Can Equity be Safe-haven for Investment?

Abstract

Popular investment choices such as fixed income, gold, and real estate have generated low returns over long horizons. Equity seems to have performed much better despite its inherent risk. Although, investors prefer safe-haven assets, they are increasingly moving to equities in search for better returns. We consider whether equity could be a safe-haven investment if chosen from quality stocks’ basket. We examine the safe-haven and hedging properties of the Nifty-50 constituent stocks over the period 2008–2020. To address this, we employ copula-based framework to model the dependence structure between stocks and five indices. We distinguish between safe-haven attributes and hedging features of the individual stocks. We show that the safe-haven properties of the Nifty-50 listed stocks are not as concentrated as gold but they show much low co-movement with the market. We call them pseudo–safe-haven as they are the safe-bets for investors seeking relatively safe-haven assets with impressive returns.

JEL Codes: G11, G12, G15

Keywords

Coronavirus volatility yield financial crisis co-movement portfolio

1. Introduction

The age-old wisdom of investing broadly in fixed income products (bonds, fixed deposits, pension accounts, etc.), gold, and real estate is still the most preferred choice among investors, especially the retail investors. These asset classes, in fact, have underperformed equity by a significant margin over the long horizon. If we consider inflation-adjusted returns, these assets often produce either very low or negative returns. Hence, they do not help investors in growing their wealth but slowly destroy it. Despite that, for a country such as India, which has one of the highest gross domestic savings (percentage of gross domestic product) rate among other emerging countries, citizens of India hold 77% and 11% of their assets in real estate (one of the most illiquid asset class) and gold, respectively, with just only 5% in liquid financial assets as per the Housing Finance Committee in 2017. A similar pattern holds for the other emerging and even most of the developed countries with a slight difference in the choice of their assets. The main reason is that investors are interested more in protecting the nominal value of our assets rather than allowing it to grow in a volatile market like equity. Intuitively, we always prefer safe-haven assets that could give capital protection.

More often than not, safe-haven assets are government securities, precious metals, oil, and certain currencies. Research on safe-haven properties of currencies (Ranaldo & Söderlind, 2010) document that Swiss Franc, Japanese Yen, and the Euro have had significant safe-haven attributes from 1993 to 2008. But instruments such as currency and oil are neither easily available nor preferred investment options for retail investors. The oil price has generated a compound annual growth rate (CAGR) of 4.6% from 2008–2009 to 2017–2018¹ while that for gold was a mere 1.5% (Nirmal, 2019), whereas the CAGR of Nifty for the last 10 years was 15% (Nathan, 2019). Though we can say that gold being a store of wealth is a reliable, risk-averse investment avenue (Van Hoang et al., 2016) and promises feasible trades, it does not yield returns as high as equity assets in comparison. While the returns from the real-estate sector in other countries are either negative or very low, in India it is around 8%. However, after the 2016 demonetization announcement, the real-estate boom has busted in India as it has generated only 2%–3% returns in the last 4 years.²

With continued fall of banks’ deposit rate, bond yields, and underperformance of gold, investors are presently looking for a better investment avenue with a mix of safety and returns. They are willing to take some amount of risk to generate decent returns. Association of Mutual Funds in India data show a 23% annual growth rate of assets under management in the equity segment in 2019. Moreover, this could be one of the best times to invest in the equity market due to a cheap valuation of stocks amid the 2020 coronavirus-led financial crisis (Varma et al., 2021). High liquidity is one of the major advantages of equity assets, unlike real-estate. However, not all stocks in equity markets generate good returns. The majority of stocks even struggle to generate positive returns over the long horizon. Further, if unlucky, an investor could even lose their whole capital in the equity market if they choose a basket of bad stocks. Therefore, the equity market portfolio needs to consist of good quality stocks, which could possibly generate decent returns with minimum risk (Das & Kayal, 2021). A good (if not the best) choice of a basket of quality stocks is the available large-cap index as most of the constituent stocks are the industry leader in their respective sectors, run by good management, and with a history of generating decent returns for the investors. With this in mind, we choose a basket of possibly quality stocks (i.e., constituent stocks of the market index) and test for their safe-haven and also the hedging properties in this paper.

Baur and Lucey (2010) refer to “safe-haven asset as having negative correlation with the stock market in the periods of extreme market declines and weak correlation on average with other asset classes offering diversification benefits,” whereas Kaul and Sapp (2006) define safe-haven assets as “an ideal venue to park money during periods of uncertainty.” In recent years with growing integration between global financial markets, there have been recurring incidents of financial crises of different magnitudes. They have had a prominent impact on portfolios and returns of different assets. Hence, cultivating an understanding of safe-haven assets with respect to equities is further important not only for retail investors but also for institutional and international investors.

India has one of the largest and vibrant financial markets around the globe. For our analysis, we pick Nifty-50, which is the benchmark based stock market index for the Indian equity market. We limit ourselves to only Nifty-50 for mainly three reasons: (a) we use it just for the representation purpose (it can be done with any other stock index of other countries); (b) we are more aware of the Indian markets, Indian companies, and their data, and hence, it becomes our preferred choice; (c) extending it for other countries in the same paper could be cumbersome as it involves extensive data work (explained in Section 3) and would make the paper unnecessarily clumsy with many large tables. In fact, we could not report all the tables (available upon request) we have due to space constraint.

Nifty-50 represents the weighted average of fifty Indian companies across thirteen sectors. We try to identify those stocks which that appear possibly immune (or less prone) to market fluctuations. Following the suit of literature such as Genest and Rivest (1993), Nelson (1999), de Melo Mendes (2005), Hu (2006), Patton (2009), and Lai et al. (2009), we identify the safe-haven and hedging properties of stocks of the companies listed under the Nifty-50 index using copulas. Though there are many empirical methods that identify dependency and co-movements such as vector autoregressive model and co-integration tests, owing to the non-linear dynamics of our return series, we rely on copula based models. In our analysis, we train a copula-based approach to test dependency across 250 index-stock pairs (50 stocks and 5 indices). Nguyen et al. (2016) created a new class of copula using existing ones such as Clayton, Frank, Gumbel, and Joe copulas to bring about a mixed copula. Christoffersen et al. (2012) discuss the dependency across stock markets for diversification purposes using an assortment of copulas. Using a similar approach, Avdulaj and Barunik (2015) and Zhua et al. (2014) explored the dependence structure of oil markets and different international stock markets. Aloui et al. (2013) used copulas to measure contagion risk in transition economies. In our work, we use the Student’s t-copula across all the 250 pairs as it adequately represents the dependence structure of index return series and individual stocks return series. Using a copula to model the dependency has several advantages. An appealing feature of this approach is that it allows us to model marginal distributions of the joint distributions separately while taking into account tail dependencies as well (Jondeau & Rockinger, 2006). It also observes the nonlinearities in the stock-index relationships as well as the empirical stylized facts of return distributions such as volatility clustering, fat tail behavior, and asymmetric impacts, while at the same time avoiding the drawbacks of the linear measures of interdependence.

We acknowledge that for any individual investors, it may be impossible to analyze and run this kind of econometric models in the process of choosing the right stocks. However, our work tries to complement the idea of choosing quality stocks explained in many popular investment books³ with academic backing.

Our study finds many substantial results. We find volatility clustering of returns as expected. We use generalized autoregressive conditional heteroskedasticity (GARCH), following Hu (2010), to model the mean and volatility. The marginal distributions prove to be robust based on the goodness of fit tests. Further, we establish the difference between hedging properties and the attributes of safe-haven. When a stock does not co-move with an index on average, that is, during regular market conditions, we resolve, following Lai and Tseng (2010), that the stock has hedging properties.

Our analysis shows that the safe-haven properties of the listed stocks are not as concentrated as gold or oil but they show much low correlation for an asset class such as equity. We use the term pseudo–safe-haven to denote such properties. The contribution of this study is dual. First, this article develops the idea of safe-haven investment (which provides decent returns with minimum risk) in an asset class-like equity. Second, it add to the literature of portfolio management by providing academic backup to the process of picking right stocks with one of best suited and relevant econometric models (copula to lay down the dependence structure, which is statistically well-grounded than linear correlation estimation). This study renders intriguing insights of the Indian stock markets and sheds light for institutional and retail investors seeking investor-friendly safe-haven assets, which could generate extra-ordinary profits and also safe-guard the investment during times of extremities.

This article is organized as follows: we present a brief review of the literature in Section 2. Section 3 describes the data and explains the methodology used in this work. In Section 4, we highlight the empirical observations, and we conclude in Section 5.

2. Literature Survey

It has been long-standing now that gold is a rational choice of investment in times of extreme market upheaval (Kayal & Maheswaran, 2021). This hypothesis was formally tested by Baur and Lucey (2010) by making the clear distinction between safe-haven and hedging properties of an asset. Reboredo (2013) propounded this idea further by contributing to the implications of such work for risk management. They find benefitting evidence of diversification and downside risk reduction having gold in a currency portfolio. Dee et al. (2013), Arouri et al. (2015), Beckmann et al. (2015), Wen and Cheng (2018), and Baur and Kuck (2019) explain extensively on the flight to gold phenomenon during turbulent markets and also against oil price fluctuations. Though taking refuge under gold during the extreme market is a behavioral bias (Baur & McDermott, 2016) stemming from the historical dimensions of gold as a currency and a store of value, Baur and Lucey (2010) find that the effect of gold as a safe-haven in a portfolio is short-lived. Hood and Malik (2013) observe volatility implied index (VIX) to be a superior hedging tool and a better safe-haven choice than gold for the period from November 1995 to November 2010. This work motivated us to check for the safe-haven properties of equities that run against the conventional wisdom.

In addition to gold, investors trust currencies that are usually considered low risk whose issuing governments are stable with strong, well-functioning economies among other reasons. For the period 1993–2008, Ranaldo and Söderlind (2010) find that Swiss franc and Japanese yen appreciate against the US dollar when there were adverse movements in the US financial markets. Fatum and Yamamoto (2016) accredit Japanese yen as the “safest” of safe-haven currencies as it stays robust irrespective of the prevailing market conditions. Most currency safe-havens work only in developed economies, as Beck and Rahbari (2011) established that dollars are better safe-haven for developed economies of Asia and Latin America whereas the Euro is the equivalent to European economies. Factors like net foreign asset position, which Habib and Stracca (2012) posit to be an indicator of exogenous vulnerability is shown to denote if a currency is a good safe-haven or not. Even the currencies of fast-growing, emerging countries such as China have not yet merited the status of safe-haven asset for their renminbi (Fatum et al., 2017). Further panoptic works that discuss the safe-haven attributes of currencies are Kaul and Sapp (2006), Fratzscher (2009), McCauley and McGuire (2009), Kohler (2012), Hoffmann and Suter (2010), Botman et al. (2013), Coudert et al. (2014), De Bock and de Carvalho Filho (2015), and Grisse and Nitschka (2015).

