Do Mutual Funds Reduce Stock Market Volatility? Evidence from Emerging Market

Abstract

Investors often seek to invest in the safer and stable avenues with the additional benefits of diversification and liquidity to evade adverse exposures to risk during the market downturn. This study investigates the dynamics of 27 different classes of mutual funds and stock market volatility in Pakistan over the period of 1991 to 2018. Using wavelets at multiple time horizons, the findings reveal the negative association between majority of mutual fund classes and stock market volatility, which imply contrarian feedback behaviour of mutual funds in response to high stock market fluctuations. This finding helps the potential investors to acquire better yields with cautious trading in fragile and risky stock market. The results confirm that the relationship between variables is assorted in nature. These results assist the investors and market traders to shift their investment avenues which, in turn, may put pressure on the stock market by reducing market volatility. The correlation between variables confirms and favors long-term relationship between low and medium frequencies; and transient coherence is observed at higher frequencies, which facilitates portfolio managers and speculators respectively to make rational decision making, based on time horizon. Moreover, the granger coherence results are momentous for some of the mutual fund classes, which reflects long-run components holding the forecasting ability. These conclusions assist in foreseeing and hedging strategies against market losses and have important policy implications for investors, portfolio managers, market analysts and policy makers.1

Keywords: Mutual funds, Stock market volatility, Wavelets, Pakistan.

JEL Classification: G2, G11, G14, G18, G23.

1. Introduction

The role of financial institutions is important and indispensable in the newly emerging developing countries which are striving to develop national economy, blending all resources- national and human towards this end. The twentieth century is distinguished for evolution, outburst and circulation of new scientific, political and economic thoughts and creations (Stiglitz, 2004). One of the new economic and institutional thoughts that has expanded fast globally and has dominated other financial institutions all over the world is “Mutual funds”. A mutual fund pools the funds and savings from many investors and invests those funds in financial securities (Such as Stock, bond, money market securities). Mutual funds, being professional or institutional managers, manage the investments for the benefit of their investors in return, for a management fee. They provide the benefits of diversification, liquidity, professional management and convenience in holding the securities.

Mutual funds play significant and crucial role in growing financial and corporate world. The asset management industry has made remarkable progress in providing financial services to its valued customers and has expanded tremendously at worldwide from the last two decades (Qureshi, Ismail, & Gee Chan, 2017).The industry has immensely increased to the size of Rs. 614 billion in 2018 from Rs. 25 billion in 2002 in 16 years,2i.e. showing a phenomenal increase of 2356 %. The notable reason for said growth of mutual funds is attributed to the increasing innovations of contemporary investment. Hussain

1 This research work is funded by Higher Education Commission (HEC) of Pakistan, No-21-1938/SRGP/R&D/HEC/2018. 2Data is taken from Pakistan & Gulf Economist, report published on Mar17-23,2008,http://www.pakistaneconomist.com/database2/cover/c2008-39.php , http://www.pakistaneconomist.com/issue2002/issue30/cover.htm

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(2018e) stated that total size of mutual fund industry in Pakistan is around Rs. 614 billion, which consists of equity market funds at Rs. 173 billion, and Money Market funds i.e. marking at Rs. 129billion for the year 2018. It is evident that mutual funds, being professional investors, are the biggest participants in the stock market and have capability to change the direction of the stock market (Hussain, 2018f). Hussain (2018c) confirmed that the funds shift their investment to secure and safer investment avenues with better yields, thus provide hedge against market losses. In addition, fixed income products (for instance, 3-year Pakistan Investment Bonds, money market and balanced mutual funds) are getting more popular in an economy which is confronted with problem of higher inflation and higher interest rates. Moreover, many analysts believe that current investment in Pakistan stock market is very risky and yields high returns for those who can sustain losses. Whereas for moderate and small investors, who can’t sustain losses must invest through a mutual fund to protect themselves against unexpected volatility (Hussain, 2018g).

The unpredictable market patterns and volatility in securities' prices compel the need to study and understand technical and analytical study of financial securities to make rational and profitable investment decisions. Mutual funds provide viable solution in such complex circumstances by offering numerous benefits and services to the investors over direct investing. Financial markets, on the other side, offer a platform to execute trade and transaction from the households to the borrowers, thus boost an efficient capital allocation and management (Cooray, 2010). Nonetheless, the efficient mechanism of the financial markets is mostly constrained by market volatility (Qureshi, Ismail, & Gee Chan, 2017). Market volatility indicates the risk and uncertainty in prices of securities, which may hinder the smooth functioning of financial market mechanism (Mundell, 2000).

Prior studies postulate that mutual funds, being the institutional traders, help in controlling the market risk and volatility through diversification and liquidity, and follow the market performance rationally (see for instance, Dennis and Strickland (2002); Faugere & Shawky(2003); Kaniel, Saar, and Titman (2008)). Conversely, some studies provide contrary evidence. For instance, Sias (1996) suggests that institutional investors depict concurrent reaction with the stock market and raise their trading activities in times of high market volatility. Being institutional investors, mutual funds may engage in herding the stock market activity that may accelerate price movements and increase volatility. Thus, the literature has provided mixed and contradictory evidences on the relationship of mutual funds with stock market volatility. Moreover, the studies such as Brown, Harlow, & Starks, (1996); Sias (1996); Dennis & Strickland(2002) find positive relationship between mutual funds and stock market volatility, while others find negative association between the professional trading and stock market volatility (Grier & Albin, 1973; Reilly, 1977; Reilly & Wachowicz Jr, 1979). Furthermore, there is voluminous research3 on the stock market returns and stock market volatility, which is mainly focused on developed countries, but the literature on mutual funds and market volatility has received scant attention, particularly in emerging economies, where security market mechanism is mostly fragile and unpredictable (Pitterle, Haufler, & Hong, 2015). There is hardly any literature on mutual fund flows and market volatility in Pakistan at macro or industry level according to the best estimate.

This study aims to investigate the role of mutual funds in stabilizing stock market volatility in emerging economy, i.e. Pakistan. Stock market volatility is viewed as a main challenge for the sustainable development of the stock markets and Pakistan is confronting this problem since last many decades due to the absence of efficient investments, regulations and proper market mechanism over the securities market (Khan & Ahmed, 2019; Shah, Hasnat, Ahmad, & Li, 2019).

Hussain (2018a) stated that stock prices showed downward trend by 30 percent after their peak position in May 2017 at all-time high of 53,123 points. There were number of factors which were accountable to this downward position but the main factor was political and economic uncertainty. Pakistan Stock exchange (PSX-100) index fell 1328 points in October 8, 2018, which was the biggest one-day stock market crash,

3Studies such as Luo, Qin, and Ye (2016), Wang, Lin, Kang, and Fung (2016), Yang (2016), Bannigidadmath and Narayan (2016), Chakraborty and Kakani (2016).

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reported in the past 15 months (Aazim, 2018). At present, the total number of companies listed on the Pakistan Stock market is 559, which is abysmally low compared to 638 companies listed six years ago. Whereas, on the other hand, the number of registered firms at the Securities and Exchange Commission of Pakistan (SECP) has shown increasing trend and stand at about 100,000. This scenario yields intense volatility in the stock market, since investors have limited options to invest and a lot of funds chase few blue-chip companies’ securities (Hussain, 2018d).

The volatile market and fragile economy of Pakistan instigate the investors to invest in more secure and safer avenues such as mutual funds. Empirical evidence in developed countries suggests that mutual funds, being the institutional investors, help in controlling the risk and volatility through information and diversification. As institutional investors, mutual funds greatly influence the stock market variables through their trading activities (Edwards & Zhang, 1998). On the other hand, the performance of financial markets also influences the mutual fund trading. Similarly, investors in the financial markets reallocate their money from risky (equity-based) securities to less-risky (fixed-income based) securities, and safe havens in case of market turmoil (Sias, 1996; Faugere & Shawky, 2003). Consequently, the shift of investment from equity to fixed income securities also influences the stock market variables, that, in turn, puts pressure on the stock market by reducing market returns and volatility (Schwert, 1990; Cao, Chang, & Wang, 2008). This study begs the fundamental question on whether the mutual funds can bring the stability in the Pakistani stock market, given the risky nature of it. The study proposes a relevant research to determine, whether mutual funds reduce stock volatility in Pakistan and whether they can facilitate challenges, faced by portfolio analysts and investors in earning stable rate of return in an unstable market. Since various strategies, chosen by mutual funds, may be offsetting (depending on the objective of funds).The overall effect of mutual fund trading on stock market fluctuations is an imperative empirical question which is examined in this study.

