Indexing CNX NIFTY 50 Momentum Effects

Abstract

The empirical literature indicates that momentum-style investing is a more effective approach than value-based or growth-based strategies. To confirm this, this article makes an attempt to construct a Momentum Index for the Indian equity market. The CNX NIFTY 50 Momentum Index is designed by calculating the volatility and volume-adjusted Momentum Index for each security in the CNX NIFTY 50 Parent Index. The estimated Momentum Index returns are compared with the CNX NIFTY 50 Index in terms of volatility, Sharpe Ratio and Treynor Ratio. Using VAR methodology, and macroeconomic, firm-specific factors which influence the momentum, index returns are analysed. This study also examined the Fama–French unconditional CAPM by including the Momentum Index return as the fourth factor alongside price–earnings, price–book ratio and dividend yield in estimating excess market returns.

JEL: G11, G12, G14

Keywords

Momentum Index Momentum Score CAPM Clustering

1. INTRODUCTION

Investors have an inclination towards maintaining low-to-medium volatility in their investment portfolios. It is observed that investors make huge profits when investments are made in high liquid and volatile assets. Momentum can help investors exploit this volatility and translate it into extraordinary returns termed as ‘momentum profits’ or ‘momentum returns’. Momentum is the one of the less-exploited market irregularities. It is the tendency of investments, in every market and asset class, to exhibit persistence in their relative performance for some time period. When applied to stock selection, momentum (like value or growth) indicates relative performance amongst stocks and does not signify overall trends in the market. This mechanism works irrespective of whether the broader market is in an upswing or downswing. Momentum is used as a powerful investment tool to identify securities expected to outperform the broader market. It is also negatively correlated to value investing, making it an effective diversification component. Irrespective of investment strategies, technically all investors can expect to improve risk-adjusted returns by considering momentum an investment strategy. In the recent past, the effectiveness of momentum and contrarian strategies has been discussed at length. A contrarian investment strategy earns excess risk-adjusted returns when investors overreact to news, whereas a momentum strategy earns excess risk-adjusted returns when investors under-react. However, identification of momentum stocks is a primary requirement for exploiting momentum strategy.

Stocks indices have played an important role in asset allocation. Stock markets all over the world at present have indices for cash and derivative segments. Indices represent stocks having the lowest impact cost, high liquidity, high market capitalisation and possibly good returns in the medium term. It is possible to construct Momentum Indices with stocks having a high momentum. This article has made an attempt to construct a Momentum Index using stocks which are included in NIFTY 50 Index of National Stock Exchange of India.

2. LITERATURE REVIEW

The profitability of momentum-based trading strategies was first documented by Jegadeesh and Titman (1993) when they examined trading strategies in the form of winner and losers so as to articulate momentum in the US stock market. They reported that a zero-cost momentum strategy of buying past winners and selling past losers generated significant average profits. The existence of a momentum effect in stock returns, that is, stocks that have out-performed (under-performed) the average stock return in the past few months tend to perform better (worse) than the average stock return over the subsequent few months. Similar evidence is also reported by Rouwenhorst (1998) for stocks traded on European markets. Grundy and Martin (2001) also used the collective return as criterion for ranking stocks into winner and loser portfolios. Chordia and Shivakumar (2002) attributed the profits arising due to momentum to common factors or macroeconomic factors and firm-specific information.

On the other hand, there have been contrasting interpretations about the potential causes of the momentum effect. The explanation given by Tversky and Kahneman (1986) and De Bondt and Thaler (1985) was based on a study about market participants’ over-reaction or under-reaction to information, which reflected in the stock prices. Literatures have explained the consistency of ‘price momentum’ through investor behaviour. Various researchers (Barberis et al., 1998; Daniel et al., 1998; Hong and Stein, 1999) have put forward theoretical (behavioural) models of investor behaviour and suggested that price momentum is consistent with cognitive biases in the way investors interpret imperfect information. Behavioural models rely on psychological factors, such as, representativeness, conservatism, overconfidence and self-attribution to explain momentum profits.