Of late, with the advent of cryptocurrencies, investors have shown interest in digital currencies like Bitcoin, mainly for their efficiency and tractability (Kayal & Balasubramanian, 2021; Kayal & Rohilla, 2021). Since such instruments are in their incubation period, despite their weak safe-haven properties, Feng et al. (2018), Wu et al. (2019), Smales (2019), and Shahzad et al. (2019) suggest refraining from classifying Bitcoin as a safe-haven. Inclined to such notable shortcomings of safe-haven assets, such as gold, currency, and potentially Bitcoin, retail investors are showing increasing interest in the equity markets over the years to seek decent returns. The inherent risk in the equity market could possibly make investors lose their capital if mistakes are made while choosing the right stocks. Therefore, they need quality stocks, which generate decent returns with much lower risk than the common equity index. Keeping that in mind, we examine the safe-haven and hedging properties of a basket of possibly quality stocks.

Customarily, correlation analysis is performed to see the co-movement, but by and large, financial data exhibit non-normality and linear correlation measures are misleading in such cases. Zhang and Wei (2010) employ co-integration tests and Granger causality to explain the co-movement in crude oil and gold markets. Dynamic conditional correlations (DCC) yield better and consistent results than the aforementioned tests. On testing gold against the US dollar using DCC, Capie et al. (2005) and Joy (2011) find gold to be a poor safe-haven. Different papers employ different variants of the GARCH model (Bollerslev, 1986), such as exponential GARCH (Nelson & Cao, 1992; Hammoudeh & Yuan, 2008), Glosten–Jagannathan–Runkle GARCH (Glosten et al., 1993), and Threshold GARCH (Zakoian, 1994), to best capture the stylized facts. It was not until the late 1990s that copulas were used in finance and quantitative techniques. Copulas are widely applied in modeling asymmetric dependences (Chollete et al., 2006; Fortin & Kuzmics, 2002; Hu, 2006; Lai et al., 2009; Li, 2000; Patton, 2009). Of many advantages that a copula holds against correlation analysis, the prime vantage point of it resides in the separation of the dependence structure and the univariate distributions of the variables. This property gives copula functions a leeway to model dependencies for any type of distribution functions. Early works (Bouyé et al., 2000; Embrechts et al., 2002, 2003) provide some holistic guide to work with copulas in finance and risk management. There is a considerable dearth of copula approach in assessing the safe-haven properties of financial assets, such as Jondeau and Rockinger (2006), Lai and Tseng (2010), Zhu et al. (2014), and Avdulaj and Barunik (2015) to name a few, in the literature. However, given the manifold perks of copulas, in this article, we employ the bivariate t-copula, as it has been shown to grasp the empirical truths of financial data the best (Cossin & Schellhorn, 2007; Fang et al., 2002). While acknowledging the relevant contribution made by prior research, our article supplements to the existing literature by examining the relationship between equities and major stock indices in the Indian financial market. Although, we do not find any stocks with strong safe-haven properties, a handful of stocks shows minimum co-movements with market indices. We term them as pseudo–safe-haven since they can produce decent returns with an acceptable level of capital protection capability. The advantage of using pseudo–safe-haven equities is that investors can generate relatively stable, much higher returns than the other safe-haven asset classes with a very low level of volatility in the investment value.

3. Data and Methodology

3.1 Data

Our data consist of the daily returns of the five indices (Nifty-50, Nifty-100, Nifty-Midcap-100, Nifty-200, and Nifty-Smallcap-100) and the daily returns of the constituent 50 companies listed under the NIFTY-50 index. We collect the data from Investing.com website for the period of January 2008 to January 2020. We chose this period considering our motive to find specific equity stocks listed under the Nifty-50 index that grew after the 2008 financial crisis and simultaneously indicated safe-haven traits in those years. The ticker symbols of the stocks follow the nomenclature adopted by Investing.com. The 50 companies predominantly fall under one or the other following industries: automobile, financial services, cement industries, cigarette manufacturers, information technology, consumer goods, engineering, metals and mining, energy, fertilizers, pharmaceuticals, shipping and cargo, and media and entertainment. Forty-one percent of the total composition is made up by financial service companies, followed by energy industries comprising of 16% and informational technology-oriented companies making up for 12%. The residual portion, on an average, is fairly spread across the remaining sectors.

3.2 Modelling the Marginal Distributions

As discussed earlier, copulas are multivariate cumulative distribution function (CDF) whose marginal functions follow a uniform distribution from the interval [0, 1]. From the descriptive statistics (see Table 1), we observe that distributions are fairly symmetrical, which implies that we do not need a threshold or an asymmetrical GARCH model. Hence, we estimate a marginal AR(p)-t-GARCH(p,q). The standardized errors from this model follow the t-distribution (Bollerslev, 1986). On plugging different values for the p and q lag parameters, we find the best model to be AR(1)-t-GARCH(1,1), based on the Akaike information criterion (AIC) comparison between 2, 12, and 36 lags for AR(p), GARCH(1,2), and GARCH(2,2). The marginal model is mathematically specified as follows:

R_{i, t} = μ_{i} + \sum_{j = 1}^{p} φ_{j} R_{i, t - j} a n d ε_{i, t} = σ_{i, t} v_{i, t} w h e r e v_{i, t} \sim i . i . ​ d (0, 1),

\sqrt{\frac{v}{σ_{i, t}^{2} (v - 2)}} . ε_{i, t} | I_{t - 1} ~ t (v),

σ_{i, t}^{2} = a_{i} + b_{i} σ_{i, t - 1}^{2} + c_{i} ε_{i, t - 1}^{2},

where R_i,t is the return on the ith stock and $σ_{i, t}^{2}$ is variance of $ε_{i, t}$ for the ith stock. We observe the estimated parameters of the AR(1)-t-GARCH(1,1) model and the AIC values for all the series. Since most return series indicate autoregressive properties and conditional heteroskedasticity, AR(1)-t-GARCH(1,1), a parsimonious model, captures the stylized facts of the stock returns impressively. The coefficient of the GARCH term (i.e., β) aptly models the conditional heteroskedasticity for all the series.

3.3 Marginal Model: Goodness of Fit Tests

Since copulas are built on marginal distributions, it is crucial to run goodness of fit tests and check for misspecifications. Any incorrectness or misspecification in the model invalidates the empirical adequacy of copulas. To ensure the validity of the marginal models, we employ Lagrange multiplier (LM) and Box–Ljung tests (Q-tests) to examine the same estimated by the aforementioned AR(1)-t-GARCH(1,1). The LM test is a method for a testing hypothesis about the parameters based on likelihoods. The test statistic is formulated as the following: Let $L (θ)$ be a log-likelihood function of a $k \times 1$ parameter vector θ, and let the score function and the information matrix be

q (θ) = \frac{\partial L (θ)}{\partial θ},

I (θ) = - E [\frac{\partial^{2} L (θ)}{\partial θ \partial θ^{'}}] .

We let $\tilde{θ}$ be the maximum likelihood estimator (MLE) of θ subject to constraints such as an $r \times 1$ vector of $h (θ) = 0.$ The Lagrangian function would be as follows:

ℒ = L (θ) - λ^{'} h (θ),

where λ is a vector of $r \times 1$ Lagrange multipliers. The first order conditions for $\tilde{θ}$ are

\frac{\partial ℒ}{\partial θ} = q (\tilde{θ}) - H (\tilde{θ}) \tilde{λ} = 0,

\frac{\partial ℒ}{\partial λ} = h (\tilde{θ}) = 0.

Here, $H (θ) = \frac{\partial h {(θ)}^{'}}{\partial θ}$ . Hence, the LM statistic is given by

L M = {\tilde{q}}^{'} {\tilde{I}}^{'} \tilde{q} = {\tilde{λ}}^{'} {\tilde{H}}^{'} {\tilde{I}}^{'} \tilde{H} \tilde{λ} .

For $\tilde{q} = q (\tilde{θ}), \tilde{I} = I (\tilde{θ})$ and $\tilde{H} = H (\tilde{θ})$ .

The Q-test statistics is a diagnostic tool to check the fit of the model. In our analysis, we fit AR(1)-t-GARCH(1,1) and apply the Q-test to the residuals after fitting the model. For a given series of values X of length n, the Q-test statistic is computed as:

Q = n (n + 2) {\sum^{​}}_{m}^{k = 1} \frac{{\hat{r}}_{k}^{2}}{n - k},

where ${\hat{r}}_{k}$ is the estimated autocorrelation of the series at lag k, and m is the number of lags being tested.

3.4 t-Copula Model

Before getting into the interpretation of results, it is necessary to understand what a copula is. As we have seen, it is of prime importance to know about the dependence between stocks in a portfolio and it is typically indicated by the correlation coefficient. The correlation coefficient measures how strong a relationship between the two variables is. The coefficients are significant only when the distributions of the variables are Gaussian. More often than not, financial data are non-Gaussian; so it is not advisable to rely on the correlation coefficient as it can be very misleading. We instead employ “copulas,” which measures the degree of dependence and the structure of dependence.

Definition: An n-dimensional copula is a function $C : {[0, 1]}^{n} \to [0, 1]$ such that C is grounded and n is increasing. Also, C has margins $C_{k}, k = 1, 2, \dots, n,$ which satisfy $C_{k} (u) = u \forall u i n [0, 1]$ .

Sklar’s theorem: (Durante et al., 2013; Sklar, 1959) states that let F_XY be a joint distribution function where the margins are F_X and F_Y Then, there exists a copula C such that $\forall (x, y) \in R$ ,

F_{X Y} (x, y) = C (F_{X} (x), F_{Y} (y)) .

We observe C to be unique if F_X and F_Y are continuous. Conversely, we can say that if C is a copula with F_X and F_Y for CDFs, then the function F_XY (also defined above) is a joint distribution function with margins F_X and F_Y (see Joe, 1997; Nelson, 1999) for further empirical examination of copulas and measures of dependence).

This theorem indicates that joint distribution can be disintegrated to its univariate marginal distributions and a copula function that captures the dependence structure between the variables X and Y. Copulas allow us to model the marginal distributions and the dependence structure of a multivariate random variable separately. Moreover, there are various other measures of dependence, among which Kendall’s τ and Spearman’s p are usually studied with copula models. More often than not the tail dependence between X and Y, as one of the copula properties, is invariant under the strictly increasing transformation of X and Y. The lower and upper tail dependence coefficients are defined as

λ_{L} = \lim_{u \to 0} \Pr (F_{Y} (y) \leq u | F_{X} (x) \leq u] = \lim_{u \to 0} \frac{C (u, u)}{u},

λ_{U} = \lim_{u \to 1} \Pr (F_{Y} (y) \geq u | F_{X} (x) \geq u] = \lim_{u \to 1} \frac{1 - 2 u + C (u, u)}{1 - u},

where λ_L and λ_U ∈ [0,1]. Different copulas usually represent different dependence structures with the association parameters indicating the strength of the dependence. For example, Gaussian copula has zero tail dependence, while Clayton copula has left tail dependence and no right tail dependence.

Copula: t-Copula represents an implicit dependence structure (Embrechts et al., 2001; Fang et al., 2002) in a multivariate t-distribution. Mashal and Zeevi (2002), Breymann et al. (2003), and Jondeau and Rockinger (2006) show that the empirical fit of a t-copula is superior to Gaussian copula—the dependence structure of the multivariate normal distribution. Further, the ability to capture the phenomenon of dependent extreme values (very often observed in financial return series) makes the t-copula a better choice.