The present study contributes to the literature in several ways. First, this study investigates the relationship of 27diverse classes of mutual funds and stock market volatility in Pakistan. It investigates the investment behaviour of each mutual fund class and impact of trading on stabilizing stock market risks and uncertainties. Thus, the study explores and compares the role of different mutual fund classes with stock market volatility. Second, our estimation approach is different from the extant literature. The study employs wavelet based techniques on daily data. It determines and segregates the components that capture information across various time scales and identify at which horizon the relationship is more prominent. Previous studies (Such as; Edwards and Zhang (1998), Ben-Rephael et al. (2012), Jank (2012)) follow Vector Auto Regressive (VAR) model to determine causal relationship between mutual fund flows and stock market variables. However, VAR model does not provide the in-depth association at different time scales. Moreover, VAR at level is applied with the condition of stationarity. Conversely, the wavelet coherence does not need any stationarity in the series of data and it also carries out more decomposition in the data. The technique provides comprehensive, thorough and detailed analysis by separating the data into numerous time scales. Thus, our study investigates the interdependence of stock market volatility and mutual fund flows based on multiple time scales to examine the in-depth extent of interaction. Furthermore, the wavelet granger coherence analysis is the ancient methods to granger causality that have given insightful causality perspectives. Third, the present study is implemented in a quite broad and interesting time frame, i.e., 1991–2018, since it covers both periods of “bull” and “bear” stock markets and periods of economic expansions and recessions. These empirical findings on different time scales are expected to shed further light on the role of mutual funds in diverse stock market and economic conditions when making rational decision making. Fourth, the study provides thorough knowledge about flight-to-quality strategies among different classes in pretext of emerging economy. The study helps the policy makers to determine the ways and methods in which mutual funds can counter and balance the stock market fluctuations in Pakistan. It may facilitate in formulating the policy for the systematic and smooth mechanism of institutional investments for reducing the stock market risk and uncertainty. The study also provides platform in examining the implications of the investments by mutual funds in Pakistan stock market. Last, the study covers almost all classes of mutual funds, presently active in emerging economy, i.e. Pakistan, which is one of the broad and comprehensive industry-wide studies

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and is rare study of its kind. The findings confirm negative association of major classes of mutual funds and stock market volatility. The correlation for most of the pairs of mutual fund-market volatility exhibits long term relationship of mutual funds with stock market volatility. The granger coherence results are momentous for some of the mutual fund classes which reflect long-run components holding the forecasting ability.

2. Theoretical Framework

Literature has provided various theories to explain the relationship between mutual funds and stock market variables. This section discusses theoretical framework of the study that includes the discussion of each theory/hypothesis followed by theoretical linkages of mutual funds and financial markets. Prior studies discuss two theories to explain the relationship between mutual funds and stock market variables. Warther (1995) explains that the price pressure theory and the feedback trading theory explain the relationship of mutual fund and financial market nexus.

2.1. Price Pressure (PP) Hypothesis/Theory

Price pressure theory states that mutual fund flows bring price pressure in the financial market by trading excessively. Excessive buying and selling by the mutual fund push the prices upward and downward respectively in the market the next day. As a result, these flows cause the market return to move and react. This reaction of market occurs due to demand and supply effects on prices rather than permanent fundamental information effect. The theory is also called investor’s sentiment theory, which proposes that mutual fund flows bring price pressure in the financial market by trading excessively. However, the price reverts back to its original position after perceiving short term price effect, triggered by fund flows (Harris &Gurel, 1986; Warther, 1995; Goetzmann & Massa, 1999; Zheng, 1999; Goetzmann et al., 2000; Ben-Rephael et al., 2011). Goetzmann & Massa (1999) test the PP theory on index funds to S&P market Index to check whether the market reacts temporary on investors’ flows or due to the permanent change. Mean reversion of prices takes place if flow of information is transitory. Ben-Rephael et al. (2011) evaluated whether the investors are informed under PP effect, as the pressure is temporary and it indicates that investors are uninformed. Mutual fund managers are forced to react to the demand from their investors as they are supposed to invest money in respective securities.

2.2. Feedback Trading (FT) Hypothesis/Theory

The Feedback trading (FT) theory is also called the feedback herding theory or performance chasing theory. It explains that the funds chase the past performance of market and react accordingly. The theory states that market returns influence the mutual fund flows. The investors buy securities when the security market price rises and sell them when it falls. Hence, it can be inferred that it is the market that brings reaction and movement in the fund flows (Warther, 1995; Edelen& Warner, 2001; Oh &Parwada, 2007).

Feedback trading theory asserts the relationship of mutual funds with financial market returns in context of performance chasing behavior of funds. Furthermore, Goetzmann et al. (2000) provide three potential explanations on the evidence of concurrent relation between flows and returns. First, the buying behavior of the investors in particular type of mutual funds leads to massive increase in the asset price in that fund (Price Pressure Theory). Second, the positive movement in the market returns and assets' prices trigger the investors to buy more equities and increase the size of their portfolios (Feedback Trading Theory). The third possible explanation is that there is another factor that influences both price and flows (Information Response Theory).

2.3. Information Response Theory (IR)

The Information Response theory emphasizes on the permanent changes (rather than temporary) in the behavior of market prices and fund flows to new macroeconomic information in the market. It entails that market returns and fund flows react simultaneously to the new information. The researchers who reject

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both PP and FT theory [such as, (Warther, 1995; Jank, 2012)] state that neither the fund flows moves the market (PP theory) nor the market moves the fund flows (FT theory), but instead, there is a third variable which is the macroeconomic variable (IR theory) which brings reactions and movements concurrently to both market returns and fund flows (Warther, 1995; Jank, 2012). IR theory has two assumptions. First, the mutual fund flows react to the macroeconomic information. Second, mutual fund flows predict macroeconomic conditions. IR theory states that fund flows respond positively to the new superior information. Fama (1981) tests information response theory in stock market and discovers that stock market returns react to new information regarding real investment. Further, the information response theory is supported by Jank (2012) who suggests that strong correlation exists between equity mutual fund flows and stock market returns concurrently due to the news regarding macroeconomic information. Moreover, Jank (2012) states that under information response theory, mutual fund flows should be able to forecast the economic conditions if they make their investment decisions based on the information about economic activity.

2.4. Theoretical Linkage

Theoretical linkages of theories on mutual funds and financial market variables are linked with the well-known "Efficient Market Theory" (Fama, 1970). The three established and testable theories (price pressure, feedback trading, and information response as discussed earlier), related to the relationship of flow-market nexus, are linked to the neoclassical efficient market theory. The ‘efficient markets theory’ states that the stock prices fully reflect the information and investors are able to respond to the market information efficiently. Under the efficient market theory, one cannot earn return in excess of average returns in market, given the information is quickly available to everyone in the financial market, as market is efficient in incorporating the information (Majumder, 2013). In other words, security prices reflect complete information about overall market, as prices adjust swiftly to the new information arriving in the market. Particularly, the semi-strong efficiency form explains that stock prices must contain all available information including public information. This information has imperative implications for financial analysts and policy makers. For instance, it is stated that stock prices should reflect the expectations about corporate world performance and that performance is dependent on the level of macroeconomic conditions. This would mean that if security prices and trade accurately reflect the economic fundamentals, the trading in security market should then be considered as predicting indicator of economic activities. Therefore, studying the trading practices (reflected in fund flows and security prices/NAVs) of institutional investors (mutual funds) and financial market variables would be considered indispensable in devising an economy’s macroeconomic policies.

Neoclassical efficient market theory asserts that independent institutional investors and decentralized markets are able to efficiently exercise the influence over investment and allocation decision making. This is happening due to the growing trend of disintermediation, liquidation, and securitization. However, despite this trend, the efficient market theory has been challenged from taking into account the “information asymmetries” and cognitive biases of individual investors (behavioral finance). The former states that investors are unable to make accurate investment decisions about securities’ future returns due to lack of information, which can lead to “adverse selection” problem (Brealey et al., 1977; Buch & Pierdzioch, 2005).

On the other hand, behavioral finance argues that some investors (mutual funds) are not fully rational, and their trades (flows) are affected either by their sentiments and beliefs (price pressure theory) or by following other investors and trends (feedback trading theory), rather than the trading process being fully justified by economic fundamentals (information response theory).

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Figure 1: Efficient market theory and related theories

[Source: Harmes (2000)]

Furthermore, neoclassical efficient market states that institutional autonomous investors contribute in asset allocation in three ways. First, institutional investors make centralized investment decision-making and influence the overall security market (price pressure theory). Second, institutional investors observe and follow the behavior of others and ignore economic fundamentals (Feedback trading theory). Finally, they evaluate economic fundamentals and incorporate information in their decision making (Information response theory).4 Thus, the neoclassical efficient market theory assumption indirectly relates with the mutual funds behavior of how efficiently they incorporate both market and economic related information, which is depicted in the trading behavior (fund flows) of mutual funds (Harmes, 2000).

2.4.1. Price Pressure Theory and Efficient Market TheoryNeoclassical assumption states that the institutional investors may make centralized investment decision-making and influence the market by increasing and decreasing the price with their trading. This assumption is reflected under PP theory which states that institutional investors bring price pressure in the financial market by trading excessively. Excessive buying (selling) by them pushes the prices upward (downward) in the market the next day. As a result, excessive trading causes the market return to move and react. This reaction of market occurs due to demand and supply effect on prices, rather than permanent fundamental information effect. This happens due to higher capital inflows (outflows) in market which lead the price of the asset to surge (decline), which further reinforces the investors’ favorable (unfavorable) view for further investment in the asset. Thus, it becomes obvious for arbitragers to not only chase the herd, but to also give rise to trend-following behavior of traders.