In spite of the significant research on momentum, researchers have no clear idea why the mechanism works so well. In the process of explaining stock returns and performance, portfolio managers generally turn to the 3-factor Fama and French (1992, 1996) or the 4-factor Carhart (1997) model. This is due to the enormous support provided by the substantial body of research indicating that factors like market return, firm size, valuation and momentum are essential drivers of stock returns. In a recent study, Bandarchuk, Pavel and Hilscher (2011) re-examined some of the factors which have earlier been shown to impact momentum in the equities market. The factors include analyst coverage, liquidity, price level, size, credit rating, book-to-market and turnover. The study established that all these factors are proxies for extreme past returns or high volatility. The effect of extreme past returns and volatility remained present and statistically significant. The evidence was consistent with Vayanos and Woolley (2010), who attributed a rational explanation of momentum to high idiosyncratic volatility and in turn extreme past returns. They proposed a rational theory of momentum and reversal based on delegated portfolio management.

Wang and Kochard (2010) presented active strategies for combining value and momentum strategies in a tactical asset allocation (TAA) framework. The study refined the basic yield approach to valuation by standardising the value signal using Z-scores. The standardisation approach helped to directly compare the valuation measure across asset classes as well as offered an insight into each asset class’s absolute valuation by its own standard. This combined model took advantage of both short-term momentum effects and long-term mean-reversion in valuation to achieve superior overall portfolio performance.

Each of the aforesaid factors explained in the 3-factor or 4-factor model, excluding momentum, has a standard market alternative in the form of a benchmark stock market index (e.g., a market cap weighted index, large and small cap indices, value and growth indices, volatility indices). The missing component in the market is the Momentum Index. This is predominantly important considering the large numbers of investors following contrarian and momentum strategies to beat benchmark index returns. The same is true of mutual funds. Grinblatt, Titman and Wermers (1995) found that 77 per cent of the 155 mutual funds in their sample engaged in momentum investing. The finding was in line with Menkhoff and Schmidt (2005) who used survey data to illustrate that momentum and contrarian strategies were common among German fund managers. Even though there is extensive use of these strategies, it is surprising that no exclusive momentum and contrarian indices are currently calculated by any of the major index providers.

One possible reason for the absence of momentum and contrarian indices in the retail domain was because of the way momentum portfolios were classically constructed. These classical investment strategies were impractical for investors for the following reasons. First, these strategies required shorting of assets, which a large number of investors were either unable to or were not entitled to do. Second, momentum portfolios resulting from empirical studies were often difficult to replicate due to the illiquidity of the constituents and high turnover. As these strategies tended to have a high turnover, this in turn resulted in very high transaction costs. Consequently, there was an obvious necessity for momentum and contrarian indices. Such indices were needed to provide insightful performance benchmarks for active managers following these strategies. The introduction of the AQR Momentum Index and MSCI Momentum Index represented a pivotal development in the wide acceptance of momentum as an investment strategy. AQR Capital Management in 2009 developed an index methodology that captured momentum in large, mid-cap and small-cap US indices in an intuitive and transparent way. The universes were screened using liquidity, volatility and trade volume criteria. Similarly, MSCI in 2013 designed the Momentum Index to reflect the performance of an equity momentum strategy by focusing on stocks with high price momentum. The MSCI Momentum Index calculates a risk-adjusted price momentum score for each security in the MSCI Parent Index and selects the top securities with the highest momentum scores. The eligible securities were weighted in proportion to their free float market capitalisation weight and momentum scores.

The present article has made an attempt to construct an innovative class of investable momentum and contrarian stock market index that separate the benchmark index, such as the CNX NIFTY50 index of the National Stock Exchange of India. The NIFTY50 Momentum Index can be used as benchmarks for momentum investment strategies, or as the basis for financial products such as exchange traded funds and structured products.