The multivariate t -distribution: Suppose there exists a d-dimensional random vector $X = {(X_{1}, Ô ø Ω . Ô ø Ω . Ô ø Ω . Ô ø Ω, X_{d})}^{'}$ that is said to have a multivariate t distribution with v degrees of freedom, mean vector μ, and positive-definite scatter matrix $\sum^{}$ and is denoted by $X ~ t_{d} (ν, μ, \sum^{})$ Then, its density is given by

f (x) = \frac{Γ (\frac{ν + d}{2})}{Γ (\frac{ν}{2}) \sqrt{{(π ν)}^{d} | \sum^{​} |}} {(1 + \frac{{(x - μ)}^{'} \sum^{- 1} (x - μ)}{ν})}^{- (\frac{ν + d}{2})} .

Multivariate t belongs to the class of multivariate normal variance mixtures and has the representation $X^{\underset{=}{d e f}} μ + \sqrt{W} Z,$ where $Z ~ N_{d} (0, \sum^{})$ with W independent of Z; equivalently, W has an inverse gamma distribution, $W ∽ I g (ν / 2, ν / 2)$ .

t -Copula: We now extend Sklar’s theorem to explain the multivariate t-copula. In this case, the copula C of the joint distribution function can be evaluated as

C (u) : = C (u_{1}, Ô ø Ω \dots, u_{d}) = F (F_{1}^{- 1} (u_{1}), Ô ø Ω \dots F_{d}^{- 1} (u_{d})),

where $F_{i}^{- 1}$ are the quantile functions of the margins. The copula C can be thought of as the distribution function of the probability transformed random vector ${(F_{1} (X_{1}), \dots, F_{d} (X_{d}))}^{'}$ . The copula does not vary if the marginal distributions are standardized. So, the copula of a $t_{d} (ν, μ, \sum^{})$ is identical to that of a $t_{d} (ν, 0, \sum^{})$ distribution, where P is the correlation matrix implied by the dispersion matrix ∑. The unique t-copula is thus given by

\begin{matrix} C_{ν, P}^{t} (u) = \int_{- \infty}^{t_{ν}^{- 1} (u_{1})} \dots \int_{- \infty}^{t_{ν}^{- 1} (u_{d})} \frac{Γ (\frac{ν + d}{2})}{Γ (\frac{ν}{2}) \sqrt{{(π ν)}^{d} | P |}} \\ {(1 + \frac{x^{,} P^{- 1} x}{ν})}^{- (\frac{ν + d}{2})} d x, \end{matrix}

where $t_{ν}^{- 1}$ is the quantile function of a standard univariate t_v distribution. In this article, we interchangeably use t-copula for unique copula of a multivariate Gaussian distribution as Gaussian copula can be thought of as a limiting case of the t-copula as $ν \to \infty$ .

To simulate a t-copula, we generate a multivariate t distribution random vector $X ~ t_{d} (ν, μ, P)$ and then return a vector $U = {(t_{ν} (X_{1}), Ô ø Ω . Ô ø Ω . Ô ø Ω . Ô ø Ω, t_{ν} (X_{d}))}^{'},$ where t_v denotes the distribution function of a standard univariate t. The estimated t-copula would have the form

\begin{matrix} ​ \\ C_{v}^{t},_{p} (u) = \frac{f_{v, p} (t_{v}^{- 1}) (u_{1}), \dots t_{v}^{- 1} (u_{d}))}{\prod_{i = 1}^{d} ​ f_{v} (t_{v}^{- 1}) (u_{i})}, u \in {(0, 1)}^{d}, \\ ​ \end{matrix}

where $f_{ν, P}$ is the joint density of a $t_{d} (ν, 0, P)$ -distributed random vector and f_v is the density of the univariate standard t distribution with v degrees of freedom.

Our results exhibit the parameter estimates of the t-copula that is fit to a stock index and its constituent stocks’ return series. The t-copula parameter ρ is very similar to the linear correlation coefficient of the data owing to the fact that t-copula is a member of the elliptical copula family with the elliptical margin being the t-distribution. The slight difference between the estimated ρs of different pairs and their linear correlation coefficient is the value yielded due to fat tails and extreme co-movements that often appear in financial return data, which linear correlation values fail to take into account. Different copulas have different tail dependence features and requirements. We chose t-copula among the various copulas available as t-copula adequately presents the dependence structure of the return series. Owing to the large degrees of freedom, the t-copula eventually converged to normal copula, which does not allow tail dependence parameters; however, the AIC and log-likelihood values show that they are significant despite the convergence.

The literature suggests that an asset is a safe-haven if it is uncorrelated or negatively correlated with another asset or portfolio in times of extreme market movements. It is essential that the dependence holds under extreme market movements for an asset to be classified as a safe-haven. On another note, if the assets portray a significant ρ positive for the whole sample period, we can sort that the asset has “hedging” properties. Thus, we can state our hypotheses as follows:

$ρ i > 0; H_{0} =$ the ith stock is not a hedge,

$\begin{matrix} λ_{L}, λ_{U} > 0; H_{0} = \end{matrix}$ the ith stock is not a safe− haven,where $λ_{L}$ is lower tail dependence and $λ_{υ}$ is the upper tail dependence parameter.

4. Empirical Results

The sample periods for some stocks are shorter than the period mentioned above (January 2008 to January 2020) as data are not available for them. The complete dataset spans over 158,778 discrete observations for 50 individual stocks and 5 indices over 2,982 days. The descriptive statistics for the stocks and their corresponding sample periods are exhibited in Table 1. One can infer that the data are approximately symmetrical from the skewness measures. The kurtosis values indicate a leptokurtic distribution, that is, these distributions have a heavier and fatter tail, as opposed to a normal distribution. Moreover, the Jarque–Bera test statistics rejects the Gaussian properties of all the series.