However, the neo classical assumption states that unfettered financial markets may remain efficient even if some investors do not adopt rationalism in their investment policies. Specifically, it argues that liberalized financial markets will always allocate the capital efficiently due to the existence of 'arbitragers'. Arbitragers are rational investors who buy and sell financial assets, which have been mispriced by other investors; thereby bringing prices towards fundamentals and thus, offsetting the price imbalances by non-rational investors (price pressurers).

4For brevity purpose, the details on Information response hypothesis are not discussed as this discussion is out of the scope of this paper.

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Efficient Market Theory

Price Pressure theory

Feedback Trading theory

Information Response theory

Behavioral Biases

Information Asymmetries

2.4.2. Feedback Trading Theory and Efficient Market Theory Earlier , it is stated that efficient market theory is challenged on the basis of not considering the information asymmetries, which can create opportunity for herding behavior (feedback trading effect) and market overreaction (price pressure effect). Under this situation, it becomes rational for the investors to chase or herd the trading behavior of other investors who have better information about underlying economic fundamentals. Thus, the investors trade on the basis of past information and feedback of overall market and chase the trend accordingly. This also happens because the institutional investors lack expertise and when the costs of collecting information are high. Taking this as a whole, FT theory explains that investors chase the past performance of overall market investors and react accordingly. The investors buy and sell securities with rise and fall in market price. It is the market that brings reaction and movement in the fund flows (Warther,1995; Edelen & Warner, 2001; Oh & Parwada, 2007).

2.4.3. Information Response Theory and Efficient Market TheoryConventional view suggests that investors under efficient market situation incorporate all underlying information comprising of market-related, micro-related, and macro-related information in their investment decision making. Keeping this view, mutual funds being professional investors are more seemingly and fully becoming rational due to better market and economic information, thus is able to suppress noise trading through arbitrage. In other words, professional mutual fund managers (and the analysts who serve them) can lessen information asymmetries through their aggressive information gathering about underlying economic fundamentals. Neoclassical 'efficient markets theory' argues that security prices will always reflect economic fundamentals because some market investors may act irrationally and may move prices away from their fundamentals, however, there will always be others to move them in the opposite direction.

Efficient market theory was challenged and criticized on the basis of information asymmetries and behavioral biases. However, this gave new rise to theories e.g. PP, FT, and IR theory. Figure 1 explains the relationship of efficient market theory with other related theories. Davis (1998) states that national financial markets are gradually tending to be chosen strategically with prompt changing in response to macroeconomic conditions. Fama (1981) tests IR theory in stock markets and discovers that stock market returns react to new information regarding real investment. Further, the IR theory is supported by Jank (2012) who suggests that strong correlation exists between equity mutual fund flows and stock market returns concurrently due to the news regarding macroeconomic information. Overall, the neoclassical 'efficient markets theory' contends that any centralization or concentration of power does not exist within the financial markets that may influence funds to be allocated in a collective (PP theory) or, herd fashion (FT theory) or in such a way that neglects economic fundamentals (IR theory).

Neoclassical Efficient market states that institutional autonomous investors contribute in asset allocation in three ways. First, institutional investors make centralizing investment decision-making and influence the overall security market (price pressure theory). Second, institutional investors observe and follow the behavior of others and ignore economic fundamentals (FT theory). Finally, they evaluate economic fundamentals and incorporate information in their decision making (IR theory). Thus, the neoclassical efficient market theory assumption relates with the mutual funds behavior of how efficiently they incorporate both market and economic related information which is depicted in the trading behavior (fund flows) of mutual funds.

2.5. Related Works

Previous literature5 focuses on two conduits of relationship of mutual funds and market volatility. First, mutual funds chase the prior performance of the market. The mutual funds forecast future market returns and fluctuations based on past performance and adopt positive feedback strategy by buying from up-market and selling in-down market. They are professional and institutional investors’ who respond rationally to the market noises (Friedman, 1953; Fama, 1965; Grier & Albin, 1973; Reilly, 1977; Reilly &

5For example, Aggarwal and Rao (1990); Kaniel, Saar, and Titman (2008), Sias (1996).

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Wachowicz Jr, 1979; Cao et al., 2008). Conversely, Goetzmann and Massa (1999) and Zheng (1999) concur that mutual funds are concomitantly linked with stock market volatility as compared to retail investors flows.

Consequently, some studies conclude that professional investors prefer volatile securities i.e. more appealing for investment, as they outperform the market.6 Thus, the funds may engage in positive feedback trading and herding that may further escalate the stock prices and accelerate the volatility. 7 In addition, certain studies (Brown et al., 1996; Sias, 1996; Dennis & Strickland, 2002) infer positive linkage between investment sentiments (mutual funds) and market volatility. However, others find opposite reaction between the variables (Grier & Albin, 1973; Reilly, 1977; Reilly & Wachowicz Jr, 1979; Cao et al., 2008). Cao et al. (2008) posit the causal relationship between market volatility and fund flows, whereas Thomas, Spataro, and Mathew (2014) find negative relationship between pension funds and stock market volatility. Overall, there are limited studies on flow-volatility link and the findings of these studies have been inconclusive and contradictory. Furthermore, majority of studies have been on micro-analysis of mutual funds.8However, the research work on macro-analysis of this relationship remains emergent and rare.9Furthermore, the studies are conducted mostly in the context of developed countries.10There is hardly any research work on mutual fund flows and market volatility from the perspective of developing markets like Pakistan. Moreover, the study in context of Pakistan has mainly been based on firm/sector level or micro level performance. For instance, Nazir et al., (2010) conduct study on the role of various factors in determining the mutual funds’ growth in Pakistan. Shah etal., (2005) find that the closed ended funds outperformed as compared to the market and due to lack of adequate diversification, the funds may underperform in comparison to its market. However, Khalid et al., (2010) conduct the study on the determination of performance and growth of closed ended mutual funds. This study seeks to determine the relationship of other all types of mutual funds in Pakistan and their aggregate reaction of confronting and countering the market risk and volatility, which is non-existent to the best of the researcher’s knowledge.

2.6. Empirical Model

2.6.1. Estimation technique-Wavelet analysisThe study employs wavelet technique to produce structural data, containing fragments of assorted lengths. Different applications of wavelet methodology in finance and economics have been incorporated by Percival &Walden (2000) and Gençay, Selçuk, & Whitcher (2001a); Gençay, Selçuk, & Whitcher, (2001b). One of the advantages of this analysis is time series decomposition into underlying functions that provides serial information. The various scales of time series retrieve functional information from the data (Qureshi, Rehman, & Qureshi, 2018).This study investigates the interdependence of stock market volatility and mutual fund flows based on multiple time scales to examine the extent of interaction using daily data. The study examines whether investment by mutual funds can help in stabilizing stock market volatility. If the mutual fund flows are found to have negative feedback/lagging behaviour, it would imply that mutual funds’ trading can reduce the market volatility by decreasing market trading activity and switching for alternative, safer avenues. Moreover, leading negative behaviour would imply negative price pressure in the market, which entail decline in market trading; thus, decrease the market price

6 See for example Falkenstein (1996); Gompers and Metrick (2001); Gabaix, Gopikrishnan, Plerou, and Stanley (2006),Klemkosky (1977); De Long, Shleifer, Summers, and Waldmann (1990); Falkenstein (1996); Nofsinger and Sias (1999); Gompers and Metrick (2001); Sias (2004); Gabaix et al. (2006).7See for example Klemkosky (1977); De Long et al. (1990); Nofsinger and Sias (1999); Sias (2004); Bohl,Brzeszczyński, and Wilfling (2009).8 For instance Grier and Albin (1973); Reilly (1977); Reilly and Wachowicz Jr (1979); Cohen, Gompers, and Vuolteenaho (2002)9Few studies exists on pension funds and market volatility on macro-level, for example Studies by,Davis and Hu (2004) ,Thomas et al. (2014).10Such as Demirer and Kutan (2006), Barber and Odean (2008), Rubin and Smith (2009), Zhou and Peng (2007), Li and Wang (2010), Azzam (2010) and Park (2015).

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fluctuations. Wavelet based analysis gave detailed analysis and estimation of casual relationship between market volatility and mutual fund flows.