3. INDEX CONSTRUCTION METHODOLOGY

3.1 Volume-volatility Adjusted Holding Period Return

The sample space for selection of stocks is the CNX NIFTY. The objective behind selecting CNX NIFTY is to provide an opportunity set with sufficient liquidity and volume having the minimal impact cost in the market. To test whether return reversal or return continuation exists in the Indian stock market, a strategy is used to select stocks on the basis of their returns over the past J months (i.e., the formation period) and holding them for K months (the holding period). This is called the J × K strategy. For momentum portfolio selection the study proposes to follow a 3 × 3 strategy. It starts with a calculation of the three-month formation period returns P_i for each stock i present in the CNX NIFTY50.

P_{i} ((1 M_{i 1}) * (1 M_{i 2}) * (1 M_{i 3})) 1

Where P_i : total formation period returns of security i;

M_i1: first month formation period returns of security i;

M_i2: second month formation period returns of security i;

M_i3: third month formation period returns of security i.

The formation period returns for each security i computed above is adjusted with its corresponding three-month formation period volatility to obtain the volatility adjusted returns.

Volatility {AdjP}_{i} P_{i} *_{i}

where

Volatility AdjP_i: volatility adjusted formation period returns

σ_i: three-month formation period returns volatility of security i

The volatility adjusted formation period returns for each security i is multiplied with its formation period end-date traded volume so as to factor in the momentum effect of the corresponding security. The model is described later:

\begin{matrix} Momentum {Value}_{i} Volatility {AdjP}_{i} * {Vol}_{i} \\ P_{i} *_{i} * {Vol}_{i} \end{matrix}

3.2 Momentum Z-score and Momentum Weight

The volatility and volume-adjusted momentum values computed above are standardised into momentum Z-scores using the standard normal distribution. Stocks for which the standardised scores (Z_i) lie between −3 to +3 are selected to constitute the Momentum Index. For a given rebalancing effective date, securities eligible for inclusion in the NIFTY Momentum Index are decided on the basis of the Z scores (−3σ to +3σ). The momentum score for each security i is computed from the momentum Z-score as follows:

\begin{matrix} {MScore}_{} (1 Z), if Z > 0 \\ (1 {Z)}^{1}, if Z < 0 \end{matrix}\}

For a given rebalancing effective date, all the securities eligible for inclusion in the Momentum Index are weighted by the product of their weight in the parent index, that is, the CNX NIFTY50, and their respective momentum score.

{MW}_{i} ({MScore}_{i} * W_{i})

Where MW_i: expected weight of the selected stock in the Momentum Index

MScore_i: momentum score of security i

W_i: weight of the security i in the parent index CNX NIFTY50

3.3 Estimation of the Momentum Index

The Momentum Index value during each day of the holding period is defined as a sum of the products of each selected security i’s daily market capitalisation with the security’s expected weight in the Momentum Index.

{MI}_{t}_{i 1}^{n} ({MCap}_{i} * {MScore}_{i})

Where MI_t: Momentum Index value on day t of the holding period

MCap_i: market capitalisation of security i on day t

MScore_i: momentum score of security i

n: total number of securities selected to form the Momentum Index

The Momentum Index would develop from the onset of the holding period and it would continue till the rebalancing date. On the rebalancing date, the stock selection process again starts as per the aforementioned methodology and a new Momentum Index again appears.

3.4 Maintaining the CNX NIFTY50 Momentum Index

In India significant information on macroeconomic variables (GDP and its composition) and corporate specific disclosures (dividends and abridged balance sheets) is published on a quarterly basis. Investors rearrange their portfolio as per the reaction of stocks to this information. We propose to re-balance the Momentum Index on a quarterly basis. The Momentum Index would be rebalanced on the close of the last day of business for the previous quarter for June, September, December and March, as per quarterly index rebalancing.