Table 1.
Descriptive Statistics

Mean SD Skew. Kurt. JB Mean SD Skew. Kurt. JB

APSE 0.001 0.027 0.457 8.531 3,897 LART 0.000 0.022 0.758 11.326 8,901

BRTI 0.000 0.023 0.632 10.129 6,514 MAHM 0.001 0.022 0.823 14.956 18,105

ASPN 0.001 0.017 0.117 6.593 1,611 MRTI 0.001 0.020 0.124 6.185 1,268

AXBK 0.001 0.025 0.345 7.387 2,450 NEST 0.001 0.014 0.252 5.744 967

BJFN 0.002 0.026 1.004 13.056 13,062 NTPC 0.000 0.018 0.035 8.815 4,227

BAJA 0.001 0.019 0.036 8.537 3,683 ONGC 0.001 0.017 0.996 10.564 7,600

BJFS 0.001 0.024 0.205 10.303 6,428 PGRD 0.000 0.018 –0.166 13.557 13,856

BPCL 0.001 0.023 0.059 7.428 2,439 REDY 0.001 0.018 –0.254 7.924 3,037

BHRI 0.000 0.023 0.180 6.234 769 RELI 0.001 0.021 0.211 11.450 8,896

BRIT 0.001 0.017 0.996 10.564 7,600 SBI 0.000 0.024 0.970 12.995 12,875

CIPL 0.000 0.016 0.465 5.926 194 SUN 0.001 0.020 0.119 11.546 9,084

COAL 0.000 0.018 0.257 6.408 1,126 TAMO 0.001 0.028 0.191 7.717 2,785

EICH 0.002 0.024 0.979 12.010 10,558 TISC 0.000 0.027 0.026 6.695 1,696

GAIL 0.000 0.020 –0.056 7.847 2,922 TCS 0.001 0.020 0.420 9.510 5,352

GRAS 0.000 0.019 0.301 8.993 4,507 TEML 0.001 0.026 –2.156 61.555 428,460

HCL 0.001 0.023 0.335 9.903 5,979 TITN 0.001 0.024 0.361 9.926 6,013

HDFC 0.001 0.022 0.675 11.282 8,752 ULTC 0.001 0.020 0.382 6.818 1,879

HDBK 0.001 0.017 0.420 10.242 6,606 UPLL 0.001 0.027 0.026 17.643 26,651

HROM 0.001 0.019 0.949 13.097 13,088 VDAN 0.000 0.030 0.217 7.230 2,241

HALC 0.000 0.028 0.231 6.027 1,163 WIPR 0.000 0.020 –0.728 15.963 21,149

HLL 0.001 0.016 0.693 10.063 6,424 YESB 0.001 0.034 0.335 17.289 25,434

ICBK 0.001 0.026 0.392 9.900 5,990 ZEE 0.001 0.026 –0.080 10.942 7,844

IOC 0.000 0.022 0.129 9.841 5,824 NIFTY100 0.000 0.014 0.332 17.921 27,762

INBK 0.001 0.026 0.332 8.751 4,163 NSEI 0.000 0.014 0.430 18.778 31,075

INFY 0.001 0.019 –0.478 16.510 22,799 NIFMDCP100 0.000 0.013 –0.427 10.957 7,971

ITC 0.001 0.017 0.047 7.205 2,197 NIFTY200 0.000 0.017 –0.382 11.191 8,424

JSTL 0.001 0.030 0.817 12.631 11,835 NIFSMCP100 0.000 0.015 –0.751 9.390 5,362

KTKM 0.001 0.024 0.055 10.615 7,209

	Mean	SD	Skew.	Kurt.	JB		Mean	SD	Skew.	Kurt.	JB
APSE	0.001	0.027	0.457	8.531	3,897	LART	0.000	0.022	0.758	11.326	8,901
BRTI	0.000	0.023	0.632	10.129	6,514	MAHM	0.001	0.022	0.823	14.956	18,105
ASPN	0.001	0.017	0.117	6.593	1,611	MRTI	0.001	0.020	0.124	6.185	1,268
AXBK	0.001	0.025	0.345	7.387	2,450	NEST	0.001	0.014	0.252	5.744	967
BJFN	0.002	0.026	1.004	13.056	13,062	NTPC	0.000	0.018	0.035	8.815	4,227
BAJA	0.001	0.019	0.036	8.537	3,683	ONGC	0.001	0.017	0.996	10.564	7,600
BJFS	0.001	0.024	0.205	10.303	6,428	PGRD	0.000	0.018	–0.166	13.557	13,856
BPCL	0.001	0.023	0.059	7.428	2,439	REDY	0.001	0.018	–0.254	7.924	3,037
BHRI	0.000	0.023	0.180	6.234	769	RELI	0.001	0.021	0.211	11.450	8,896
BRIT	0.001	0.017	0.996	10.564	7,600	SBI	0.000	0.024	0.970	12.995	12,875
CIPL	0.000	0.016	0.465	5.926	194	SUN	0.001	0.020	0.119	11.546	9,084
COAL	0.000	0.018	0.257	6.408	1,126	TAMO	0.001	0.028	0.191	7.717	2,785
EICH	0.002	0.024	0.979	12.010	10,558	TISC	0.000	0.027	0.026	6.695	1,696
GAIL	0.000	0.020	–0.056	7.847	2,922	TCS	0.001	0.020	0.420	9.510	5,352
GRAS	0.000	0.019	0.301	8.993	4,507	TEML	0.001	0.026	–2.156	61.555	428,460
HCL	0.001	0.023	0.335	9.903	5,979	TITN	0.001	0.024	0.361	9.926	6,013
HDFC	0.001	0.022	0.675	11.282	8,752	ULTC	0.001	0.020	0.382	6.818	1,879
HDBK	0.001	0.017	0.420	10.242	6,606	UPLL	0.001	0.027	0.026	17.643	26,651
HROM	0.001	0.019	0.949	13.097	13,088	VDAN	0.000	0.030	0.217	7.230	2,241
HALC	0.000	0.028	0.231	6.027	1,163	WIPR	0.000	0.020	–0.728	15.963	21,149
HLL	0.001	0.016	0.693	10.063	6,424	YESB	0.001	0.034	0.335	17.289	25,434
ICBK	0.001	0.026	0.392	9.900	5,990	ZEE	0.001	0.026	–0.080	10.942	7,844
IOC	0.000	0.022	0.129	9.841	5,824	NIFTY100	0.000	0.014	0.332	17.921	27,762
INBK	0.001	0.026	0.332	8.751	4,163	NSEI	0.000	0.014	0.430	18.778	31,075
INFY	0.001	0.019	–0.478	16.510	22,799	NIFMDCP100	0.000	0.013	–0.427	10.957	7,971
ITC	0.001	0.017	0.047	7.205	2,197	NIFTY200	0.000	0.017	–0.382	11.191	8,424
JSTL	0.001	0.030	0.817	12.631	11,835	NIFSMCP100	0.000	0.015	–0.751	9.390	5,362
KTKM	0.001	0.024	0.055	10.615	7,209

Source: The authors.

Note: This table consists of descriptive statistics. One can infer that the data are approximately symmetrical from the skewness measures. The kurtosis values indicate a leptokurtic distribution, that is, these distributions have a heavier and fatter tail as opposed to a normal distribution. Moreover, the Jarque–Bera test statistics rejects the Gaussian properties of all the series.

All the JB test statistics have a p-value < 0.05. For some stocks, data are not available from 2008. We have considered the maximum period for them.

4.1 Results from Marginal Model

As discussed earlier, the marginal model employed is AR-t-GARCH (1,1). Table 2 shows that the intercept (µ) is asymptomatically zero for all the stocks and indices. The other coefficients similarly are statistically significant. The βs of the marginal model show large values, which indicate that GARCH(1,1) adequately captures the heteroskedastic effects. The values range from 0.502 to 0.983. Furthermore, the AIC values are small enough to vouch for the robustness of the marginal models. The LM test verifies whether the probability transformations are independent, identically distributed (IID). On the other hand, the Q-test checks the model fit. The ρ-values of the LM test and the Q-test are shown in Table 3. The large ρ-values suggest no serial correlation, as necessary and no autoregressive conditional heteroskedasticity in the standardized residuals. The Kolmogorov–Smirnov (KS) test can also be used for diagnostic checking in lieu of Q-tests. More often than not, the standard LM test and Q-test are sufficient to check the fit of such marginal models. The ρ-values of our LM test ranges from 6% to 99.41% and the ρ-values of Q-test ranges from 11.21% to 100%. These results assure that the dependence structure of the return series that will further be modeled by copulas is not misspecified.

Table 2.
Estimation of Marginal Models

µ ϕ α β AIC µ ϕ α β AIC

APSE 0.001 –0.013 0.031 0.960 –4.533 LART 0.001 0.069 0.066 0.917 –5.071

BRTI 0.001 –0.020 0.087 0.826 –4.833 MAHM 0.001 0.017 0.059 0.931 –5.049

ASPN 0.001 0.019 0.085 0.845 –5.407 MRTI 0.001 0.064 0.039 0.950 –5.163

AXBK 0.001 0.056 0.071 0.910 –4.782 NEST 0.001 0.011 0.077 0.807 –5.652

BJFN 0.002 0.051 0.091 0.876 –4.663 NTPC 0.000 –0.047 0.076 0.890 –5.371

BAJA 0.001 0.052 0.036 0.955 –5.309 ONGC 0.000 0.005 0.092 0.880 –5.063

BJFS 0.002 0.104 0.083 0.868 –4.788 PGRD 0.000 –0.050 0.126 0.845 –5.522

BPCL 0.001 0.024 0.071 0.894 –4.781 REDY 0.001 0.024 0.083 0.883 –5.269

BHRI 0.000 –0.022 0.140 0.730 –4.847 RELI 0.001 0.053 0.060 0.922 –5.168

BRIT 0.001 0.019 0.038 0.921 –5.401 SBI 0.000 0.071 0.155 0.790 –4.789

CIPL 0.000 –0.059 0.114 0.770 –5.507 SUN 0.001 0.010 0.030 0.961 –5.036

COAL 0.000 –0.001 0.039 0.935 –14.823 TAMO 0.001 0.055 0.068 0.904 –4.469

EICH 0.002 0.074 0.028 0.964 –4.741 TISC 0.000 0.021 0.070 0.912 –4.603

GAIL 0.000 –0.030 0.034 0.954 –5.053 TCS 0.001 0.027 0.076 0.903 –5.258

GRAS 0.001 0.031 0.056 0.930 –5.238 TEML 0.000 0.066 0.056 0.908 –4.577

HCL 0.001 0.000 0.068 0.920 –5.012 TITN 0.002 –0.018 0.113 0.789 –4.736

HDFC 0.001 0.017 0.061 0.923 –5.174 ULTC 0.001 0.044 0.021 0.973 –5.159

HDBK 0.001 0.042 0.043 0.951 –5.659 UPLL 0.001 0.021 0.155 0.737 –4.559

HROM 0.001 0.048 0.051 0.933 –5.173 VDAN 0.000 0.025 0.059 0.915 –4.282

HALC 0.000 0.019 0.058 0.925 –4.445 WIPR 0.001 –0.038 0.102 0.821 –5.207

HLL 0.001 –0.021 0.244 0.502 –5.549 YESB 0.002 0.052 0.078 0.921 –4.269

ICBK 0.001 0.047 0.079 0.898 –4.762 ZEE 0.001 –0.018 0.040 0.953 –4.721

IOC 0.000 0.022 0.165 0.764 –4.951 NIFTY100 0.001 0.079 0.088 0.905 –6.233

INBK 0.002 0.041 0.076 0.918 –4.857 NSEI 0.001 0.065 0.084 0.911 –6.229

INFY 0.001 –0.004 0.010 0.983 –5.150 NIFMDCP100 0.001 0.168 0.122 0.853 –6.069

ITC 0.001 –0.018 0.057 0.912 –5.420 NIFTY200 0.001 0.115 0.113 0.866 –5.652

JSTL 0.001 –0.009 0.070 0.916 –4.500 NIFSMCP100 0.001 0.221 0.145 0.809 –5.879

KTKM 0.001 –0.006 0.061 0.928 –5.085

	µ	ϕ	α	β	AIC		µ	ϕ	α	β	AIC
APSE	0.001	–0.013	0.031	0.960	–4.533	LART	0.001	0.069	0.066	0.917	–5.071
BRTI	0.001	–0.020	0.087	0.826	–4.833	MAHM	0.001	0.017	0.059	0.931	–5.049
ASPN	0.001	0.019	0.085	0.845	–5.407	MRTI	0.001	0.064	0.039	0.950	–5.163
AXBK	0.001	0.056	0.071	0.910	–4.782	NEST	0.001	0.011	0.077	0.807	–5.652
BJFN	0.002	0.051	0.091	0.876	–4.663	NTPC	0.000	–0.047	0.076	0.890	–5.371
BAJA	0.001	0.052	0.036	0.955	–5.309	ONGC	0.000	0.005	0.092	0.880	–5.063
BJFS	0.002	0.104	0.083	0.868	–4.788	PGRD	0.000	–0.050	0.126	0.845	–5.522
BPCL	0.001	0.024	0.071	0.894	–4.781	REDY	0.001	0.024	0.083	0.883	–5.269
BHRI	0.000	–0.022	0.140	0.730	–4.847	RELI	0.001	0.053	0.060	0.922	–5.168
BRIT	0.001	0.019	0.038	0.921	–5.401	SBI	0.000	0.071	0.155	0.790	–4.789
CIPL	0.000	–0.059	0.114	0.770	–5.507	SUN	0.001	0.010	0.030	0.961	–5.036
COAL	0.000	–0.001	0.039	0.935	–14.823	TAMO	0.001	0.055	0.068	0.904	–4.469
EICH	0.002	0.074	0.028	0.964	–4.741	TISC	0.000	0.021	0.070	0.912	–4.603
GAIL	0.000	–0.030	0.034	0.954	–5.053	TCS	0.001	0.027	0.076	0.903	–5.258
GRAS	0.001	0.031	0.056	0.930	–5.238	TEML	0.000	0.066	0.056	0.908	–4.577
HCL	0.001	0.000	0.068	0.920	–5.012	TITN	0.002	–0.018	0.113	0.789	–4.736
HDFC	0.001	0.017	0.061	0.923	–5.174	ULTC	0.001	0.044	0.021	0.973	–5.159
HDBK	0.001	0.042	0.043	0.951	–5.659	UPLL	0.001	0.021	0.155	0.737	–4.559
HROM	0.001	0.048	0.051	0.933	–5.173	VDAN	0.000	0.025	0.059	0.915	–4.282
HALC	0.000	0.019	0.058	0.925	–4.445	WIPR	0.001	–0.038	0.102	0.821	–5.207
HLL	0.001	–0.021	0.244	0.502	–5.549	YESB	0.002	0.052	0.078	0.921	–4.269
ICBK	0.001	0.047	0.079	0.898	–4.762	ZEE	0.001	–0.018	0.040	0.953	–4.721
IOC	0.000	0.022	0.165	0.764	–4.951	NIFTY100	0.001	0.079	0.088	0.905	–6.233
INBK	0.002	0.041	0.076	0.918	–4.857	NSEI	0.001	0.065	0.084	0.911	–6.229
INFY	0.001	–0.004	0.010	0.983	–5.150	NIFMDCP100	0.001	0.168	0.122	0.853	–6.069
ITC	0.001	–0.018	0.057	0.912	–5.420	NIFTY200	0.001	0.115	0.113	0.866	–5.652
JSTL	0.001	–0.009	0.070	0.916	–4.500	NIFSMCP100	0.001	0.221	0.145	0.809	–5.879
KTKM	0.001	–0.006	0.061	0.928	–5.085

Source: The authors.

Note: This table encompasses the coefficients of the AR(1)-t-GARCH(1,1) model. It shows that the intercept (µ) is asymptomatically zero for all the stocks and indices. The other coefficients similarly are statistically significant. The βs of the marginal model show large values which indicate that GARCH(1,1) adequately captures the heteroskedastic effects. The values range from 0.502 to 0.983. Furthermore, the AIC values are small enough to vouch for the robustness of the marginal models.

