Hedging the Brazilian stock index in the era of low interest rates: What has changed?
| Autor | Aiube, Fernando Antonio Lucena |
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Introduction
At the end of 2019, the interest rate in Brazil reached its lowest level in more than 20 years. This was a consequence of a prior period of recession and a recent economic environment of low inflation. The creation of the Real Plan in 1994 allowed the Brazilian economy to achieve macroeconomic stabilization. In the same direction, institutional reforms adopted in the ensuing years reinforced macro and fiscal policies (floating exchange rate, inflation targeting system and primary surplus target), keeping inflation low (Afonso et al.; 2016).
The Brazilian Central Bank (BCB) found sufficient conditions to start cutting the interest rate in 2016 as a response to economic stagnation. On the other hand, the nominal interest rates in central economies at that time had been low since 2009, a situation that has continued. Indeed, both short- and long-term rates have been persistently low in recent years. In Japan and the Euro Zone many government bonds have been traded at negative yields for several years; see Borio and Hofmann (2017).
From the investment perspective, this big movement in the Brazilian market prompted many agents to look for better returns in equity markets. Hence, the B3 (Brazilian Stock Exchange in Sao Paulo) received a huge volume of funds and the number of investors more than doubled in the last two years (see the B3 report). The economic rationale behind this fact is that in a low-interest-rate regime, firms' cash flows are discounted with lower cost of capital, so they naturally become more valuable.
Because of the greater risks of equity markets, investors need more efficient risk control measures for their allocations. This can come from using diversification strategies or derivative instruments. In both cases, investors aim to reduce their exposure. The diversification strategy is related to the correlation between assets. In this paper, we examine the conditional correlations of the Brazilian equity market considering a portfolio with different asset classes in the period of low interest rates. We compare these results with the previous period of high interest rates. We also analyze a broad period encompassing low and high interest rates. We consider potential assets for hedging from two different perspectives. First, we use only locally-traded (domestic) assets (the stock index, exchange rate, a local commodity index, a local fixed-income asset, a cryptocurrency, and gold). Second, we consider a foreign agent investing in Brazilian equities traded in U.S. dollars. We examine the potential use of foreign assets (the domestic stock index, a commodity index, a fixed income asset, a cryptocurrency, and gold, all traded in U.S. dollars). We estimate the conditional correlation among these assets in each case. To this end, we use multivariate generalized autoregressive conditional heteroskedastic (MGARCH) models.
The main goal is to distinguish from among different asset classes those that are more appropriate for hedging/diversification purposes. Sadorsky (2014) and Manera et al. (2013) use the same method, although with different objectives. The motivation of this type of analysis is the fact that markets quickly react to changes in interest rate dynamics.
The paper contributes to the analysis of hedging possibilities in a low-interest regime of an emerging economy using domestic and foreign assets. This study has clear implications for investors, portfolio managers and practitioners facing new challenges for asset allocation in a new environment of low interest rates that seemingly will prevail for a long time.
The paper is organized as follows: Section 2 presents an overview of the literature; Section 3 details the models used; Section 4 exhibits the data; Section 5 discusses the results; and Section 6 concludes.
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Literature overview
The literature on portfolio allocation is fundamentally based on the assessment of the correlation coefficient among the assets composing a portfolio. The terms "hedging" and "diversification" are important topics in the financial literature. Efforts to study these issues evolved notably in the mid1990s and 2000s, when many conditional correlation models were developed. Engle and Kroner (1995) explore the specification of Baba et al. (1990), calling it the BEKK representation. Tse and Tsui (2002) propose a multivariate autoregressive conditional heteroskedastic model with time-varying correlations, belonging to the class of dynamic conditional correlation (DCC) models. They adopt the conditional variance formulation of GARCH models where the conditional correlation is considered an autoregressive moving average. In this direction, Engle (2002) proposes a simpler DCC model, compared to the previous ones. The author joins the univariate variance models of the GARCH family with a more parsimonious correlation specification, where the conditional correlation is specified as a weighted sum of past correlations. Another convenience of this formulation is that the parameters of the variance and correlation equations can be estimated separately in two steps. We call the Engle (2002) model DCC-GARCH from now on. McAleer et al. (2008) propose a generalized autoregressive conditional correlation model (VARMA-AGARCH). Unlike the formulations of Engle (2002) and Tse and Tsui (2002), this model imposes no restrictions on the parameters of the conditional correlation.