4. MOMENTUM INDEX WEIGHTS AND RETURNS

The study covers the 14 sectors of the CNX NIFTY 50, which are auto, banks, capital goods, cement, finance, FMCGs, IT, metals and mining, oil and gas, pharmaceuticals, realty, telecom and others (utilities and paints). The quarterly performance of the CNX NIFTY 50 parent index and the CNX NIFTY 50 Momentum Index is plotted for the four quarters across the period, July 2012 to September 2013. The shift in the sectoral weights constituting the respective indices is also shown. It can be noted that the assignment of momentum weights based on momentum scores results in shifting of the weights from one sector to another, based on their formation period volatility, formation period returns and the trading volume. It is observed that due to a change in the weights of the constituents, the CNX NIFTY 50 Momentum Index in general performs better than the parent CNX NIFTY 50. For the holding period October–December 2012, the Momentum Index has a higher exposure to sectors like auto, banks, capital goods, finance and pharmaceuticals.

Table 1
Index Weight: Quarter, October–December 2012

Index Weight: Quarter Oct–Dec 2012

Sector Nifty-50 MI

Auto 8.65 11.57

Banks 17.47 21.15

Capital goods 4.86 10.73

Cements 2.20 2.35

Finance 6.96 8.77

FMCG 12.40 10.40

IT 16.24 10.67

Metals and mining 6.49 3.47

Oil and gas 12.03 8.69

Others 1.62 0.98

Pharmaceutical 5.45 6.80

Power 3.07 2.28

Realty 0.53 1.61

Telecom 2.03 0.54

Index Weight: Quarter Oct–Dec 2012
Auto	8.65	11.57
Banks	17.47	21.15
Capital goods	4.86	10.73
Cements	2.20	2.35
Finance	6.96	8.77
FMCG	12.40	10.40
IT	16.24	10.67
Metals and mining	6.49	3.47
Oil and gas	12.03	8.69
Others	1.62	0.98
Pharmaceutical	5.45	6.80
Power	3.07	2.28
Realty	0.53	1.61
Telecom	2.03	0.54

Source: The Nifty-50 Index Weight, NSE India Sectoral Weight, and MI Sectoral Weight have been computed by the authors.

Together these sectors constitute almost 60 per cent of the weightage in the Momentum Index compared to a 44 per cent weightage in the NIFTY-50 Index. For the same period, in the Momentum Index, weightage in sectors like FMCG, IT, metals and mining, and oil and gas has been significantly reduced to 33 per cent compared to 47 per cent in the NIFTY-50 Index. During the January–March 2013 holding period, the Momentum Index increased its exposure in the auto sector from 12 per cent to 17 per cent and reduced the weightage of the IT sector from 11 per cent to 6 per cent. It is observed that buying past winner sectors and selling past loser sectors continues to generate significant momentum profits. This finding is in line with Jegadeesh and Titman (1993) who documented strategies to buy stocks (sectors) that have performed well in the past and sell stocks (sectors) that have performed poorly in the past to generate significant positive returns over a three-month holding period.

For the holding period April–June 2013 a momentum reversal trend is noted. The Momentum Index has reduced weightage of sectors like auto and banks which had been past winners, whereas exposure in sectors like FMCG, IT and oil and gas which had been past losers has been significantly increased to 45 per cent compared to 30 per cent and 23 per cent in the previous two quarters respectively, indicating a momentum reversal trend.

Table 2

Index Weight: Quarter January–March 2013

Index Weight: Quarter Jan–March 2013
Sector	Nifty-50	MI
Auto	8.65	16.60
Banks	17.47	22.64
Capital goods	4.85	2.92
Cements	3.18	2.08
Finance	6.96	8.83
FMCG	12.40	9.14
IT	16.24	6.43
Metals and Mining	4.41	8.12
Oil and Gas	12.03	7.70
Pharmaceutical	6.55	5.08
Power	3.07	2.37
Realty	0.53	−0.68
Telecom	2.03	7.64
Others	1.63	1.12

Source: The Nifty-50 Index Weight, NSE India Sectoral Weight, and MI Sectoral Weight have been computed by the authors.