Table 3.

Goodness of Fit Tests for the Marginal Model

	Q(2)	Q(4)	ARCH(3)	ARCH(5)	ARCH(7)		Q(2)	Q(4)	ARCH(3)	ARCH(5)	ARCH(7)
APSE	0.637	0.403	0.651	0.861	0.923	LART	0.254	0.197	0.263	0.624	0.632
BRTI	0.127	0.112	0.063	0.205	0.374	MAHM	0.995	0.614	0.870	0.741	0.882
ASPN	0.957	0.907	0.112	0.218	0.225	MRTI	0.984	0.934	0.848	0.983	0.950
AXBK	0.950	0.539	0.994	0.858	0.946	NEST	0.999	0.416	0.664	0.688	0.772
BJFN	0.999	0.984	0.161	0.294	0.479	NTPC	0.623	0.782	0.646	0.868	0.928
BAJA	1.000	0.729	0.623	0.854	0.887	ONGC	0.681	0.366	0.327	0.539	0.736
BJFS	0.941	0.390	0.907	0.944	0.834	PGRD	0.817	0.076	0.456	0.715	0.683
BPCL	0.931	0.819	0.422	0.692	0.610	REDY	0.994	0.949	0.834	0.837	0.770
BHRI	0.403	0.209	0.870	0.540	0.235	RELI	0.994	0.482	0.441	0.599	0.738
BRIT	0.999	0.794	0.537	0.894	0.963	SBI	0.912	0.864	0.379	0.726	0.866
CIPL	0.991	0.982	0.932	0.617	0.787	SUN	0.849	0.562	0.806	0.978	0.990
COAL	0.976	0.909	0.215	0.234	0.300	TAMO	0.898	0.779	0.298	0.686	0.796
EICH	0.896	0.233	0.135	0.304	0.482	TISC	0.905	0.848	0.184	0.416	0.221
GAIL	0.397	0.079	0.369	0.155	0.224	TCS	0.992	0.402	0.291	0.590	0.623
GRAS	0.568	0.400	0.899	0.871	0.901	TEML	1.000	1.000	0.857	0.996	1.000
HCL	0.596	0.038	0.233	0.609	0.812	TITN	0.891	0.602	0.335	0.614	0.733
HDFC	0.915	0.941	0.544	0.682	0.791	ULTC	1.000	0.622	0.103	0.103	0.140
HDBK	0.750	0.925	0.655	0.864	0.964	UPLL	0.121	0.125	0.683	0.919	0.985
HROM	0.734	0.180	0.861	0.924	0.906	VDAN	0.999	0.997	0.294	0.531	0.532
HALC	1.000	0.998	0.584	0.360	0.486	WIPR	0.977	0.608	0.795	0.974	0.996
HLL	0.997	0.949	0.204	0.487	0.645	YESB	0.354	0.384	0.792	0.987	0.976
ICBK	0.508	0.208	0.504	0.806	0.907	ZEE	0.063	0.016	0.801	0.985	0.993
IOC	0.605	0.873	0.675	0.687	0.672	NIFTY100	0.946	0.923	0.871	0.751	0.862
INBK	0.977	0.302	0.297	0.462	0.187	NSEI	0.418	0.177	0.510	0.807	0.908
INFY	0.314	0.624	0.660	0.961	0.984	NIFMDCP100	0.621	0.249	0.547	0.719	0.823
ITC	0.129	0.153	0.322	0.562	0.402	NIFTY200	0.253	0.340	0.570	0.777	0.881
JSTL	0.861	0.755	0.624	0.108	0.201	NIFSMCP100	0.158	0.132	0.699	0.834	0.903
KTKM	0.987	0.613	0.708	0.829	0.797

Source: The authors.

Note: Table 3 presents the results for the goodness of fit tests for the AR(1)-t-GARCH(1,1). Q(2) denotes Q-statistic for 2 lags, and similarly Q(4) is for 4 lags. The ARCH(3), ARCH(5), and ARCH(7) indicate the p-values of the ARCH LM tests for their corresponding lags in parentheses.

4.2 Results from t-Copula

We can observe that (see Table 4) in most cases, the dependence among the individual stocks and the Nifty-50 index lies between –3% and 34.5%. This degree of co-movement can be attributed to industry-specific risks and their composition in the index. The dependence between the Nifty-100 index and the stocks are from –3.9% to 36.4%, following a similar suit to the dependence between the same stocks and the Nifty-50 index. Likewise, the Nifty-200 index and the Nifty-Midcap-100 index show respective dependence structures: –3.626% to 3.659% and –2.075% to 34.92%. The Nifty-Smallcap index shows relatively less dependence with the copula estimates ranging from 2.98% to 29.25%. The stock that shows large co-movement with all the indices is BJFN (Bajaj Finance) and the stock with a least co-movement is CIPL (Cipla).