2.6.1.1. Discrete wavelet transformation (DWT)Two types of wavelet (father φand mother wavelets ψ) in general can be distinguished, relying on normalization principles. The mother wavelet integrates to 0 (∫ψ ( t ) dt=0 )and father wavelet integrates

to 1(∫ φ (t )dt=1). The father wavelet reflects low frequency signals or smooth components of signal, whereas the mother wavelet reflects high frequency signals or detailed components of signal. By transmuting any function i.e. y(t) in L2(R) (the space for square summable functions) into divergent frequency constituents through a resolution matched to its scale, the wavelet function can be constructed as a series of projections over mother and father wavelets, originated from the scaling and translation as follows:

φ j , k ( t )=2− j/2 φ(2− j t−k) (1)ψ j , k (t )=2− j /2 ψ (2− jt−k) (2)Where j is equal to 1,2,…; J and k are the scaling and translation parameters respectively in a J-level decomposition. Hence, the wavelet illustration of the signal y(t) in L2(R) can be articulated as:y(t)= ∑

kSJ ,k ∅ J , k (t )+∑

kdJ ,k ψ j , k (t )+ ∑

kdJ−1 ,k ψ j−1 , k ( t )+…+∑

kd1 , k ψ1 , k ( t ) (3)

Wheres j ,k=∫ y (t )∅ j , k (t ) dtand d j ,k=∫ y (t )ψ j ,k (t ) dt . J in Equation (3) represents the number of multi-resolution constituents, i.e.s j ,k indicates the smooth coefficients, and d j ,k indicates the detail coefficients. The coefficients’ value estimates contribution of the corresponding wavelet function in relation to the total signal.In equations 1 and 2,2 j designates the dilation factor, whereas 2 jk ,i.e. the translation parameter, signifies the location parameter. The greater value of index j corresponds to greater value of the scale factor2 j. Therefore, the function turns to be broader. The broader functions ∅ J , k ( t ) and ψ1 ,k (t ) cause the 2 jk translation parameters to increase correspondingly.

The multi-resolution decomposed signals are characterized as follows:

s j (t )=∑k

s j ,k φ j ,k ( t)(4)

D j (t )=∑k

d j ,k ψ j , k (t) (5)

In equations 4 and 5, s j (t )is the smooth signal and D j (t ) is the detail signal. They comprise signal disintegration in orthogonal components at diverse scales. Consequently, a y(t) signal can be modified as:y t = S j(t) + D j(t) + D j−1(t ) + · · · + D1(t )(6)The high-level estimation s j(t) the smooth signal, and D1 ( t ) , D2 ( t ) … D j (t )are linked to 2–4, 4–8, ...2 j…2 j+1oscillations of length. A y(t) valued function for the discrete wavelet transform is stipulated as:ω=Wy (7)Where, the coefficients are structured from ‘coarse to fine’ scales in the ω vector. W is established as a low-pass filter and y is termed as band-pass filter. W and y are orthogonal vectors through N×1 elements. The filter coefficients are formed by the kind of mother wavelet. Since n is dividable by 2 j , ω can be precised as:

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ω=(s j

d j

d j−1...

d 1

) (8)

s j=¿d j=¿

d j−1=¿ ………………

d1=¿

Each s j , d j , d j−1 , ,d1 set of coefficients is a crystal, in which the wavelet coefficients accord with⋯ a set of translated wavelet functions’ set on a normal lattice.

2.6.1.2. Wavelet Coherence Transformation (WCT)Wavelet analysis is a method that separates the data into numerous time scales. Wavelet coherence does not need any stationarity in the series of data and it also carries out more decomposition in the data. So, as to measure the joint interactive coherence between the variables, it is good to have confidence on Wavelet coherence. It is a very supportive tool that considers the time intervals, frequency space and distinguishes feasible relationships between the two time series. Particularly, wavelet coherence strengthens correlation analysis by unveiling infrequent periodic correlations between the series. It declares the importance of the correlation of two time series. In time-frequency space, it clarifies the consistency and logic of cross wavelet of the series. In contrast to cross wavelet power, which exemplifies areas with high common power, this technique implements the wavelet coherence analysis for the studies i.e. recognizing associations, even at interims, where high coherence appears. So, wavelet coherence is relatively more valuable and beneficial. However, the wavelet power spectrum of the two time series exhibits only slight power (Grinsted, Moore, & Jevrejeva, 2004; Soares, 2011; Uddin, Tiwari, Arouri, & Teulon, 2013). The wavelet coherence can be defined as the cross spectra normalized by the two related auto-spectra, on the bases of cross wavelet spectra and the auto-wavelet power. Torrence and Webster (1999) represent the wavelet coherence of the time series as:

R n

2

( s)=|∀(s−1wn

xy

( s ))|2

∀(s−1

|w n

x

|(s )|2)∀(s−1|

|w n

y

(s )|2) (10)

Where, Rn2 (s )refers the squared value of wavelet coherence and ∀ is a smoothing operator. This

smoothing operator is defined as, ∀ (W )=∀ scale ¿. Smoothing along the wavelet scale axis is represented by ∀ scale and smoothing in time is symbolized as∀ time. The correlation properties in the wave function, over a specific period, among two non-stationary time series, are explained by the wavelet coherence value and its assortment is between 0 and 1. It demonstrates the weak or strong dependency between the series.(Akoum, Graham, Kivihaho, Nikkinen, & Omran, 2012).

Phase-difference is basically the angle of the arrow of the wavelet coherenceϑ XY , which entails the phase lead of X over Y .Moreover, similar and opposite direction movement is represented by phase and anti-phase respectively. Zero phase-difference indicates that the two time series move collectively at the certain time-frequency. π or −π indicates an anti-phase relation. If ϑ XY∈ (0, π/2), then the time series is led by the Y over X. Conversely if ϑ XY∈ (−π/2, 0), then in the time series, X leads Y.

10

There is an arrow in the wavelet coherence. If this arrow points to left-up or right-down, it describes that the first variable is the leading variable. On the other hand, if arrow is directing towards left-down or right-up, then the second variable is the leading variable. In the wavelet coherence, the time period is charted on horizontal axis, whereas scale or frequency is charted on vertical axis. The analysis is performed in these axes to recognize those areas, which disclose wavelet coherence. The warmer colors in the graph show the significant interdependence among the series, whereas, the colder colors describe the lower dependence between time and frequencies. To evaluate the significance level of wavelet coherence, Monte Carlo method is used.

2.6.1.3. Wavelet Granger Coherence AnalysisThe antiquated methods to granger causality have been added astonishingly in giving insightful causality perspectives, whereas, in the setting of identifying the strength and direction of causality fluctuating over frequencies, these tactics remain implicit in this context. Spectral density is the process which gives a complete scenario and is the only measure which can be applied across all time periodicities, which includes both, the short-run and the long-run. Pierce in 1979 invented a technique specifically for moldering granger causality among the time series across the spectrum. At each frequency, granger causality was estimated by intending R square for the time process, which was decomposed over the spectrum’s frequency p. The dependence of granger causality test is on modified coherence coefficient, for which the non-parametric estimation is used to derive the distributional properties. The measure is executed on ut and vt, univariate innovation series, that results from the derivation of Xt and Yt, which are then formed as univariate ARMA model.

θx

(L ) X t=C x

+φx

( L )u t

θ y

( L )Y t=C y

+φ y

( L )v t (11)

The auto-regressive polynomials areθx (L)∧θy (L) respectively; moving average polynomials are denoted as ∅ x(L) and ∅ y (L ); and C xand C y are the potential deterministic components. Once the series has been filtered, the innovation series of ut and vt is obtained with the mean zero, as a white noise process. There are the chances that at different lags, they can correlate with each other.

Let the spectral density functions be Suλ andSvof ut∧vtat frequencyλ∈ ]0 , π [ delineated as:

Su λ= 12π ∑k=−∞

∞γu (k )e−1 λk

and S v λ= 12 π ∑k=−∞

∞γv (k )e−1 λk

(12)

Where the auto-covariance of ut∧vt at k lag is represented as γ u (k) = cov (ut, ut-k)andγ v (k) = cov (vt,vt-k). The notion of the demonstration is to breakdown each series into integral of components that are uncorrelated, and each one is associated with a specific frequency. Koopmans (1995) gives the detailed analysis on spectral time series. In order to evaluate the stochastic process, the allying ut∧vt cross spectrum Suvλ is considered.

Suv λ=Cuv ( λ )+iQuv ( λ)= 12 π ∑k=−∞

∞γ uv (k )e−1 λk

(13)

The segments of cross spectrum are presented as co-spectrum Cuv(λ ) and the quadrature spectrum Quv. The γ u (k) = cov(ut, ut-k)is the cross-covariance at lag k for ut∧vt . The non-parametric modeling of cross spectrum, which is said to be the weighted covariance estimator with the cross covariance, is shown by:

γ¿

uv (k )=Cov¿

(ut , vt−k )

11

S¿

uv λ= 12 π

¿¿ (14)

Koopmans (1995) describes that the cross spectrum allows the computation of coefficient of coherence as:

huv( λ )=|suv ( λ)|

√su ( λ )sv ( λ ) (15)

The linear relationship strength is described by the coherence coefficient, using the frequency among the series; yet it does not account for the associative direction in the time series.