Table 3

Index Weight: Quarter April–June 2013

Index Weight: Quarter April–June 2013
Sector	Nifty-50	MI
Auto	8.65	6.65
Banks	18.31	17.05
Capital goods	4.02	3.70
Cements	2.63	2.52
Finance	6.96	6.95
FMCG	12.40	13.81
IT	14.59	18.67
Metals and mining	4.92	2.97
Oil and gas	12.03	11.98
Pharmaceutical	6.54	6.85
Power	3.07	2.72
Realty	0.53	0.60
Telecom	2.03	1.75
Others	3.32	3.78

Source: The Nifty-50 Index Weight, NSE India Sectoral Weight, and M I Sectoral Weight have been computed by the authors.

In the concluding quarter July–September 2013, exposure in sectors like FMCG and oil and gas continued to be raised, whereas weightage in past winner sectors like auto, banking, capital goods and pharmaceuticals has been significantly reduced compared to the previous quarters. This phenomenon indicates the continuation of the momentum reversal trend.

Table 4

Index Weight: Quarter July–September 2013

Index Weight: Quarter July–Sept 2013
Sector	Nifty-50	MI
Auto	8.65	8.86
Banks	18.31	16.29
Capital goods	4.02	3.36
Cements	3.19	2.67
Finance	6.96	6.91
FMCG	12.40	16.98
IT	14.59	10.08
Metals and mining	4.92	3.74
Oil and gas	12.03	17.83
Pharmaceutical	6.54	6.00
Power	3.07	2.71
Realty	0.53	0.12
Telecom	2.03	1.76
Others	2.77	2.69

Source: The Nifty-50 Index Weight, NSE India Sectoral Weight and M I Sectoral Weight have been computed by the authors.

Figure 1 and Table 5 exhibit the performance of the Momentum Index and the parent CNX NIFTY 50 Index during the holding periods. It is evident that the holding period returns of the Momentum Index are superior to the Nifty-50 index.

Figure 1

Source: Holding period returns computed by the authors.

Table 5

Performance of Momentum Index

Quarter	Holding Period Return (in %)		Standard Deviation (in %)		Beta
Quarter	Nifty 50	MI	MI	Nifty 50	MI
Oct12–Dec12	3.26	3.76	0.76	0.67	1.10
Jan13–Mar13	−4.51	−0.07	1.17	0.70	1.14
Apr13–Jun13	−0.39	1.22	1.63	1.09	1.01
Jul13–Sep13	−1.11	0.23	2.27	1.58	0.92

Source: Holding period returns computed by the authors.

The holding period returns of the Momentum Index are more positive when the NIFTY returns are positive; and when the NIFTY returns are negative, the Momentum Index returns are less negative and in some cases even positive. The standard deviation values which are a measurement of volatility indicate that the Momentum Index returns are marginally more volatile than the benchmark Nifty-50 Index. The beta of the Momentum Index are comparably higher compared to the Nifty-50 when the Nifty-50 Index has positive returns and comparably lower than when the Nifty-50 Index has negative returns.

Table 6

Risk–Return Profile of Momentum Index

Quarter	Nifty-50 Index (in %)			Momentum Index (in %)
Sharpe Ratio	Treynor Ratio	Coefficient of Variation	Sharpe Ratio	Treynor Ratio	Coefficient of Variation
Oct12–Dec12	264.12	1.76	20.44	298.61	2.05	20.13
Jan13–Mar13	−859.18	−6.01	−15.51	−134.47	−1.37	−1739.39
Apr13–Jun13	−173.27	−1.89	−281.67	−17.39	−0.28	134.01
Jul13–Sep13	−164.78	−2.61	−142.69	−55.99	−1.38	986.22

Source: Values computed by the authors.

To understand the risk–return performance of the Momentum Index compared to the NIFTY-50 Index, the Sharpe Ratio and Treynor Ratio of the portfolios (NIFTY-50 Index and Momentum Index) are estimated. The Sharpe Ratio measures the risk-adjusted return from a stock or portfolio. The estimated Sharpe Ratio indicates that the Momentum Index is a better investment option.