Table 4.
Estimation of Copula Parameters

NSEI NIFTY–100 NIFMDCP 100 NIFTY– 200 NIFSMCP 100 NSEI NIFTY– 100 NIFMDCP 100 NIFTY– 200 NIFSMCP 100

Part A

ρ APSE 0.044 0.046 0.053 0.050 0.032 BRTI 0.220 0.216 0.174 0.175 0.022

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.019 0.019 0.019

∂ι 3.370 3.890 6.804 5.928 7.101 78.310 76.330 54.310 53.840 1.783

AIC –2.739 –3.780 –9.607 –7.857 –10.201 –152.619 –148.655 –104.621 –103.674 0.433

ρ ASPN 0.108 0.114 0.142 0.126 0.073 AXBK 0.322 0.325 0.305 0.298 0.058

SE 0.018 0.018 0.019 0.019 0.019 0.017 0.017 0.017 0.017 0.019

∂ι 17.500 19.710 34.090 25.150 9.393 169.800 174.300 153.700 145.600 7.837

AIC –30.994 –35.410 –64.189 –46.292 –14.786 –335.589 –344.659 –303.353 –287.282 –11.673

ρ BJFN 0.355 0.365 0.366 0.349 0.293 BAJA 0.000 –0.002 –0.001 0.011 0.107

SE 0.017 0.017 0.017 0.017 0.018 0.019 0.019 0.019 0.019 0.020

∂ι 213.200 227.700 232.900 211.400 141.700 0.477 0.519 1.521 2.222 28.810

AIC –422.437 –451.488 –461.706 –418.762 –279.403 3.046 2.962 0.959 –0.445 –53.614

ρ BJFS –0.014 –0.013 –0.001 0.003 0.011 BPCL 0.131 0.132 0.120 0.118 0.002

SE 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019

∂ι 0.745 1.017 1.777 1.985 2.174 –53.079 –54.324 –47.043 –44.670 3.832

AIC 2.510 1.967 0.445 0.029 –0.349 28.540 29.160 25.520 24.330 0.084

ρ BHRI 0.012 0.018 0.036 0.028 0.024 BRIT 0.261 0.275 0.306 0.284 0.226

SE 0.024 0.024 0.024 0.024 0.024 0.018 0.018 0.017 0.018 0.018

∂ι 0.248 0.312 1.096 0.682 1.081 109.600 121.900 158.800 135.200 88.710

AIC 3.505 3.375 1.807 2.637 1.837 –215.112 –239.787 –313.635 –266.496 –173.411

ρ CIPL –0.039 –0.039 –0.036 –0.021 0.030 COAL 0.064 0.000 –0.014 –0.006 –0.011

SE 0.048 0.048 0.048 0.048 0.048 0.019 0.021 0.021 0.021 0.021

∂ι 1.383 1.433 0.746 0.907 0.205 9.412 0.447 0.223 0.046 0.152

AIC 1.234 1.134 2.508 2.187 3.591 –14.823 3.106 3.553 3.907 3.697

ρ EICH 0.046 0.047 0.055 0.047 0.039 GAIL 0.223 0.225 0.203 0.209 0.058

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.018 0.018 0.019

∂ι 9.005 8.609 9.469 8.609 5.974 80.790 82.260 68.620 71.830 5.384

AIC –14.009 –13.217 –14.938 –13.217 –7.948 –157.581 –160.518 –133.235 –139.664 –6.767

ρ GRAS 0.235 0.233 0.196 0.200 0.060 HCL 0.226 0.222 0.185 0.189 0.018

SE 0.018 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019

∂ι 94.240 93.110 69.440 71.540 6.475 93.880 91.410 67.580 67.320 4.794

AIC –184.475 –182.219 –134.888 –139.081 –8.949 –183.770 –178.829 –131.163 –130.644 –5.588

Part B

ρ HDFC 0.275 0.271 0.233 0.239 0.042 HDBK 0.287 0.284 0.250 0.257 0.063

SE 0.018 0.018 0.018 0.018 0.019 0.018 0.018 0.018 0.018 0.019

∂ι 135.100 130.800 92.080 97.900 4.542 147.000 144.700 107.600 115.500 6.503

AIC –266.171 –257.635 –180.153 –191.796 –5.084 –289.972 –285.368 –211.275 –227.015 –9.005

ρ HROM 0.006 0.009 0.017 0.019 0.014 HALC 0.014 0.014 0.019 0.019 0.031

SE 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019

∂ι 0.590 0.773 1.697 2.701 0.489 2.915 3.330 4.400 3.697 2.218

AIC 2.819 2.453 0.607 –1.403 3.023 –1.829 –2.659 –4.799 –3.394 –0.436

ρ HLL –0.003 –0.006 –0.018 –0.016 0.019 ICBK 0.353 0.352 0.303 0.299 0.062

SE 0.019 0.019 0.019 0.019 3.645 0.018 0.018 0.018 0.018 0.019

∂ι 1.075 1.597 4.728 4.317 3.645 230.300 230.600 167.300 160.100 7.643

AIC 1.849 0.806 –5.455 –4.635 –3.291 –456.664 –457.209 –330.552 –316.274 –11.285

ρ IOC 0.129 0.134 0.139 0.136 0.027 INBK 0.261 0.268 0.275 0.276 0.086

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.018 0.018 0.019

∂ι 30.160 32.460 36.630 35.920 1.557 114.800 122.300 136.500 136.200 18.020

AIC –56.318 –60.911 –69.261 –67.845 0.885 –225.622 –240.599 –269.038 –268.319 –32.040

ρ INFY 0.272 0.266 0.208 0.217 0.005 ITC 0.194 0.189 0.157 0.158 0.010

SE 0.018 0.018 0.018 0.018 0.019 0.019 0.019 0.019 0.019 0.019

∂ι 124.100 118.300 68.880 75.150 0.962 66.470 64.390 43.530 45.570 2.979

AIC –244.270 –232.633 –133.762 –146.305 2.076 –128.937 –124.786 –83.054 –87.148 –1.958

ρ JSTL 0.255 0.260 0.249 0.265 0.076 KTKM 0.284 0.289 0.274 0.272 0.048

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.018 0.018 0.019

∂ι 118.500 123.800 118.700 137.200 11.280 146.700 153.700 139.100 135.500 7.013

AIC –233.013 –243.669 –233.309 –270.429 –18.552 –289.396 –303.495 –274.282 –267.021 –10.027

ρ LART 0.310 0.310 0.281 0.273 0.064 MAHM 0.248 0.247 0.242 0.238 0.062

SE 0.018 0.018 0.018 0.018 0.019 0.019 0.019 0.019 0.019 0.019

∂ι 177.800 179.200 149.800 139.800 9.412 118.000 118.700 106.800 105.300 10.400

AIC –351.693 –354.458 –295.627 –275.625 –14.823 –231.906 –233.319 –209.682 –206.607 –16.797

ρ MRTI 0.005 0.006 0.008 0.001 –0.004 NEST 0.002 0.002 –0.005 –0.009 –0.029

SE 0.018 0.018 0.018 0.019 0.019 0.020 0.020 0.020 0.020 0.020

∂ι 0.035 0.049 0.191 0.107 1.100 0.008 0.016 0.031 0.084 1.009

AIC 3.930 3.903 3.617 3.786 1.801 3.984 3.968 3.939 3.832 1.982

Part C

ρ NTPC 0.264 0.265 0.228 0.230 0.056 ONGC 0.224 0.222 0.182 0.189 0.051

SE 0.018 0.018 0.018 0.018 0.019 0.018 0.018 0.019 0.019 0.019

∂ι 119.400 120.300 89.100 92.200 5.893 84.590 83.790 58.300 64.400 6.840

AIC –234.883 –236.602 –174.197 –180.394 –7.787 –165.170 –163.583 –112.608 –124.801 –9.679

ρ PGRD 0.012 0.012 0.009 0.005 0.000 REDY –0.007 –0.005 0.018 0.012 0.021

SE 0.019 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.018 0.018

∂ι 0.919 1.135 1.009 0.513 0.452 0.137 0.066 0.450 0.201 0.664

AIC 2.162 1.730 1.982 2.975 3.097 3.727 3.868 3.100 3.598 2.671

ρ RELI 0.324 0.317 0.240 0.256 0.029 SBI 0.310 0.315 0.296 0.289 0.056

SE 0.018 0.018 0.019 0.018 0.019 0.018 0.018 0.018 0.018 0.019

∂ι 190.600 181.900 104.500 118.100 1.516 164.600 171.600 162.700 151.700 9.253

AIC –377.158 –359.885 –204.976 –232.274 0.967 –325.194 –339.163 –321.401 –299.309 –14.507

ρ SUN 0.119 0.119 0.111 0.111 0.033 TAMO 0.279 0.281 0.269 0.269 0.081

SE 0.019 0.019 0.019 0.019 0.020 0.018 0.019 0.019 0.019 0.019

∂ι 25.310 25.670 21.030 22.520 10.360 143.900 147.000 147.900 145.900 15.390

AIC –46.616 –47.341 –38.062 –41.046 –16.725 –283.774 –290.001 –291.871 –287.895 –26.780

ρ TISC 0.316 0.317 0.284 0.300 0.070 TCS 0.006 0.007 0.001 –0.003 –0.002

SE 0.018 0.018 0.018 0.019 0.020 0.019 0.019 0.019 0.019 0.018

∂ι 184.000 188.600 161.700 179.700 16.630 2.266 1.857 0.410 1.034 0.007

AIC –364.069 –373.176 –319.352 –355.420 –29.259 –0.531 0.286 3.180 1.932 3.987

ρ TEML 0.223 0.225 0.203 0.209 0.058 TITN 0.030 0.030 0.030 0.026 0.014

SE 0.018 0.018 0.018 0.018 0.019 0.018 0.018 0.018 0.018 0.018

∂ι 80.790 82.260 68.620 71.830 5.384 1.302 1.367 1.349 1.022 0.317

AIC –157.581 –160.518 –133.235 –139.664 –6.767 1.397 1.266 1.301 1.956 3.366

ρ ULTC 0.053 0.055 0.050 0.047 0.046 UPLL 0.193 0.201 0.220 0.224 0.106

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.019 0.019 0.019

∂ι 7.587 7.383 4.699 4.010 5.045 58.210 64.510 88.880 91.350 20.330

AIC –11.175 –10.766 –5.398 –4.020 –6.090 –112.424 –125.016 –173.755 –178.700 –36.659

ρ VDAN 0.026 0.027 0.032 0.032 0.033 WIPR 0.253 0.246 0.198 0.207 0.014

SE 0.019 0.019 0.019 0.019 0.019 0.018 0.018 0.019 0.019 0.019

∂ι 1.933 2.298 1.956 2.241 2.078 111.100 105.700 66.940 73.250 0.576

AIC 0.133 –0.595 0.089 –0.481 –0.156 –218.215 –207.473 –129.881 –142.509 2.847

ρ YESB 0.278 0.284 0.298 0.286 0.086 ZEE 0.192 0.197 0.201 0.192 0.082

SE 0.018 0.018 0.018 0.018 0.019 0.018 0.018 0.018 0.019 0.019

∂ι 136.800 144.200 169.900 155.900 0.019 57.850 61.000 68.330 63.870 11.520

AIC –269.556 –284.328 –335.718 –307.761 –29.650 –111.710 –118.009 –132.661 –123.745 –19.033

		NSEI	NIFTY–100	NIFMDCP 100	NIFTY– 200	NIFSMCP 100		NSEI	NIFTY– 100	NIFMDCP 100	NIFTY– 200	NIFSMCP 100
Part A
ρ	APSE	0.044	0.046	0.053	0.050	0.032	BRTI	0.220	0.216	0.174	0.175	0.022
SE	0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.019	0.019	0.019
∂ι	3.370	3.890	6.804	5.928	7.101		78.310	76.330	54.310	53.840	1.783
AIC	–2.739	–3.780	–9.607	–7.857	–10.201		–152.619	–148.655	–104.621	–103.674	0.433
ρ	ASPN	0.108	0.114	0.142	0.126	0.073	AXBK	0.322	0.325	0.305	0.298	0.058
SE	0.018	0.018	0.019	0.019	0.019		0.017	0.017	0.017	0.017	0.019
∂ι	17.500	19.710	34.090	25.150	9.393		169.800	174.300	153.700	145.600	7.837
AIC	–30.994	–35.410	–64.189	–46.292	–14.786		–335.589	–344.659	–303.353	–287.282	–11.673
ρ	BJFN	0.355	0.365	0.366	0.349	0.293	BAJA	0.000	–0.002	–0.001	0.011	0.107
SE	0.017	0.017	0.017	0.017	0.018		0.019	0.019	0.019	0.019	0.020
∂ι	213.200	227.700	232.900	211.400	141.700		0.477	0.519	1.521	2.222	28.810
AIC	–422.437	–451.488	–461.706	–418.762	–279.403		3.046	2.962	0.959	–0.445	–53.614
ρ	BJFS	–0.014	–0.013	–0.001	0.003	0.011	BPCL	0.131	0.132	0.120	0.118	0.002
SE	0.019	0.019	0.019	0.019	0.019		0.019	0.019	0.019	0.019	0.019
∂ι	0.745	1.017	1.777	1.985	2.174		–53.079	–54.324	–47.043	–44.670	3.832
AIC	2.510	1.967	0.445	0.029	–0.349		28.540	29.160	25.520	24.330	0.084
ρ	BHRI	0.012	0.018	0.036	0.028	0.024	BRIT	0.261	0.275	0.306	0.284	0.226
SE	0.024	0.024	0.024	0.024	0.024		0.018	0.018	0.017	0.018	0.018
∂ι	0.248	0.312	1.096	0.682	1.081		109.600	121.900	158.800	135.200	88.710
AIC	3.505	3.375	1.807	2.637	1.837		–215.112	–239.787	–313.635	–266.496	–173.411
ρ	CIPL	–0.039	–0.039	–0.036	–0.021	0.030	COAL	0.064	0.000	–0.014	–0.006	–0.011
SE	0.048	0.048	0.048	0.048	0.048		0.019	0.021	0.021	0.021	0.021
∂ι	1.383	1.433	0.746	0.907	0.205		9.412	0.447	0.223	0.046	0.152
AIC	1.234	1.134	2.508	2.187	3.591		–14.823	3.106	3.553	3.907	3.697
ρ	EICH	0.046	0.047	0.055	0.047	0.039	GAIL	0.223	0.225	0.203	0.209	0.058
SE	0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.018	0.018	0.019
∂ι	9.005	8.609	9.469	8.609	5.974		80.790	82.260	68.620	71.830	5.384
AIC	–14.009	–13.217	–14.938	–13.217	–7.948		–157.581	–160.518	–133.235	–139.664	–6.767
ρ	GRAS	0.235	0.233	0.196	0.200	0.060	HCL	0.226	0.222	0.185	0.189	0.018
SE	0.018	0.019	0.019	0.019	0.019		0.019	0.019	0.019	0.019	0.019
∂ι	94.240	93.110	69.440	71.540	6.475		93.880	91.410	67.580	67.320	4.794
AIC	–184.475	–182.219	–134.888	–139.081	–8.949		–183.770	–178.829	–131.163	–130.644	–5.588
Part B
ρ	HDFC	0.275	0.271	0.233	0.239	0.042	HDBK	0.287	0.284	0.250	0.257	0.063
SE	0.018	0.018	0.018	0.018	0.019		0.018	0.018	0.018	0.018	0.019
∂ι	135.100	130.800	92.080	97.900	4.542		147.000	144.700	107.600	115.500	6.503
AIC	–266.171	–257.635	–180.153	–191.796	–5.084		–289.972	–285.368	–211.275	–227.015	–9.005
ρ	HROM	0.006	0.009	0.017	0.019	0.014	HALC	0.014	0.014	0.019	0.019	0.031
SE	0.019	0.019	0.019	0.019	0.019		0.019	0.019	0.019	0.019	0.019
∂ι	0.590	0.773	1.697	2.701	0.489		2.915	3.330	4.400	3.697	2.218
AIC		2.819	2.453	0.607	–1.403	3.023		–1.829	–2.659	–4.799	–3.394	–0.436
ρ	HLL	–0.003	–0.006	–0.018	–0.016	0.019	ICBK	0.353	0.352	0.303	0.299	0.062
SE		0.019	0.019	0.019	0.019	3.645		0.018	0.018	0.018	0.018	0.019
∂ι	1.075	1.597	4.728	4.317	3.645		230.300	230.600	167.300	160.100	7.643
AIC	1.849	0.806	–5.455	–4.635	–3.291		–456.664	–457.209	–330.552	–316.274	–11.285
ρ	IOC	0.129	0.134	0.139	0.136	0.027	INBK	0.261	0.268	0.275	0.276	0.086
SE		0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.018	0.018	0.019
∂ι	30.160	32.460	36.630	35.920	1.557		114.800	122.300	136.500	136.200	18.020
AIC	–56.318	–60.911	–69.261	–67.845	0.885		–225.622	–240.599	–269.038	–268.319	–32.040
ρ	INFY	0.272	0.266	0.208	0.217	0.005	ITC	0.194	0.189	0.157	0.158	0.010
SE		0.018	0.018	0.018	0.018	0.019		0.019	0.019	0.019	0.019	0.019
∂ι	124.100	118.300	68.880	75.150	0.962		66.470	64.390	43.530	45.570	2.979
AIC	–244.270	–232.633	–133.762	–146.305	2.076		–128.937	–124.786	–83.054	–87.148	–1.958
ρ	JSTL	0.255	0.260	0.249	0.265	0.076	KTKM	0.284	0.289	0.274	0.272	0.048
SE		0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.018	0.018	0.019
∂ι	118.500	123.800	118.700	137.200	11.280		146.700	153.700	139.100	135.500	7.013
AIC	–233.013	–243.669	–233.309	–270.429	–18.552		–289.396	–303.495	–274.282	–267.021	–10.027
ρ	LART	0.310	0.310	0.281	0.273	0.064	MAHM	0.248	0.247	0.242	0.238	0.062
SE	0.018	0.018	0.018	0.018	0.019		0.019	0.019	0.019	0.019	0.019
∂ι	177.800	179.200	149.800	139.800	9.412		118.000	118.700	106.800	105.300	10.400
AIC	–351.693	–354.458	–295.627	–275.625	–14.823		–231.906	–233.319	–209.682	–206.607	–16.797
ρ	MRTI	0.005	0.006	0.008	0.001	–0.004	NEST	0.002	0.002	–0.005	–0.009	–0.029
SE		0.018	0.018	0.018	0.019	0.019		0.020	0.020	0.020	0.020	0.020
∂ι	0.035	0.049	0.191	0.107	1.100		0.008	0.016	0.031	0.084	1.009
AIC	3.930	3.903	3.617	3.786	1.801		3.984	3.968	3.939	3.832	1.982
Part C
ρ	NTPC	0.264	0.265	0.228	0.230	0.056	ONGC	0.224	0.222	0.182	0.189	0.051
SE		0.018	0.018	0.018	0.018	0.019		0.018	0.018	0.019	0.019	0.019
∂ι	119.400	120.300	89.100	92.200	5.893		84.590	83.790	58.300	64.400	6.840
AIC	–234.883	–236.602	–174.197	–180.394	–7.787		–165.170	–163.583	–112.608	–124.801	–9.679
ρ	PGRD	0.012	0.012	0.009	0.005	0.000	REDY	–0.007	–0.005	0.018	0.012	0.021
SE		0.019	0.019	0.019	0.019	0.019		0.019	0.018	0.018	0.018	0.018
∂ι	0.919	1.135	1.009	0.513	0.452		0.137	0.066	0.450	0.201	0.664
AIC	2.162	1.730	1.982	2.975	3.097		3.727	3.868	3.100	3.598	2.671
ρ	RELI	0.324	0.317	0.240	0.256	0.029	SBI	0.310	0.315	0.296	0.289	0.056
SE		0.018	0.018	0.019	0.018	0.019		0.018	0.018	0.018	0.018	0.019
∂ι	190.600	181.900	104.500	118.100	1.516		164.600	171.600	162.700	151.700	9.253
AIC	–377.158	–359.885	–204.976	–232.274	0.967		–325.194	–339.163	–321.401	–299.309	–14.507
ρ	SUN	0.119	0.119	0.111	0.111	0.033	TAMO	0.279	0.281	0.269	0.269	0.081
SE		0.019	0.019	0.019	0.019	0.020		0.018	0.019	0.019	0.019	0.019
∂ι	25.310	25.670	21.030	22.520	10.360		143.900	147.000	147.900	145.900	15.390
AIC	–46.616	–47.341	–38.062	–41.046	–16.725		–283.774	–290.001	–291.871	–287.895	–26.780
ρ	TISC	0.316	0.317	0.284	0.300	0.070	TCS	0.006	0.007	0.001	–0.003	–0.002
SE		0.018	0.018	0.018	0.019	0.020		0.019	0.019	0.019	0.019	0.018
∂ι	184.000	188.600	161.700	179.700	16.630		2.266	1.857	0.410	1.034	0.007
AIC		–364.069	–373.176	–319.352	–355.420	–29.259		–0.531	0.286	3.180	1.932	3.987
ρ	TEML	0.223	0.225	0.203	0.209	0.058	TITN	0.030	0.030	0.030	0.026	0.014
SE	0.018	0.018	0.018	0.018	0.019		0.018	0.018	0.018	0.018	0.018
∂ι	80.790	82.260	68.620	71.830	5.384		1.302	1.367	1.349	1.022	0.317
AIC	–157.581	–160.518	–133.235	–139.664	–6.767		1.397	1.266	1.301	1.956	3.366
ρ	ULTC	0.053	0.055	0.050	0.047	0.046	UPLL	0.193	0.201	0.220	0.224	0.106
SE	0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.019	0.019	0.019
∂ι	7.587	7.383	4.699	4.010	5.045		58.210	64.510	88.880	91.350	20.330
AIC	–11.175	–10.766	–5.398	–4.020	–6.090		–112.424	–125.016	–173.755	–178.700	–36.659
ρ	VDAN	0.026	0.027	0.032	0.032	0.033	WIPR	0.253	0.246	0.198	0.207	0.014
SE	0.019	0.019	0.019	0.019	0.019		0.018	0.018	0.019	0.019	0.019
∂ι	1.933	2.298	1.956	2.241	2.078		111.100	105.700	66.940	73.250	0.576
AIC	0.133	–0.595	0.089	–0.481	–0.156		–218.215	–207.473	–129.881	–142.509	2.847
ρ	YESB	0.278	0.284	0.298	0.286	0.086	ZEE	0.192	0.197	0.201	0.192	0.082
SE	0.018	0.018	0.018	0.018	0.019	0.018	0.018	0.018	0.019	0.019
∂ι	136.800	144.200	169.900	155.900	0.019	57.850	61.000	68.330	63.870	11.520
AIC	–269.556	–284.328	–335.718	–307.761	–29.650	–111.710	–118.009	–132.661	–123.745	–19.033