There is a vast literature on the applications of these models. In general, these applications aim to investigate the correlation among different asset classes and the implication for portfolio allocation. Many authors examine the ability of commodity and cryptocurrencies to diversify/hedge equity positions. Sadorsky (2014) examines the correlations between emerging-market stock prices and the prices of copper, oil, and wheat. He compares the models of McAleer et al. (2008) (VARMA-AGARCH) and the DCC of Engle (2002) (DCC-GARCH). He concludes that the DCC-GARCH fits the data better and that oil provides the cheapest hedge for emerging-market stock prices. Creti et al. (2013) use the DCC-GARCH method to investigate the links between commodities and stocks in the period from January 2001 to November 2011. Their main conclusion relates to gold's behavior, which exhibited a negative correlation with stocks most of the time. Manera et al. (2013) analyze energy and agricultural commodities, examining whether macroeconomic factors affect these commodity sectors. They find that the S&P 500 index and exchange rate significantly affect returns. Chang et al. (2013) investigate the conditional correlations and spillovers between crude oil (six different types) and financial markets (four equity indexes). They use different conditional correlation models and compare the results. They find that the VARMA-AGARCH model provides little evidence of volatility spillovers between crude oil and financial markets. The results of DCC-GARCH are always significant. Olson et al. (2017) investigate whether commodities are effective hedges for equity investors. They use different methods to estimate hedge ratios: realized variance and covariance, the BEKK model of Engle and Kroner (1995), and recursive OLS regressions. They find evidence that commodities were not good hedges for the S&P 500 in the period analyzed. Klein et al. (2018) study the behavior of Bitcoin, gold, and silver in a portfolio of equity indexes and WTI (West Texas Intermediate) crude oil. They find that Bitcoin does not present stable hedging performance and is correlated positively with downward markets. Moreover, they find that gold and Bitcoin have fundamentally different properties related to equity markets.
Applications of MGARCH models to the Brazilian market are also extensive. Ferreira and De Mattos (2014) use the BEKK model to investigate the contagion effect of the subprime crises on the Brazilian stock market. Using a sample of indexes from 2007 to 2010, they find evidence of contagion between U.S. and Brazilian stock indexes. Marcal and Valls Pereira (2009) examine signals of contagion during the 1990s coming from many financial crises in that decade. They investigate the behavior of bond markets in different countries using MGARCH models and find evidence supporting the contagion hypothesis. Vartanian (2020) analyzes the linkage between commodity prices (Commodity Research Bureau index) and the Brazilian stock market index (Ibovespa) through the BEKK model. Although Ibovespa is a diversified index, it contains many stocks of commodity-producing firms (e.g. Vale and Petrobras). He finds that the conditional correlation is relatively small and that the commodity index is useful for risk diversification of equities, proxied by the Brazilian stock index.
In this paper we investigate the conditional correlation among Brazilian equity prices, focusing on the most popular MGARCH models: the BEKK of Engle and Kroner (1995) and DCC-GARCH of Engle (2002).
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The model setup
We describe the dynamic correlation between the Brazilian equity index and different asset classes using the BEKK and DCC-GARCH models. Consider [y.sub.t] the vector of log-returns of n assets. The mean equation is written as
[PHI](L)[y.sub.t] = [mu] + [THETA] (L) [[epsilon].sub.t] = 1, ..., T (1a)
[[epsilon].sub.t] = [z.sub.t][H.sup.1/2.sub.t], (1b)
where L is the lag operator of the AR and MA polynomials [PHI] (L) = 1 - [[phi].sub.1]L - ... -[[phi].sub.r][L.sup.r] and [THETA](L) = 1 + [[theta].sub.1]L + ... + [[theta].sub.s][L.sup.s], respectively. [z.sub.t] is an n-dimensional iid process with mean zero and covariance identity matrix [I.sub.n]. In this formulation one can write E [[[epsilon].sub.t] |...
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