The Treynor Ratio helps to evaluate the performance of the Index based on its systematic risk. In the Treynor Ratio, the investor looks at the beta of the portfolio (in this case the Index), that is, the degree of ‘momentum’ that has been built into the portfolio by the fund manager in order to derive the excess returns. High momentum or high beta (where beta is > 1) implies that the portfolio will move faster (up as well as down) than the market. As the Momentum Index has a higher Treynor Ratio than the NIFTY-50, it can be considered a better investment instrument when compared to the NIFTY-50 Index.

5. FACTORS INFLUENCING MOMENTUM RETURN

Based on the literature review, the following macroeconomic and firm-specific factors influencing the Momentum Index returns were identified and tested.

Macroeconomic factors: the Dow Jones Industrial Average Index, net foreign institutional inflows, Index Volatility of NSE (India VIX) and bank credit.

Firm-specific factors and factors affecting investor sentiment: dividend yield, price–earnings ratio and price–book ratio; the sentiment dummy takes the value 1 if the Nifty-50 return is positive and 0 if the Nifty-50 return is negative or zero.

Table 7
VAR Equation, Lag Order 1, Dependent Variable: Momentum Index

Coefficient Std. Error t-ratio p-value

Constant −0.148788 0.0775917 −1.9176 0.05639

Momentum Index (−1) −0.351918 0.0480743 −7.3203 <0.00001

Dow Jones Index Return (−1) −0.143111 0.0778035 −1.8394 0.06714

Bank Credit (−1) 0.0455602 0.0676135 0.6738 0.50109

Net FII (−1) −1.45161e−06 7.14824e−07 −2.0307 0.04342

Dividend Yield (−1) 0.0622097 0.0310354 2.0045 0.04618

Price–Earnings Ratio (−1) 0.000246649 0.00130963 0.1883 0.85078

Price–Book Ratio (−1) 0.0198922 0.0129612 1.5347 0.12621

Sentiment Dummy (−1) −0.00767702 0.00113363 −6.7720 <0.00001

Nifty Return (−1) 1.0359 0.0607227 17.0594 <0.00001

Mean Dependent Variable 0.000242 S.D. Dependent Variable 0.015361

Sum squared Residual 0.013683 S.E. of regression 0.007680

R-squared 0.759379 Adjusted R-squared 0.750045

F(9, 232) 55.01528 P-value(F) 1.15e-52

Rho 0.092199 Durbin–Watson 1.915575

	Coefficient	Std. Error	t-ratio	p-value
Constant	−0.148788	0.0775917	−1.9176	0.05639
Momentum Index (−1)	−0.351918	0.0480743	−7.3203	<0.00001
Dow Jones Index Return (−1)	−0.143111	0.0778035	−1.8394	0.06714
Bank Credit (−1)	0.0455602	0.0676135	0.6738	0.50109
Net FII (−1)	−1.45161e−06	7.14824e−07	−2.0307	0.04342
Dividend Yield (−1)	0.0622097	0.0310354	2.0045	0.04618
Price–Earnings Ratio (−1)	0.000246649	0.00130963	0.1883	0.85078
Price–Book Ratio (−1)	0.0198922	0.0129612	1.5347	0.12621
Sentiment Dummy (−1)	−0.00767702	0.00113363	−6.7720	<0.00001
Nifty Return (−1)	1.0359	0.0607227	17.0594	<0.00001
Mean Dependent Variable	0.000242	S.D. Dependent Variable	0.015361
Sum squared Residual	0.013683	S.E. of regression	0.007680
R-squared	0.759379	Adjusted R-squared	0.750045
F(9, 232)	55.01528	P-value(F)	1.15e-52
Rho	0.092199	Durbin–Watson	1.915575

Source: Values, Author’s computed.

The aforementioned factors, along with the Momentum Index series is put through a VAR process to understand their interrelationship. By minimising the AIC, the optimum lag length among the aforesaid variables has been identified. With an optimum lag-length of 1, the VAR equation is estimated (Table 7).