Source: The authors.

Note: In the following table, ρ denotes the t-copula estimate. SE, ∂l, and AIC are the corresponding standard error values, log-likelihood values, and AIC measures, respectively.

Regarding hedging property of these stocks, we observe 45 of them to exhibit a positive and significant ρ against all the five indices. Whereas, BAJA (Bajaj Auto), BJFS (Bajaj Finserv), CIPL (Cipla), NEST (Nestle), and REDY (Dr. Reddy’s Laboratories) show zero or negative ρs, thereby nullifying their hedging properties. Finally, we check the safe-haven properties. Student’s t-copulas always exhibit lower and upper tail dependence and since all the pairs modeled in our work are based on t-copulas, we determine the stocks with ρs ≥ 0.2 to have a pseudo–safe-haven properties. Stocks such as MRTI (Maruti Suzuki), TCS (Tata Consultancy Services), HLL (Hindustan Unilever), REDY (Dr. Reddy’s), HROM (Hero Motorcorp), COAL (Coal India), BAJA (Bajaj Auto), NEST (Nestle), EICH (Eicher Motors), CIPL (Cipla), BJFN (Bajaj Finance), APSE (Adani Port and Special Economic Zone), ULTC (Ultratech Cements), BHRI (Bharti Infratel), HALC (Hindalco Industries), TITN (Titan), and PGRD (Power Grid Corporation of India) show very low dependency. These findings are more or less pervasive across indices.

These copula estimates for these stocks with respect to the Nifty-100 index vary from estimates as low as –0.20% to 5.27%. NIFTY-100 represents the top 100 companies based on full market capitalization from NIFTY-500. The intention of this index is to measure the performance of large market capitalization companies. It evaluates the behavior of a combined portfolio of two indices, that is, NIFTY-50 and NIFTY Next 50, whereas the NIFTY-200 index is contrived to reflect the behavior and performance of large and mid-market capitalization companies. NIFTY-200 includes all companies forming part of NIFTY-100 and NIFTY Full Midcap 100 index. The copula estimates for the above-mentioned equities corresponding to the Nifty-200 index are from –0.11% to 5.47%. Similarly, the values with respect to Nifty-Midcap-100 solely are ranging from 0.34% to 4.70%. We document increasing lower limits as the equivalence among the stocks and the indices reduce. Finally, we check with the Nifty-Smallcap-100 index. The values for this are bound from –0.36% to 4.62%. However, we do not find the copula values, that is, the dependency structure, to be as modest and low as copulas calculated for gold and currencies from our literature. Owing to such disparities, we term the as pseudo–safe-haven. They are the possibly best bets among the NIFTY-50 stocks to generate, which could generate extra-ordinary profits and also safeguard the investment during times of extremities. The stocks that are pseudo–safe-haven are mostly consumer goods oriented companies and automobile industries. Moreover, mutual funds rated five stars by CRISIL include these stocks in predominant portions for the respective fund.

5. Conclusion

The popular investment choices such as fixed income, gold, and real estate have generated low or negative real returns for the investors over long horizons. Equity, which although comes with inherent risk, has performed much better. Indian investors are showing increasing interest in the equity markets over the years to seek decent returns. The recent crisis in the financial markets due to coronavirus makes a good starting point for digging good stocks, as they are available for a much cheaper price. They should be aware that the inherent risk in the equity market could possibly make investors lose their capital. Therefore, we need to look for quality stocks that are investor-friendly, that is, generates decent returns with much lower risk than a common equity index. Keeping that in mind, we examine the safe-haven and hedging properties of a basket of possibly quality stocks (Nifty-50 stocks) using a copula-based method. The capability to deal with fat tails and extreme co-movements of financial return data makes copula a better choice for our analysis.

We observe that stocks such as Maruti Suzuki, Tata Consultancy, Hindustan Unilever, Dr. Reddy’s, Hero Motor, Coal India, Bajaj Auto, Nestle, Eicher Motors, Cipla, Bajaj Finance, Adani Port, Ultratech Cements, Bharti Infratel, Hindalco Industries, Titan, and Power Grid act good as hedging instruments at times and also are a moderate version of safe-haven assets. We call them pseudo–safe-haven. Investors could benefit from investing in them, which could possibly generate decent returns with an acceptable level of capital protection. We expect our analysis to aid retail and institutional investors in making better investment decisions while keeping in mind that this is just a fragment that supplements to an extensive stock analysis.

Our contribution is dual. First, we develop the idea of pseudo–safe-haven investment (which provides decent returns with an acceptable level of capital protection) in an asset-class-like equity. Second, we add to the literature of portfolio management by providing academic backup to the process of picking the right stocks with one of the best suited and relevant econometric models.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

>Notes

References

Aloui

, Hammoudeh

, & Nguyen

D. K.

(2013). A time-varying copula approach to oil and stock market dependence: The case of transition economies. Energy Economics, 39, 208–221.

Arouri

M. H.

, Lahiani

, & Nguyen

D. K.

(2015). World gold prices and stock returns in China: Insights for hedging and diversification strategies. Economic Modelling, 44, 272–282.

Avdulaj

, & Barunik

(2015). Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data. Energy Economics, 51, 31–44.

Baur

D. G.

, & Lucey

B. M.

(2010). Is gold a hedge or a safe-haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217–229.