The explanation of squared coefficient of coherence is same like the R squared regression. The regression R squared of vton every past and future values of ut is fundamental over the frequencies of squared coefficient of coherence. According to Pierce (1979), the cross spectrum (14) performs the decomposition into following parts:

i. Su↔v, the instant ut∧vt relationship

ii. Su→v, the immediate direct relationship of vt∧lagged u t

iii. Sv→u, the immediate direct relationship of ut∧lagged v t

That is, Suvλ = [Su↔v + Su→v +Sv→u]

=1

2π [ γ uv(0 )+∑k=−∞

−1 γ uv( k )e−iλk

+∑k=1

∞ γ uv (k )e−iλk

](16)

The proposed measures of spectral GC helps the property that Xt does not Granger cause Yt if γuv (k )=0for all k ¿ 0 (Gouriéroux, 2012). Therefore, if the objective is to regulate the predictive ability of Xt respective to Yt ,one’s concern would be in second part of equation (16): Thus, granger coefficient coherence is indicated as:

hu↔ v ( λ )=|su↔ v ( λ)|

√su ( λ )sv( λ ) (17)

3. Data and VariablesTo assess the fund flows’ association with stock market volatility in Pakistan, we extracted the daily data from 1/1/1991 to 30/6/2018 i.e. the data of mutual funds and market returns from Databases. However, due to the non-availability and missing data problem of mutual funds, various sample time periods are selected and analyzed. The details of the total number of firms and observations of each mutual funds and sample time period are given in Table 1.

Table 1 shows that total data of 922 mutual funds under eight different classes have been taken for analysis separately. This selection of period is based on the data availability. We feel this sample is large enough to capture the multi-horizon behavior of the variables. To calculate the total/aggregate mutual fund flows, we follow Ferreira, Keswani, Miguel, and Ramos (2012) and Ferson and Kim (2012).

Flowsi , t=[TNA i ,t−TNA i ,t−1 (1+Ri ,t )]/TNA i , t−1 (18)

WhereTNAi ,t stands for the total net asset of fund i in dollar, amounts at the end of time period t, and Ri , t stands for fund і's return in time period t. The TNA and return data of each firm of each time were extracted to calculate the mutual fund flows of each firm. Then, the flows of each firm were calculated based on the formula in equation 18. Then, flows of all firms were aggregated of each period to find out

12

total net sales/trading by each mutual fund. To extract the data of each firm’s TNA and returns, tickers of each firm were identified and generated from database. Our sample consists of Pakistan and noted that the mutual fund industry has experienced immense growth for the past years. The total sample consists of 27 different classes of mutual funds, including closed-end flows, open-end flows, fund of fund flows, bond fund flows, equity fund flows, balanced fund flows, money market flows, AAA fund flows, BBB fund flows, large cap fund flows, broad market fund flows, index fund flows, Islamic fund flows, short-term fund flows, intermediate fund flows, aggregate fund flows, aggressive strategy fund flows, conservative fund flows, global allocation fund flows, global strategy fund flows, government strategy flows, growth strategy flows, blend strategy fund flows, inflation protected fund flows, growth equity fund flows, value equity fund flows, blend equity fund flows. The details of different classes of mutual fund firms, taken under this study are given in Table A-1 appendix. We could not find the data of long-term mutual funds, capital protection funds, socially responsible funds, commodity funds, corporate mutual funds and currency mutual funds.

The market index return (PSX) data is obtained from DataStream. The calculation of returns is based on first difference of log of prices. The stock market volatility is calculated by estimation of GARCH (1,1) model and conditional variances are predicted from the model following Cao et.al(2008), Qureshi et al (2017, 2019).

4. Result and Discussion4.1. Descriptive Statistics

Table 2 reports the descriptive statistics of mutual fund classes and stock market volatility. The Jarque-Bera (JB) test results show that the hypothesis of normality is rejected for all the variables. The average value of closed-end flows and global strategy fund flows is negative, implying negative trend of the flows. And the average value of money market flows, open-end flows and Islamic fund flows is high compared to other variables. Further, the higher standard deviation of open-end flows indicates higher volatility persistence. The coefficients of skewness for all the variables exhibit positive skewness except broad market fund flows, inflation protected fund flows and closed-end flows. The coefficients of kurtosis confirm the presence of leptokurtic properties.

Figure 1 displays the plots for empirical data. It is observed that fund of fund flows, open end flows, money market flows, conservative fund flows, global strategy fund flows and inflation protected fund flows are characterized by low variability of returns, whereas the balanced fund flows, bond fund flows, closed-end flows, equity fund flows, AAA fund flows, BBB fund flows, short term fund flows, blend aggressive fund flows and growth strategy fund flows are characterized by high variability of returns and clusters of volatilities. Moreover, it can be seen that the mutual fund flows are highly volatile in the beginning of the mid of 2007until end of the period. The flows fluctuate more after the global financial crisis. The stability in flows is observed on average for pre-2006 period. Further, the persistent trend of fluctuations is seen in the stock market volatility throughout the sample period. The change in variances over time is followed by large or small changes in either sign. However, the phenomenon of the volatility clustering is particularly strong in the stock market returns series. It is further noticed that the intermittent volatility clusters persist for balanced fund flows, equity fund flows, closed fund flows, government strategy fund flows and large cap fund flows.

4.2. Results of Wavelet Correlations

Table 4 provides the wavelet correlations for DWT of mutual fund classes and stock market volatility. It is perceived that the degree of correlation of stock market volatility with balanced fund flows, large cap fund flows, blend fund flows, money market flows, aggregate fund flows, government strategy fund flows and BBB fund flows decreases till D4 scale and increases for subsequent two scales (D5 and D6). However, the magnitude declines at D7 and D8 scale, indicating an inconsistent pattern. Similarly, this unpredictable pattern of stock market volatility is also observed with growth strategy fund flows and inflation protected fund flows, since each scale reveals a different magnitude of increase and decrease in

13

the correlation coefficients. This shows its inconsistent relationship with stock market volatility. They either have contrarian or momentum behavior, implying that they can go against the stock market and may move together.

Moreover, the correlation coefficients of stock market volatility are weak with closed-end flows, fund of fund flows, money market flows, index fund flows, and conservative fund flows. The plausible reason is that all these funds do not invest directly into portfolio of stock market, except index fund. For index funds, the study observed that presently, only five mutual fund companies are active in Pakistan,11 which shows declining trend of index mutual fund firms and thus, reduced stock market investment.

11The names and details of each mutual fund firm have not been provided for brevity purpose. They will be provided on request.

14

Table 1. Mutual Funds Data Description

Total Number of firms Sampling time period total observation for analysis Total firms’ observationsClassification based on General CategoryOpen ended mutual funds 233 4/23/2008 6/29/2018 2658 619314Close-ended mutual funds 11 1/2/1991 6/29/2018 7173 78903Fund of Funds 10 4/30/2009 6/29/2018 2392 23920Classification based on Investment objectives

Balanced Funds 68 5/16/2006 6/29/2018 3164 215152Bond funds 80 10/3/2006 6/29/2018 3064 245120Money Market Funds 41 5/2/2008 6/29/2018 2651 108691Equity funds 87 8/10/2006 6/29/2018 3102 269874

Classification based on Fund rating class focus

AAA rated mutual funds 10 6/2/2008 6/29/2018 2630 26300BBB rated mutual funds 10 10/3/2006 6/29/2018 3064 30640

Classification based on Market capitalization focusBroad market cap mutual funds 8 5/5/2008 6/29/2018 2650 21200Large market cap mutual funds 5 1/1/2009 6/29/2018 2477 12385

Classification based on Maturity band

Short term mutual funds 10 5/2/2008 6/29/2018 2651 26510intermediate mutual funds 5 1/4/2010 6/29/2018 2215 11075Long term mutual funds NA NA NA

Classification based on Strategyaggressive mutual funds 5 6/2/2008 6/29/2018 2630 13150conservative mutual funds 3 9/5/2011 6/29/2018 1780 5340blend mutual funds 44 8/10/2006 6/29/2018 3103 136532

15

aggregate mutual funds 71 8/24/2007 6/29/2018 2832 201072government mutual funds 15 5/2/2008 6/29/2018 2651 39765inflation-protected mutual funds 2 11/1/2007 6/29/2018 2782 5564international/global mutual funds 1 7/4/2011 6/29/2018 1825 1825global allocation strategy mutual funds 7 4/24/2008 6/29/2018 2657 18599Corporate mutual funds NA NA NACurrency mutual funds NA NA NAGrowth Strategy 12 8/10/2006 6/29/2018 3103 37236

Classification based on General Attributes. index funds 5 1/12/2009 6/29/2018 2470 12350Islamic funds 92 4/24/2008 6/29/2018 2657 244444capital protection funds NA NA NA NAsocially responsible funds NA NA NA NAcommodity funds NA NA NA NA

Classification based on equity style basedblend funds 21 8/11/2006 6/29/2018 3101 65121growth funds 13 6/2/2008 6/29/2018 2630 34190value funds 53 5/16/2006 6/29/2018 3164 167692Total 922 77276 2671964

16

Table 2: Descriptive Statistics

Stock Market Volatility

Balanced Fund Flows

Bond Fund Flows Equity Fund Flows

Money Market Flows Closed End Flows

Open End Flows Fund of Fund Flows AAA Fund Flows

Mean 0.000164 0.012382 0.016189 0.013673 0.031226 -3.92E-05 0.037866 0.0016590.002007

Median 0.000130 0.0000 0.0000 0.0000 0.0000 5.68E-05 0.0000 0.0000-0.000493

Std. Dev. 0.000153 0.415869 0.438817 0.435333 0.545046 0.065526 0.835985 0.0600970.109556

Skewness 5.806688 0.079478 8.205506 3.292281 21.80595 -2.697736 10.30724 2.6997401.489331

