典型事实、极值理论与金融市场动态风险测度研究

本文在金融市场典型事实约束下,运用ARFIMA模型对金融市场条件收益率建模,运用GARCH、GJR、FIGARCH、APARCH、FIAPARCH等5种模型对金融波动率进行建模,进而运用极值理论(EVT)对标准收益的极端尾部风险建模来测度各股市的动态风险,并用返回测试(Back-testing)方法检验模型的适应性。实证结果表明,总的来说,FIAPARCH-EVT模型对各个市场具有较强的适应性,风险测度能力较为优越。进一步,本文在ARFIMA-FIAPARCH模型下,假定标准收益分别服从正态分布(N)、学生t分布(st)、有偏学生t分布(skst)、广义误差分布(GED)共4种分布,对各股市的动态风险测度的准确性进行检验,并和EVT方法的测度结果进行对比分析。结果表明,EVT方法风险测度能力优于其他方法,有偏学生t分布假设下的风险测度模型虽然略逊于EVT方法,但也不失为一种较好的方法;ARFIMA-FI-APARCH-EVT不仅在中国大陆沪深股市表现最为可靠,而且在其他市场也表现出同样的可靠性。     

El efecto de la volatilidad del peso mexicano en los rendimientos y riesgo de la Bolsa Mexicana de Valores

The effect of heavy tails due to rare events and different levels of asymmetry associated with high volatility clustering in the emerging financial markets requires sophisticated models for statistical modelling of such stylized facts. This article applies extreme value theory (EVT) to quantify tail risk on the daily returns of Mexican stock market under aggregation of foreign exchange rate risk from January 1971 to December 2010. This study focuses on the maximum-block method and generalized extreme value distribution (GEVD) to model the asymptotic behavior of extreme returns in US dollars. The empirical results show that EVT-Based VaR measured at high confidence levels performs better than simulation historical and delta-normal VaR models on capturing fat-tails in the returns of highly volatile stock markets. Additionally, international investors holding long positions in Mexican stock market are more prone to experience larger potential losses than investors with short positions during local currency depreciation and financial crisis periods.     

Extreme observations and risk assessment in the equity markets of MENA region: Tail measures and Value-at-Risk

The standard “delta-normal” Value-at-Risk methodology requires that the underlying returns generating distribution for the security in question is normally distributed, with moments which can be estimated using historical data and are time-invariant. However, the stylized fact that returns are fat-tailed is likely to lead to under-prediction of both the size of extreme market movements and the frequency with which they occur. In this paper, we use the extreme value theory to analyze four emerging markets belonging to the MENA region (Egypt, Jordan, Morocco, and Turkey). We focus on the tails of the unconditional distribution of returns in each market and provide estimates of their tail index behavior. In the process, we find that the returns have significantly fatter tails than the normal distribution and therefore introduce the extreme value theory. We then estimate the maximum daily loss by computing the Value-at-Risk (VaR) in each market. Consistent with the results from other developing countries [see Gencay, R. and Selcuk, F., (2004). Extreme value theory and Value-at-Risk: relative performance in emerging markets. International Journal of Forecasting, 20, 287–303; Mendes, B., (2000). Computing robust risk measures in emerging equity markets using extreme value theory. Emerging Markets Quarterly, 4, 25–41; Silva, A. and Mendes, B., (2003). Value-at-Risk and extreme returns in Asian stock markets. International Journal of Business, 8, 17–40], generally, we find that the VaR estimates based on the tail index are higher than those based on a normal distribution for all markets, and therefore a proper risk assessment should not neglect the tail behavior in these markets, since that may lead to an improper evaluation of market risk. Our results should be useful to investors, bankers, and fund managers, whose success depends on the ability to forecast stock price movements in these markets and therefore build their portfolios based on these forecasts.     

Alternative statistical distributions for estimating value-at-risk: theory and evidence

A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student??s t and SGT distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student??s t and normal distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student??s t and normal distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student??s t) on VaR estimates in stock markets for a long position.     

Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying

In this study, we analyze the properties of Bitcoin as a diversifier asset and hedge asset against the movement of international market stock indices: S&P500 (US), STOXX50 (EU), NIKKEI (Japan), CSI300 (Shanghai), and HSI (Hong Kong). For this, we use several copula models: Gaussian, Student-t, Clayton, Gumbel, and Frank. The analysis period runs from August 18, 2011 to June 31, 2019. We found that the Gaussian and Student-t copulas are best at fitting the structure dependence between markets. Also, these copulas suggest that under normal market conditions, Bitcoin might act as a hedge asset against the stock price movements of all international markets analyzed. However, the dependence on the Shanghai and Hong Kong markets was somewhat higher. Also, under extreme market conditions, the role of Bitcoin might change from hedge to diversifier. In a time-varying copula analysis, given by the Student-t copula, we found that even under normal market conditions, for some markets, the role of Bitcoin as a hedge asset might fail on a high number of days.     

Global economic activity as an explicator of emerging market equity returns

This paper evaluates whether global economic activity, measured by the maritime index and commodity index, is a distinct common factor in explaining equity returns in emerging markets. We document two important features of global equity markets that show that emerging market equities are a segregated part of the global stock market. First, our results show that increases in global economic activity are associated with higher emerging market equity returns. Second, companies in developed markets that have a significant exposure in emerging markets have incremental exposure to commodity returns. By allocating more capital to emerging market equities, an investor increases portfolio exposure to changes in global economic activity.     

Stock returns and beta,firms size,E/P,CF/P,book-to-market,and sales growth: evidence from Singapore and Malaysia

Using data from Singapore and Malaysia for the period 1988–1996, this paper examines the relationship between stock returns and beta, size, the earnings-to-price ratio, the cash flow-to-price ratio, the book-to-market equity ratio, and sales growth (SG). We find the presence of anomalies in these emerging markets. There is a conditional relationship between beta and stock returns for both countries. During months with positive market excess returns, there is a significant positive relationship. We also find a negative relationship between beta and stock returns during months with negative market excess returns. We document the existence of a negative relationship between stock returns and size for both countries. For Singapore, we also document a negative relationship between returns and SG. For Malaysia, we find a positive relationship between returns and the E/P ratio. These relationships are only significant in non-January months.     

Integration of emerging stock markets with global stock markets

Financial integration for emerging economies should be seen as a long-term objective. In this paper, we examine stock market integration among five selected emerging stock markets (Brazil, China, Mexico, Russia and Turkey) and developed markets of the US, UK and Germany. The bounds testing approach to cointegration and error-correction modeling are used on monthly data from January 2001 to December 2014 to determine the short-run and long-run relationship between emerging stock market returns and the returns of the developed stock markets. The results show evidence of the existence of short-run integration among stock markets in emerging countries and the developed markets. However, the long-run coefficients for stock market returns in all emerging countries show a significant relationship only with Germany stock market return. The empirical findings in this study have important implications for academicians, international investors, and policymakers in emerging markets.     

Volatility and correlation in international stock markets and the role of exchange rate fluctuations

This paper develops a direct, explicit model for the role of exchange rate fluctuations in international stock markets and examines how and to what extent volatility and correlations in equity markets are influenced by exchange rate fluctuations. Evidence presented in this paper indicates that a higher foreign exchange rate variability mostly increases local stock market volatility but decreases volatility for the US stock market. The extent to which stock market volatility is influenced by foreign exchange variability is greater for local markets than for the US market, due to the fact that exchange rate changes are more strongly correlated with local equity market returns than the US market returns. We find that a higher exchange rate fluctuation marginally decreases the US/local equity market correlation. While exchange rate fluctuations held a relatively large fraction of the variation in local stock market returns, there was no significant influence on the US/local equity market correlation.     

International Equity Index and Currency Futures: Commodity Currencies or Emerging Versus Developed Markets?

Equity index futures in both emerging and developing markets that are net commodity exporters are strongly linked to their respective currency futures markets. Unconditional correlations among equity and currency futures are the highest for these net basic materials producers in both emerging and developed markets. Granger causality tests also indicate that stock market returns are more strongly related to currency futures returns for commodity-exporting countries. Additionally, conditional correlations among currency and equity futures returns are the strongest for commodity-producing countries in both emerging and developed economies. Volatility spillover analysis provides consistent results. The overall results indicate that the status of a country as a net importer or exporter of raw materials is more important to the relationship between equity and currency futures than whether it is an emerging or developed economy.     