Baur

D. G.

, & McDermott

T. K.

(2016). Why is gold a safe-haven? Journal of Behavioral and Experimental Finance, 10, 63–71.

Baur

D. G.

, & Kuck

(2019). The timing of the flight to gold: An intra-day analysis of gold and the S&P500. Finance Research Letters. 10.1016/j.frl.2019.05.005

Beck

, & Rahbari

(2011). Optimal reserve composition in the presence of sudden stops. Journal of International Money and Finance, 30(6), 1107–1127.

Beckmann

, Berger

, & Czudaj

(2015). Does gold act as a hedge or a safe-haven for stocks? A smooth transition approach. Economic Modelling, 48, 16–24.

Bollerslev

(1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3), 307–327.

10.

Botman

D. P.

, Carvalho Filho

I. E.

, & Lam

M. R. W.

(2013). The curious case of the yen as a safe-haven currency: A forensic analysis (No. 13–228). International Monetary Fund.

11.

Bouyé

, Durrleman

, Nikeghbali

, Riboulet

, & Roncalli

(2000). Copulas for finance—A reading guide and some applications. https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.1032533

12.

Breymann

, Dias

, & Embrechts

(2003). Dependence structures for multivariate high-frequency data in finance. Quantitative Finance, 3(1), 1–14.

13.

Capie

, Mills

T. C.

, & Wood

(2005). Gold as a hedge against the dollar. Journal of International Financial Markets, Institutions and Money, 15(14), 343–352.

14.

Chollete

, De la Pena

, & Lu

(2006). Security comovement: Alternative measures, and implications for portfolio diversification (Unpublished Working paper). Columbia University and NHH.

15.

Cossin

, & Schellhorn

(2007). Credit risk in a network economy. Management Science, 53(10), 1604–1617.

16.

Coudert

, Guillaumin

, & Raymond

(2014). Looking at the other side of carry trades: Are there any safe-haven currencies? (Working Papers No. 2014-03). CEPII Research Center.

17.

Christoffersen

, Errunza

, Jacobs

, & Langlois

(2012). Is the potential for international diversification disappearing? A dynamic copula approach. The Review of Financial Studies, 25(12), 3711–3751.

18.

Das

, & Kayal

(2021). Super growth portfolio—A study of Indian stocks. Macroeconomics and Finance in Emerging Market Economies, 1–15. 10.1080/17520843.2021.1969086

19.

De Bock

, & de Carvalho Filho

(2015). The behavior of currencies during risk-off episodes. Journal of International Money and Finance, 53, 218–234.

20.

Dee

, Li

, & Zheng

(2013). Is gold a hedge or a safe-haven? Evidence from inflation and stock market. International Journal of Development and Sustainability, 2(1), 1–16.

21.

de Melo Mendes

B. V.

(2005). Computing conditional VaR using time-varying copulas. Brazilian Review of Finance, 3(2), 251–265.

22.

Durante

, Fernandez-Sanchez

, & Sempi

(2013). A topological proof of Sklar’s theorem. Applied Mathematics Letters, 26(9), 945–948.

23.

Embrechts

, Lindskog

, & McNeil

(2001). Modelling dependence with copulas (Rapport technique, p. 14). Département de mathématiques, Institut Fédéral de Technologie de Zurich.

24.

Embrechts

, McNeil

, & Straumann

(2002). Correlation and dependence in risk management: Properties and pitfalls. Risk Management: Value at Risk and Beyond, 1, 176–223.

25.

Embrechts

, Höing

, & Juri

(2003). Using copulae to bound the value-at-risk for functions of dependent risks. Finance and Stochastics, 7(2), 145–167.

26.

Fang

H. B.

, Fang

K. T.

, & Kotz

(2002). The meta-elliptical distributions with given marginals. Journal of Multivariate Analysis, 82(1), 1–16.

27.

Fatum

, & Yamamoto

(2016). Intra-safe-haven currency behavior during the global financial crisis. Journal of International Money and Finance, 66, 49–64.

28.

Fatum

, Yamamoto

, & Zhu

(2017). Is the renminbi a safe-haven? Journal of International Money and Finance, 79, 189–202.

29.

Feng

, Wang

, & Zhang

(2018). Can cryptocurrencies be a safe-haven: A tail risk perspective analysis. Applied Economics, 50(44), 4745–4762.

30.

Fortin

, & Kuzmics

(2002). Tail-dependence in stock-return pairs. Intelligent Systems in Accounting, Finance & Management, 11(2), 89–107.

31.

Fratzscher

(2009). What explains global exchange rate movements during the financial crisis? Journal of International Money and Finance, 28(8), 1390–1407.

32.

Genest

, & Rivest

L. P.

(1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88(423), 1034–1043.

33.

Glosten

L. R.

, Jagannathan

, & Runkle

D. E.

(1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779–1801.

34.

Grisse

, & Nitschka

(2015). On financial risk and the safe-haven characteristics of Swiss franc exchange rates. Journal of Empirical Finance, 32, 153–164.

35.

Habib

M. M.

, & Stracca

(2012). Getting beyond carry trade: What makes a safe-haven currency? Journal of International Economics, 87(1), 50–64.

36.

Hammoudeh

, & Yuan

(2008). Metal volatility in presence of oil and interest rate shocks. Energy Economics, 30(2), 606–620.

37.

Hoffmann

, & Suter

(2010). The Swiss franc exchange rate and deviations from uncovered interest parity: global vs domestic factors. Swiss Journal of Economics and Statistics, 146(1), 349–371.

38.

Hood

, & Malik

(2013). Is gold the best hedge and a safe-haven under changing stock market volatility? Review of Financial Economics, 22(2), 47–52.

39.

(2006). Dependence patterns across financial markets: a mixed copula approach. Applied Financial Economics, 16(10), 717–729.

40.

(2010). Dependence structures in Chinese and US financial markets: A time-varying conditional copula approach. Applied Financial Economics, 20(7), 561–583.

41.

Jondeau

, & Rockinger

(2006). The copula-GARCH model of conditional dependencies: An international stock market application. Journal of International Money and Finance, 25(5), 827–853.

42.

Joe

(1997). Parametric families of copulas. In Joe

(Ed.), Multivariate models and dependence concepts (pp. 139–168). Springer.

43.

Joy

(2011). Gold and the US dollar: Hedge or haven? Finance Research Letters, 8(3), 120–131.

44.

Kaul

, & Sapp

(2006). Y2K fears and safe-haven trading of the U.S. dollar. Journal of International Money and Finance, 25(5), 760–779.

45.

Kayal

, & Balasubramanian

(2021). Excess volatility in Bitcoin: Extreme value volatility estimation. IIM Kozhikode Society & Management Review. 10.1177/2277975220987686

46.

Kayal

, & Maheswaran

(2021). A study of excess volatility of gold and silver. IIMB Management Review, 33(2), 133–145.

47.

Kayal

, & Rohilla

(2021). Bitcoin in the economics and finance literature: A survey. SN Business & Economics, 1(7), 1–21.

48.

Kohler

(2012, March). Exchange rates during financial crises. BIS Quarterly Review. https://www.bis.org/publ/qtrpdf/r_qt1003f.pdf

49.

Lai

, Chen

C. W.

, & Gerlach

(2009). Optimal dynamic hedging via copula-threshold-GARCH models. Mathematics and Computers in Simulation, 79(8), 2609–2624.

50.

Lai

, & Tseng

J. C.

(2010). The role of Chinese stock market in global stock markets: A safe-haven or a hedge? International Review of Economics & Finance, 19(2), 211–218.

51.

D. X.

(2000). On default correlation: A copula function approach. The Journal of Fixed Income, 9(4), 43–54.

52.

Mashal

, & Zeevi

(2002). Beyond correlation: Extreme co-movements between financial assets (Unpublished thesis). Columbia University.

53.

McCauley

R. N.

, & McGuire

(2009, December). Dollar appreciation in 2008: Safe-haven, carry trades, dollar shortage and overhedging. BIS Quarterly Review. https://www.bis.org/publ/qtrpdf/r_qt0912i.htm

54.

Nathan

(2019, March 5). Should you jump onto index Next 50s bandwagon now? The Economic Times. https://economictimes.indiatimes.com/markets/stocks/news/should-you-jump-onto-index-next-50s-bandwagon-now/articleshow/68263780.cms?from=mdr

55.

Nelson

D. B.

, & Cao

C. Q.

(1992). Inequality constraints in the univariate GARCH model. Journal of Business & Economic Statistics, 10(2), 229–235.

56.

Nelson

(1999). An introduction to copulas (Lecture notes in statistics). Springer.

57.

Nguyen

, Bhatti

M. I.

, Komorníková, M., & Komorník

(2016). Gold price and stock markets nexus under mixed-copulas. Economic Modelling, 58, 283–292.

58.

Nirmal

(2019, August 11). Gold prices soar. Should you invest? The Hindu Business Line. https://www.thehindubusinessline.com/portfolio/big-story/gold-makes-a-comeback-should-you-invest/article28982630.ece

59.

Patton

A. J.

(2009). Copula–based models for financial time series. In Patton

A. J.

(Ed.), Handbook of financial time series (pp. 767–785). Springer.

60.

Ranaldo

, & Söderlind

(2010). Safe-haven Currencies. Review of Finance, 14(3), 385–407.

61.

Reboredo

J. C.

(2013). Is gold a safe-haven or a hedge for the US dollar? Implications for risk management. Journal of Banking and Finance, 37(8), 2665–2676.

62.

Shahzad

S. J. H.

, Bouri

, Roubaud

, Kristoufek

, & Lucey

(2019). Is Bitcoin a better safe-haven investment than gold and commodities? International Review of Financial Analysis, 63, 322–330.

63.

Sklar

(1959). Distribution functions with n dimensions and their margins. Publications of the Institute of Statistics of the University of Paris

64.

Smales

L. A.

(2019). Bitcoin as a safe-haven: Is it even worth considering? Finance Research Letters, 30, 385–393.

65.

Van Hoang

T. H.

, Lahiani

, & Heller

(2016). Is gold a hedge against inflation? New evidence from a nonlinear ARDL approach. Economic Modelling, 54, 54–66.

66.

Varma

, Venkataramani

, Kayal

, & Maiti

(2021). Short-term impact of COVID-19 on Indian stock market. Journal of Risk and Financial Management, 14(11), 558.

67.

Wen

, & Cheng

(2018). Which is the safe-haven for emerging stock markets, gold or the US dollar? Emerging Markets Review, 35, 69–90.

68.

, Tong

, Yang

, & Derbali

(2019). Does gold or Bitcoin hedge economic policy uncertainty? Finance Research Letters, 31, 171–178.

69.

Zakoian

J. M.

(1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931–955.

70.

Zhang

Y. J.

, & Wei

Y. M.

(2010). The crude oil market and the gold market: Evidence for cointegration, causality and price discovery. Resources Policy, 35(3), 168–177.

71.

Zhu

H. M.

, Li

, & Li

(2014). Modelling dynamic dependence between crude oil prices and Asia-Pacific stock market returns. International Review of Economics & Finance, 29, 208–223.