The VAR equation (Table 7), with the dependent variable the Momentum Index Series, indicates the significance of momentum-generating factors. Parameters like the Dow Jones Index, dividend yield, net FII investments and the sentiment dummy are found to be significant. The negative coefficients indicate a decline in the momentum returns which might be a result of domestic fund managers’ overreaction or negative sentiments associated with these variables.

5.1 The Impulse Response Function

To understand the response of the Momentum Index series to the change in factors, the earlier VAR equation is given a one-sigma shock for each factor.

The impulse response for a shock in dividends leads to an initial surge in Momentum Index returns for the first two days, followed by a sharp decline till the 18th trading day, after which it became flat (Figure 2).

With an impulse response shock in the Dow Jones Index, a downside is seen in Momentum Index returns, which lasts for about two trading days. The index returns increase sharply after the second trading day; the upside is equally steep and the positive returns accrued are equivalent to the negative returns witnessed during the initial two days. The effects of the shock end after the fifth trading day (Figure 3).

An impulse response shock in net FII inflows has a negative influence on momentum returns for the initial two days. A steep decline in returns is followed by an overreaction and positive sentiments associated with the FII investment phenomenon which results in positive returns on the subsequent trading day. This cycle continues for the next two trading days; the effects of the shock are not felt after the fifth trading day (Figure 4).

Figure 2

Source: Authors’ computation.

Figure 3

Source: Authors’ computation.

Figure 4

Source: Authors’ computation.

An impulse response shock in bank credit has a positive influence on momentum returns for the initial two days. A steep increase in returns is followed by an under-reaction and negative sentiment associated with the bank credit which results in negative returns on the subsequent trading days. This cycle continues for 18 trading days, after which the effects of the shock are not felt any more (Figure 5).

Figure 5

Source: Authors’ computation.

An impulse response shock in the price–book ratio has a positive influence on momentum returns for the initial two days. A steep increase in the returns is followed by an under-reaction and negative sentiments which result in negative returns on the subsequent trading days. This cycle continues beyond the 20 trading days (Figure 6).

An impulse response shock in the price–earnings ratio inflows has a negative influence on momentum returns for the initial two days. A steep decline in returns is followed by an overreaction and positive sentiments, which result in positive returns on subsequent trading days. After a few trading days, the effects of the shock disappear, and beyond the fifth trading day returns became flat (Figure 7).

5.2 Momentum Clustering: Factors Affecting Momentum Index Volatility

Given the persistent of volatility of the Momentum Index for prolonged periods, it can be assumed that the index volatility is clustered or that the momentum return is clustered.

Figure 6

Source: Authors’ computation.

Figure 7

Source: Authors’ computation.

The ARCH test for the daily Momentum Index return (Figure 8) indicates the presence of momentum clustering. The null hypothesis of no ARCH effect is rejected indicating the presence of alternative periods of high and low momentum return volatility. The persistence of momentum return clustering is further empirically examined with a GARCH (1, 1) model. The variance equation is estimated with independent variables like volume trade, net FII inflows, the Dow Jones Index and India VIX, besides past volatility in the form of GAR.

Figure 8

Source: Authors’ computation.

Table 8

ARCH Effect

Lags	Coefficient	Std Error	t-ratio	P-Value	Significance
0	0.0001	3.82744e-05	2.792	0.0057	***
1	0.424958	0.0659979	6.439	6.94e-010	***
2	−0.228426	0.0716097	−3.190	0.0016	***
3	0.138285	0.0727495	1.901	0.0586	*
4	0.161516	0.0738052	2.188	0.0296	**
5	0.0826209	0.0764452	1.081	0.2809
6	−0.0240906	0.0696557	−0.3459	0.7298
Null Hypothesis: No ARCH effect is present Test statistic : LM = 57.3034 P(Chi-square(6)>57.3034) = 1.58596e-010

Source: Values computed by the authors.

