-negative alpha. The low-risk effect remains robust after controlling for size, value, and momentum factors. The low-risk portfolio shows systematic growth-tilt as against value-tilt observed in developed markets. The low-risk anomaly remains robust after controlling for ticket-size and liquidity exposures. The low-risk effect remains robust after controlling for sector exposure, which means the low-risk effect is both macro (sector level) and micro (stock level) effect. Contrary to developed markets, where low-risk portfolios have significant sector concentration towards real estate and utility sectors, low-risk portfolio in Indian markets is less concentrated, and the sector concentration is even less than the broad-based market index. The performance of low-risk investment strategies improves significantly by eliminating low-risk but poor momentum stocks and focusing on constructing low-risk investment strategies that systematically prefer high-momentum stocks. Such improvement in performance is robust to alternative approaches. It is established that while the low-risk effect is universal, the characteristics of low-risk portfolios are different in different markets. The authors further show that the performance of simple low-risk investment strategies can be enhanced by integrating the benefits of momentum effect into low-risk effect.