Kurtosis 64.19209 118.1034 185.7303 79.27219 612.2904 124.7278 226.9982 107.3541130.7766

Jarque-BeraObservations

511426.7

3164

1841033

3335

4437469

3164

968253.6

3965

44387737

2855

4437328

7173

6670784

3164

1088253

2392

18636362738

BBB Fund Flows Blend Equity Fund Flows

Broad Market Fund Flows

Growth Fund Flows

Index Fund Flows Intermediate Fund Flows

Islamic Fund Flows Large cap Fund Flows

Short term Fund Flows

Mean 0.001757 0.002201 0.001971 0.004156 0.001460 0.002964 0.022505 0.000309 0.005146Median -0.000368 0.000000 0.000000 -3.54E-05 0.000000 -0.000240 0.000000 0.000502 -0.000381

Std. Dev. 0.109167 0.195452 0.108716 0.169848 0.069269 0.045185 0.321830 0.029985 0.146663Skewness 3.687263 1.006812 -2.313471 1.051915 5.628199 7.918680 1.717495 0.039960 2.033317Kurtosis 129.3413 51.94884 99.88761 56.79704 131.2069 135.1438 42.38557 83.06794 120.0725

Jarque-BeraObservations

21168493172

321005.83210

10823832761

330675.92738

17792202578

17144532323

180138.32766

690505.42585

1577517.2759

Value Fund Flows Aggregate Fund Flows

Aggressive strategy Fund Flows

Global allocation

Fund Flows

Global strategy Fund Flows

Government strategy Fund

Flows

Growth strategy Fund Flows

Inflation protected Fund Flows

Conservative Fund Flows

Mean 0.012955  0.018881  6.97E-05  0.002261 -0.000147  0.003658  0.002748  0.000498  0.000787Median 0.000000 -0.001165  0.000000  0.000000 -0.000179 -0.000532 -0.000779 -0.000192  0.000000

Std. Dev. 0.395625  0.317528  0.070234  0.084328  0.056716  0.183011  0.147431  0.029519  0.030703Skewness 1.595401  2.343885  0.975599  3.959443  1.420524  2.301390  1.244116 -0.238410  8.086812Kurtosis 38.33850  52.48548  70.11735  69.80431  172.6847  79.16547  44.76077  126.6634  269.3054

Jarque-BeraObservations

171642.43172

 183456.01782

334759.51782

336020.21782

21384731782

432310.61782

 129948.91782

11354951782

52851281782

Note: The table reports the summary statistics of various mutual fund classes and stock market volatility

17

Blend Strategy Fund Flows

Mean  0.012959Median -0.000337

Std. Dev.  0.396364Skewness  2.566407Kurtosis  35.86732

Jarque-BeraObservations

 143028.91782

Note: The table reports the summary statistics of various mutual fund classes and Stock market volatility

Balanced Fund Flows

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

-8

-6

-4

-2

0

2

4

Balanced Fund Flows

18

19

20

21

Figure 2: Plots of mutual fund classes and stock market volatility series

22

Table 3: Wavelet correlations for Market volatility-Mutual fund pairs

Scale Stock Market Volatility-Balanced Fund Flows

Stock Market

Volatility-Bond Fund

Flows

Stock Market Volatility-Equity Flows

Stock Market Volatility-Money Market Flows

Stock Market

Volatility-Closed End

Flows

Stock Market

Volatility-Open End

Flows

Stock Market

Volatility-Fund of

Fund Flows

Stock Market

Volatility-AAA Fund

Flows

Stock Market

Volatility-BBB Fund

Flows

D1 0.0330 -0.0265 -0.0105 -0.0145 -0.0089 -0.0293 -0.0024 -0.0195 -0.0186D2 0.0290 0.0131 -0.0171 -0.0076 -0.0039 -0.0100 -0.0430 0.0223 0.0170D3 -0.0260 -0.0063 -0.0812 0.0187 -0.0099 -0.0345 -0.0057 -0.0428 -0.0204D4 0.0211 -0.0128 -0.0458 0.0381 -0.0268 0.0063 0.0132 -0.0124 -0.0176D5 0.0535 0.0214 -0.0064 -0.0317 -0.0162 -0.1335 -0.1890 -0.0307 -0.0548D6 0.1777 -0.1094 0.0866 -0.0153 0.0271 -0.0516 0.0014 -0.1453 -0.2863D7 -0.0745 -0.2176 0.0840 0.0763 0.1384 -0.1471 -0.1637 -0.0472 -0.2834D8 -0.0342 -0.2086 0.1229 -0.0034 0.0179 -0.3099 0.7512 -0.1321 -0.0715S8 0.6799 0.5660 0.5229 0.8004 0.0062 0.8245 0.7751 0.3370 0.6943

Scale

Stock Market

Volatility-Blend Equity Fund Flows

Stock Market

Volatility-Broad Market Fund Flows

Stock Market

Volatility-Growth Fund Flows

Stock Market

Volatility-Index Fund

Flows

Stock Market Volatility-

Intermediate Fund Flows

Stock Market Volatility-Islamic Fund Flows

Stock Market

Volatility-Large cap

Fund Flows

Stock Market Volatility-Short term Fund Flows

Stock Market Volatility-Value Fund Flows

D1 -0.0151 -0.0033 -0.0472 -0.0009 0.0100 -0.0427 -0.0130 -0.0373 -0.0143D2 -0.0406 -0.0080 -0.0236 -0.0002 -0.0213 0.0111 0.0063 -0.0003 -0.0122D3 -0.0669 -0.0209 -0.1002 -0.0862 0.0218 -0.0489 -0.0313 -0.0612 -0.1106D4 -0.0220 0.1565 -0.0585 -0.0402 0.0557 0.0759 -0.0108 -0.0326 -0.0430D5 -0.0119 0.1322 -0.0717 -0.0535 0.0499 0.0223 -0.0506 0.0641 0.0187D6 0.2598 -0.0545 -0.1180 -0.0447 0.1033 0.1026 -0.1070 0.0433 0.0858D7 0.4455 0.2548 -0.0311 -0.0035 0.2253 0.1500 -0.4440 -0.0305 0.0118D8 -0.4114 0.5887 0.0492 0.5077 0.3841 0.3790 -0.0430 0.6208 0.3832S8 0.1122 0.5998 0.6578 0.5058 0.4633 0.9287 0.1847 0.2204 0.5698

Scale Stock Market

Volatility-Aggregate

Fund Flows

Stock Market

Volatility-Aggressive

strategy Fund Flows

Stock Market

Volatility-Blend

Strategy Fund Flows

Stock Market Volatility-

Conservative Fund Flows

Stock Market

Volatility-Global

allocation Fund Flows

Stock Market Volatility-Global strategy Fund Flows

Stock Market

Volatility-Government

strategy Fund Flows

Stock Market Volatility-Growth strategy Fund Flows

Stock Market Volatility-Inflation protected Fund Flows

D1 -0.0310 -0.0198 -0.0223 -0.0009 -0.0280 -0.03737 -0.0299 -0.0313 0.0195D2 0.0002 -0.0346 -0.0302 -0.0002 -0.0303 -0.0872 0.0260 -0.0131 0.0907D3 0.0023 -0.0803 -0.0729 -0.0008 -0.0598 -0.0542 0.0068 -0.0690 -0.0036D4 -0.0252 -0.0667 -0.0112 -0.0040 -0.0919 0.0124 0.1124 0.0350 -0.0670D5 0.0907 -0.0007 0.0646 -0.0053 0.0500 0.1677 0.0146 0.0006 -0.2185D6 -0.0746 0.0698 0.1751 -0.0044 0.1726 0.4713 -0.1211 -0.0034 -0.5080D7 -0.0405 0.1517 0.1670 -0.0038 -0.1127 0.4301 -0.0769 0.0329 -0.1837D8 0.4781 0.4643 0.1199 0.0050 -0.6078 -0.8366 0.6446 -0.3576 -0.3757S8 0.7217 -0.0258 0.6592 0.0050 0.6715 -0.9983 0.4235 -0.0780 0.6837

However, there exists high degree of correlation at higher time scale of stock market volatility with fund of fund flows, broad market fund flows, index fund flows, blend strategy fund flows, global allocation fund flows and global strategy fund flows, revealing the strong association of stock market volatility and fund flows in the long run. It is noticed that overall, there is negative correlation between stock market volatility and mutual fund classes, except intermediate fund flows and Islamic fund flows, suggesting that intermediate and Islamic funds increase their trading with rise in stock price fluctuations. However, this relation diverges to positive over brief time spans. These results corroborate with the findings of Table 3.

23

4.3. Results of Wavelet Coherence

Figure 3 illustrates the wavelet coherence transforms of the variables, based on the continuous wavelet transformation (CWT). The strong interdependence is represented by the red area. However, the plots also provide relative time series phasing by means of phase arrows, which signify the cause and effect interactions among mutual fund classes and stock market volatility. The in-phase pairs are indicated by the arrows, pointing to the right. While, the anti-phase pairs are indicated by the arrows, pointing to left. If an arrow points to left-up or right-down, it means that the first variable is leading. Whereas, if an arrow points to left-down or right-up, it means that the second variable is leading.