Table 9

GARCH (1, 1), Variance Equation, Dependent Variable: Momentum Index Return

Variable	Coefficient	Std Error	t-ratio	P-Value
Constant	−0.000114	6.61E-05	−1.7298	0.0837
ARCH(−1)	0.228450	0.099850	2.2879	0.0221
GARCH(−1)	0.363032	0.191970	1.8911	0.0586
Volume Trade	0.000106	4.49E-05	2.3567	0.0184
Net FII	−1.38E-08	6.07E−09	−2.2755	0.0229
Dow Jones Index	−0.000888	0.001631	−0.5444	0.5860
India VIX	1.15E-05	5.43E-06	2.12036	0.0340

Source: Values computed by the authors.

The results (Table 9) indicate that both the ARCH and GARCH effects are statistically significant which imply that the momentum returns are not only time varying but also persistent, as future return volatilities are being influenced by past volatilities. The study also found that the exogenous variables net FII, volume trade and India VIX are also contributing to the momentum returns clustering.

6. UNCONDITIONAL CAPM AND MOMENTUM RETURNS

The study examined the Fama–French unconditional CAPM by including momentum payoffs as the fourth factor alongside price–earnings, price–book and dividend yield.

R_{pt} R_{ft} c_{i 1} {DIV}_{t 1} c_{i 2} PE {}_{t 1} c_{i 3} {PB}_{t 1} c_{i 4} R_{it 1} e_{it}

Where:

R_pt – R_ft: excess returns of Index

R_it–1: momentum series on Index

DIV_t–1: dividend yield of Index

PE_t–1: price–earnings ratio of Index

PB_t–1: price-to-book value ratio of Index

The results (Table 10) indicate that along with price–earnings, price–book and dividend yield, momentum payoffs was also significant in deciding excess market returns.

Table 10
Cochrane-Orcutt: Observation Period; 1 January 2012 to 25 September 2013; Dependent Variable: Excess Market Return

Coefficient Std. Error t-ratio p-value

Constant −0.339 0.1673 −2.032 0.0432

Price–Earnings Ratio 0.0041 0.00603 0.6772 0.4989

Price–Book Ratio 0.123 0.04128 2.980 0.0032

Dividend Yield −0.0700 0.05637 −1.243 0.2152

Momentum Index Return 0.3779 0.01682 22.47 1.17e-06

Adjusted R-Squared: 0.7128F(4.237): 249.3560 (1.13e-83) Durbin–Watson: 1.83Rho: 0.971124

	Coefficient	Std. Error	t-ratio	p-value
Constant	−0.339	0.1673	−2.032	0.0432
Price–Earnings Ratio	0.0041	0.00603	0.6772	0.4989
Price–Book Ratio	0.123	0.04128	2.980	0.0032
Dividend Yield	−0.0700	0.05637	−1.243	0.2152
Momentum Index Return	0.3779	0.01682	22.47	1.17e-06
Adjusted R-Squared: 0.7128F(4.237): 249.3560 (1.13e-83)	Durbin–Watson: 1.83Rho: 0.971124

Source: Values computed by the authors.

7. CONCLUSION

This study has formulated a methodology for designing the CNX NIFTY Momentum Index to capture the momentum effects witnessed in the NIFTY-50 constituents. Based on the comparison of the risk–return performance (the Sharpe Ratio and Treynor Ratio) of the Momentum Index and NIFTY, it can be concluded that the Momentum Index performs better than the NIFTY both during the upside and downside phases. The better performance of the Momentum Index is attributed to the assignment of momentum weights based on momentum scores. This results in the shifting of weights from one sector to another based on their formation period volatility, formation period returns and the trading volume. This is in contrast to the traditional assignment of weights in the NIFTY Index based on market capitalisation. The Sharpe Ratio and Treynor Ratio also indicate that the performance of the Momentum Index is better than the NIFTY-50 Index. The VAR model results indicate that the Dow Jones Index, dividend yield, net FII investments and sentiment dummy significantly generate momentum. The GARCH test concludes that the Momentum Index returns are time-varying, clustered with prolong periods of high and low volatilities. The Dow Jones Index, trading volume, India VIX and net FII investments are exogenous variables which contribute to the momentum-return clustering. Momentum Index payoffs is also established as a fourth factor in the unconditional CAPM test.

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