According to Figure 3, the relationship of stock market volatility and balanced fund flows shows significant high association at 256 days scale during 2007-2009 and at the end of the sample. The plot shows that the ‘stock market volatility-balanced fund flows’ pair is in phase in the significant area, indicating that the stock market volatility greatly mirrors with that of the balanced fund flows at 256 days scale from 2007 to 2009 and 2016 to 2017. The plot also illustrates the areas of significant interdependence at higher frequency scales over diverse periods. Specifically, we note that the significant area covers the entire sample period at 32 days scale. The pointing of arrows indicates that balanced fund flows can be predicted accurately, based on the volatility of stock market because balanced fund flows strongly chase the prior patterns of the stock market.

The relationship between stock market volatility and fund of fund flows shows significant, high interrelationship only around 2017 and 2018 at a 1024 days scale. The significant area is also observed at 64 days scale around 2010, 2014 and 2017 with the arrows, pointing left-down. This result indicates that the fund of fund flows lead the stock market volatility at the mid and long term scale. Similarly, the association of stock market volatility and AAA fund flows displays strong relation from 2016 to 2018 at 256 days scale, notifying the leading role of fund flows. The wavelet coherence figure of stock market volatility and BBB fund flows show that there exists high coherency during start and end of the sample, particularly from 128 to 256 days scale. The predictive content of fund flows is further confirmed.

The dependence of stock market volatility and blend equity fund flows is witnessed from 2007 to 2011 over different frequency scales with a mixed pattern for direction of arrows. The blend equity fund flows lead stock market volatility in the mid run, while fund flows lag behind the stock market volatility in the long run. Furthermore, the relationship of stock market volatility and broad market fund flows has been observed in different periods from the Figure 3, whereby the variables are mostly in phase throughout the period. Interestingly, in low frequency term exceeding 1 year, prolonged significant relationship between the variables is manifest from 2008 to 2012 and 2015 to 2018. Further, the stock market volatility controls the broad market fund flows.

The stock market volatility and growth fund flow relationship is represented in the plot, whereby the variables typically fell within red regions in long term. This significant interrelation is apparent from 2013 to 2018. There was anti-phase movement during 2013-2015, and returned to in phase after 2016. The change in direction of arrows from right-up to right-down at 64 and 256 days scale respectively reveals that both variables preside over each other at different scales.

Figure 3 shows the index fund flows and stock market volatility are generally in phase between 2015 and 2018. The arrows are pointing right-down during this particular period, indicating that the fund flows are controlled by stock market volatility. Further, the intermediate fund flows and stock market volatility coherency is mostly insignificant in high frequency terms. However, in 1024 days scale, stock market volatility leads the fund flows from 2016 to 2018.

The coherence of Islamic fund flows and stock market volatility shows that in the variables from 2014 to 2018, the scale interrelation fell in about 512 days scale, while from 2010 to 2015, the interrelation was significant in different frequencies. Since the arrows are in phase and downward-right, implying that rise in stock market volatility increases the fund flows. Additionally, the coherence of stock market volatility and value fund flows can be observed whereby the variables predominantly lie in warmer region between

24

2014 and 2018. It is noticed that pointing of arrows divulge the leading position of fund flows in 2015 and leading position of stock market volatility in 2017.

With regard to stock market volatility-equity flows, we note significant coherence at a 512 days scale, specifically during the global financial crisis. For this pair, high wavelet coherences can also be observed at the low time scale of 32–64 days from 2008 to 2017. The direction of arrows confirms that the stock market volatility leads equity fund flows. Moreover, for the stock market volatility-bond flows, we find that few significant areas cover different scales, thereby explaining the distractions in high integration of the pair. The degree of correlation between the stock market volatility and bond flows increased during the financial crises, indicating the effect of financial contagion and implying investors’ switch towards fixed and safer investment securities.

The interdependence of stock market volatility with open-end flows, money market flows, growth strategy fund flows and government strategy fund flows is minimal in the long run. However, momentary significant areas are evinced at higher frequency scales from 2007 to 2009 and 2014 to 2017. Where, the movement of arrows shows that the money market flows, growth strategy fund flows and government strategy flows lag behind stock market volatility. For stock market volatility-open end flows pair, open-end flows lead stock market volatility. Moreover, the stock market volatility coherency with closed-end flows, large cap fund flows and short term fund flows show no significant area in the coherence plots. Thus, an obvious judgment on frail significance can be formed.

A glance on coherence plots of stock market volatility-aggressive strategy fund flows; and stock market volatility-blend strategy fund flows confirms strong dependence at lower frequency scale. These fund flows are strongly related to stock market volatility over many periods with a lag position. Further, the relation between stock market volatility and global allocation fund flows is observed at many frequencies. The interdependence is particularly dominated from 2014 to 2018 with both leading and lagging the volatility of stock market. There are brief time periods with changing phases, where global allocation fund flows seem to be leading the stock market volatility, but the directional influence is not consistent. Similarly, long run dependence from 2014 to 2018 is confirmed in the stock market volatility and global strategy funds relationship. However, in this case, global strategy flows lead the stock market volatility. The pattern suggests that the variables reveal both phase and anti-phase relation, since they are distinguished by cyclical and anti-cyclical effects on each other.

It is interesting to see the mid-run association of the stock market volatility and inflation protected fund flows. The direction of arrows notifies the lead position of market volatility along with anti-phase movements. The relationship is significant from 2008 to 2010 and in 2018 too. Moreover, Figure 3 shows the interrelation of stock market volatility with aggregate and conservative fund flows. It is exhibited that during period of 2015 to 2018, in the various time scales, arrows are right-up, indicating that the variables are in phase (cyclical effects) and fund flows are leading.

In general, we can see that the dependence is vastly dynamic as it varies in time. The stock market volatility with bond flows, equity flows, Islamic fund flows, balanced fund flows, aggressive flows, global allocation flows and inflation protected flows point that the dependence occurs with breaks till the 64 days scale for different time periods. However, an anti-phase pattern is observed in the relationship of stock market volatility with equity flows, open-end flows, AAA fund flows, BBB fund flows, growth fund flows, value fund flows, fund of fund flows, government strategy flows, global strategy fund flows and blend aggressive flows for 64 and 128 days scale from 2010 to 2014, which indicates that the mutual fund trading activities mostly reflects that of the stock market volatility and can reduce it. Table 5 presents the summary of fund flows classes with stock market volatility.

25

26

27

28

29

Figure 3: Wavelet coherence plots of mutual fund classes and stock market volatility

Table 4: Wavelet Coherence Summary: Fund flows versus Stock Market Volatility

Fund Flows High Coherency (Period)

High Coherency (Scale)

Phase-Difference

Fund Flows (Lead/ Lag)

Balanced Fund Flows 2006-20092013-2018

8-4512-1024

In phaseAnti-phase

LaggingLeading

Bond Fund Flows 2008-20122016-2017

16-64128

Anti-phase Lagging

Equity Fund Flows 2008-20112013-2018

16-64512

Anti-phase Lagging

Money Market Fund Flows

2016-2018 16-64 In-phase Lagging

Closed End Flows No any No any

Open End Flows 20082014-2017

8-64128

Anti-phase Leading

Fund of Fund Flows 2009-20102016-2018

8-641024

Anti-phase Leading

AAA Fund Flows 2010-20122016-2018

8-64128-256

In-phaseAnti-phase

LaggingLeading

BBB Fund Flows 2006-20092016-2018

8-64128-256

In phaseAnti-phase

Leading

Blend equity Fund Flows

2007-20132014-2017

16-1281024

In phaseAnti-phase

LaggingLeading

Broad Market Fund Flows

2008-20122015-2018

8-64128-1024

In phase Lagging

Growth Fund Flows 20102014-2018

16-512 In phaseAnti-phase

LaggingLeading

Index Fund Flows 2010-20112015-2018

16-256 In phase Lagging

30

Intermediate Fund Flows

2013-20142017-2018

1024 In phaseAnti-phase

LaggingLeading

Islamic Fund Flows 2010-20112014-2018

16-64512

In phase Lagging

Large cap Fund Flows No any No any

Short term Fund Flows 20082017

32256

In phase Lagging

Value Fund Flows 2007-20112014-2018

16-2561024

In phaseAnti-phase

LaggingLeading

Aggregate Fund Flows 2016-2018 8-32256

In phase Leading

Aggressive Strategy Fund Flows

2008-20122014-2018

8-64256-1024

In phase Lagging

Blend Strategy Fund Flows

2008-20112015-2017

64-128256-1024

In phaseAnti-phase

Lagging

Conservative Fund Flows

2015-2016 64-128 In phase Leading

Global Allocation Fund Flows

2014-2018 16-64256-512

In phase LaggingLeading

Global Strategy Fund Flows

2014-2018 64-2561024

In phaseAnti-phase

Leading

Government Strategy Fund Flows

2017 8-16 Anti-phase Lagging

Growth Strategy Fund Flows

2008-20112018

16-32 In phase Lagging

Inflation Protected Fund Flows

2008-20102018

16-64256

Anti-phase Lagging

The table summarizes the overall wavelet coherence findings of Fund Flows classes and Stock Market volatility variables of Pakistan

31

32

33

34

Figure 4: Granger coherence plots of mutual fund classes with stock market volatility

4.4. Results of Granger Causalities

We then examine the granger causalities at various frequencies to scrutinize the forecasting ability and alternating causalities among variables. The granger coefficients of coherence are displayed in Figure 4 (Tables reported in Appendix1).12 The coherence coefficients identify the magnitude, to which stock market volatility granger causes mutual fund classes at diverse frequencies. The higher granger causality pertains to greater value of estimated coefficients over a definite frequency. The bottom line of the figures is the critical value at 5% probability level for no granger causality. An unswerving trend is observed for most of the pairs, which represents that the statistical significance is hardly reached. However, the causality for index fund flows, broad market fund flows, blend equity fund flows, growth fund flows, balanced fund flows, fund of fund flows, inflation protected fund flows, global allocation fund flows and global strategy fund flows is evident. There is an increase in the Granger causality around 0.5 and 1.5 frequencies for fund of fund flows, broad market fund flows, blend equity fund flows, BBB fund flows, and global allocation fund flows. In contrast, causalities of intermediate fund flows, large cap fund flows, aggressive strategy fund flows and government strategy fund flows are observed to rise over 3 term frequencies. In addition, balanced fund flows, growth fund flows and inflation protected fund flows causalities are significant throughout the higher and lower frequencies.

5. Conclusion and Policy Implications

This study investigates the relationship between different classes of mutual funds and stock market volatility in Pakistan. The findings of wavelet correlation suggest that there exists negative correlation between fund flow classes and stock market volatility, indicating contrarian behaviour of mutual funds in response to high stock market fluctuations. It is witnessed that the correlation tends to increase at lower frequencies for most of the pairs, implying greater long term effect between pairs. The coherence analysis is inferred into three main conclusions; explicitly, fund flows lead stock market volatility, stock market volatility leads fund flows, and the relationship keeps varying. For most of the sample pairs, fund flows are lagging against stock market volatility, supporting the feedback trading hypothesis, which implies that mutual funds trace the stock market’s prior performance and then take decision. With contrarian approach of mutual funds, they can lessen the market volatility to the next period.

The findings of this study have a number of implications for theory, methodology and practice. First, this study contributes to the knowledge in this area by studying 27 various major mutual fund classes in relation to stock market volatility, which is one of the industry-wide extensive and comprehensive study. Second, this study contributes towards determining the predictive ability and risk-reduction ability of mutual funds in emerging economy like Pakistan. Third, the present study differentiates from previous works in terms of methodological approach by applying wavelet based technique for in-depth and micro level analysis. Using daily data, the study determines the behaviour of variables at different time scales. Fourth, the study adds new empirical evidence for understanding the investment patterns and behaviour of fragile and vulnerable financial market of emerging economy.

The findings of the study have significant implications for market players, portfolio manager, investors and policy makers. Market players may have benefit over various time horizons by matching their investment heterogeneity. These consequential strategies may be derived from wavelet coherence which pertains to the decomposition of causal links. Moreover, the results confirm that the interaction among variables is diverse in nature. For most of the pairs, transient coherences are seen at higher frequencies. However, strong coherence is found between the fund flows and stock market volatility for low and medium frequencies, which grasps attention of portfolio managers and speculators respectively. The granger coherence results are momentous for index fund flows, broad market fund flows, blend equity

12 The complete list of tables of the granger coefficients of coherence for mutual fund classes is available on request.

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fund flows, growth fund flows, balanced fund flows, fund of fund flows, inflation protected fund flows and global allocation fund flows, suggesting that the long-run constituents possess forecasting ability.

Studying mutual fund flows with respect to the financial market vulnerabilities provides a better understanding of the relationship between these variables and also aids policy makers and portfolio analysts in creating optimal portfolio strategies. Moreover, a bearish trend in the stock market diverts the investors to fly to quality allocating decisions. Accordingly, they increase their portfolio returns by shifting their investments from equity to fixed income securities (Ferson & Kim, 2012).Understanding the link between mutual fund flows and Stock market volatility provides additional information about investors’ heterogeneity and preferences; and thus, helps the portfolio managers and analysts to formulate their portfolio strategies and make decisions on behalf of their investors(Chan & Kogan, 2002; Jank, 2012). Fund flows can be used as a source of information in assessing and forecasting investment and re-balancing the decisions.

The study assists policy makers and portfolio managers to make better planning, hedging and forecasting decisions and to implement their investment and asset allocation decisions. The findings could be of help to investors and portfolio managers in making efficient investment and asset allocation decisions at the worldwide and international level, particularly in regional developing countries. Professional managers need a detailed understanding as well as sufficient experience, knowledge, evaluation and assessment of the financial security market, and the business sector in the economy. The findings provide significant information to portfolio managers, concerning flight-to-quality since the investors make flight-to-quality allocating decisions and increase their portfolio returns by shifting investment from equity to fixed income securities in the case of an economic downturn and vice versa in boom times. The future research could be conducted in other classes of mutual funds in other developing regions.

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Appendix

Table A-1

Term Definition Data Sources

Stock Market Volatility Standard deviation of log of stock prices. The stock market volatility is calculated by estimation of GARCH (1,1) model and conditional variances. Thomson DataStream

Classification based on General Category

Open-ended mutual funds Mutual funds issue unlimited issuance of Initial Public offerings (IPOs) and shares by company to meet the demands of the investors Bloomberg

Closed-ended mutual funds Mutual funds raise fixed amount of capital by issuing fixed number of shares as IPOs once only. Bloomberg

Fund of Funds A fund of funds is multi-manager investment approach of holding a portfolio of other mutual funds rather than trading and investing in securities directly. Bloomberg

Classification based on Investment objectivesBalanced Funds Balanced funds are investments in a combination of both equity and bond securities Bloomberg

Bond funds Bond mutual funds are one of the types of income funds/debt funds which invest specifically in corporate bonds and other debt instruments Bloomberg

Money Market FundsMoney market funds invest in liquid, short term, low risk securities. These short term securities include commercial papers, treasury bills, and government securities with maturity up to one year.

Bloomberg

Equity funds Equity mutual funds are defined as investment by funds in medium to long term equities and equity-related-securities. Bloomberg

Classification based on Fund rating class focusAAA rated mutual funds This classification is based on the higher ranking and performance of mutual funds. BloombergBBB rated mutual funds This classification is based on the lower ranking and performance of mutual funds. BloombergClassification based on Market capitalization focus

Broad market cap mutual fundsInvest in broad market index, which is characterized by including the stocks of all sizes (large-, mid- and small-cap) of companies based on the values of the companies according to their stock prices and total outstanding shares.

Bloomberg

Large market cap mutual funds Large/big cap mutual funds invest in companies whose market capitalization value of more than $10 billion. Bloomberg

Classification based on Maturity bandShort term mutual funds This classification is based on short investment time horizon (15 to 91 days). BloombergIntermediate mutual funds This classification is based on medium investment time horizon (1-3 years). Bloomberg

40

Classification based on Strategy

Aggressive mutual funds These funds mainly focus on achieving the investment goals and objective, based on aggressive strategy. Aggressive investing accepts more risk in pursuit of greater return. Bloomberg

Conservative mutual fundsThese funds focus on conservative strategy of investment.Conservative investing seeks to protect an investment portfolio's value by investing in lower risk securities such as fixed-income and money market securities.

Bloomberg

Blend strategy mutual funds Combination of aggressive and conservative strategies. Bloomberg

Aggregate mutual funds Aggregate Fixed Income Strategy seeks attractive total returns from income and price appreciation. Bloomberg

Government mutual funds The mutual funds invest primarily in government based securities. Bloomberg

Inflation-protected mutual funds ‘Inflation-protected’ refers to investments that provide a hedge against the rise in prices of goods and services over time. Bloomberg

International/global mutual fundsInternational funds consist of securities from all countries except the investor's home country. These funds provide diversification outside of the investor's domestic investments.

Bloomberg

Global allocation strategy mutual fundsGlobal allocation funds are mutual funds’ investment all around the world, including home country. The funds can rapidly switch between asset classes and geographic regions, making it possible to generate higher returns at a lower risk.

Bloomberg

Growth Strategy Growth investing is an investment style and strategy that is focused on increasing an investor's capital. Bloomberg

Classification based on General Attributes.

Index funds An index fund is a type of mutual fund with a portfolio, constructed to match or track the components of a financial market index Bloomberg

Islamic funds These funds invest primarily in Shariah-based securities. BloombergClassification based on style based

Blend funds A blend fund is a type of equity mutual fund that includes a mix of value and growth stocks. Bloomberg

Growth funds Growth stock mutual funds primarily invest ingrowth stocks, which are stocks of companies that are expected to grow at a rate faster in relation to the overall stock market. Bloomberg

Value funds Value stock mutual funds primarily invest in value stocks which, an investor believes, are selling at a price, that is low in relation to earnings or other fundamental value measures. Bloomberg

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