Causality in volatility and volatility spillover effects between US, Japan and four equity markets in the South China Growth Triangular

In examining co-movement across international stock markets, previous researchers usually pre-determine the direction of causation and neglect the Chinese equity markets. In this study, we examine the spillover effects of volatility among the two developed markets and four emerging markets in the South China Growth Triangular using Chueng and Ng's causality-in-variance test. Several findings deserve mention: (1) the Japanese stock market affects the US stock market and there is a feedback relationship between the Hong Kong and US stock market. (2) Markets of the SCGT are contemporaneously correlated with the return volatility of the US market. (3) Econometric models constructed according to the results of variance-in-causality tests have greater explanatory power than the conventional GARCH(1,1) model. (4) Using the return volatility of foreign exchange as a proxy for informational arrival can explain excess kurtosis of a stock return series, especially for the less open emerging market. (5) Geographic proximity and economic ties do not necessarily lead to a strong relationship in volatility across markets.     

What moves international stock and bond markets?

We study the relation between international mutual fund flows and the different return components of aggregate equity and bond markets. First, we decompose international equity and bond market returns into changes in expectations of future real cash payments, interest rates, exchange rates, and discount rates. News about future cash flows, rather than discount rates, is the main driver of international stock returns. This evidence is in contrast with the typical results reported only for the US. Inflation news instead is the main driver of international bond returns. Next, we turn to the interaction between these return components and international portfolio flows. We find evidence consistent with price pressure, short-term trend chasing, and short-run overreaction in the equity market. We also find that international bond flows to emerging markets are more sensitive to interest rate shocks than equity flows.     

A Generalized Extreme Value Approach to Financial Risk Measurement

This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in-sample and out-of-sample performance results indicate that the Box–Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions.     

Common Volatility: An Empirical Investigation of Closed-End Country Funds

The study of international integration of equity markets has received a great deal of interest. This paper investigates whether returns of forty-one closed-end country funds share a common volatility process with three comparable return series: the underlying net asset value (NAV), U.S. stock market returns, and foreign stock market returns. Country funds are a natural setting to test for international market integration, as they are traded in the U.S. market, whereas their underlying assets are traded in foreign stock markets. Our results indicate that only a few emerging markets' country funds share common volatility processes with their comparable asset returns. This, in turn, suggests weak linkages through the second moment of related assets.     

Interest Rate Risk of European Financial Corporations

We investigate the interest rate exposure of large European financial corporations' equity returns. For the period from January 1982 to March 1995 we estimate multifactor index models to examine the sensitivity of equity returns to market index returns and domestic as well as global interest rate movements. In addition, we specify an APT‐model to test whether an exposure to interest rate movements is rewarded in the cross‐section of expected returns. In the four European markets both domestic and global interest rate shifts constitute driving forces of stock returns beyond the influence of the domestic market indices. However, the exposure to interest rate movements does not seem to be rewarded in the same fashion among the markets.     

Local risk factors in emerging markets: Are they separately priced?

We provide new evidence on the pricing of local risk factors in emerging stock markets. We investigate whether there is a significant local currency premium together with a domestic market risk premium in equity returns within a partial integration asset pricing model. Given previous evidence on currency risk, we conduct empirical tests in a conditional setting with time-varying prices of risk. Our main results support the hypothesis of a significant exchange risk premium related to the local currency risk. Exchange rate and domestic market risks are priced separately for our sample of seven emerging markets. The empirical evidence also suggests that although statistically significant, local currency risk is on average smaller than domestic market risk but it increases substantially during crises periods, when it can be almost as large as market risk. Disentangling these two factors is thus important in tests of international asset pricing for emerging markets.     

Linkages among European and world stock markets

Causal relations and dynamic interactions among equity returns in ten countries for the period 1983–1994 are analysed. An innovation accounting approach based on a multivariate vector autoregressive (VAR) model is used to estimate the proportion of each market return's forecast error attributable to innovations in foreign market returns. Three major results appear. The variance decompositions indicate a strong degree of economic interaction among stock markets. The US stock market has a considerable influence on stock market performance in almost every country, while there is no substantial inter-continental influence from the European stock markets on the world's two largest equity markets in New York and Tokyo. Finally, the pattern of the impulse-response functions illustrates a rapid international transmission of stock market events, supporting the hypothesis of international stock market efficiency.     

The relationship between stock returns and volatility in international stock markets

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.     

Random Walks and Market Efficiency Tests: Evidence from Emerging Equity Markets

We use the multiple variance-ratio test of Chow and Denning (1993) to examine the stochastic properties of local currency- and US dollar-based equity returns in 15 emerging capital markets. The technique is based on the Studentized Maximum Modulus distribution and provides a multiple statistical comparison of variance-ratios, with control of the joint-test's size. We find that the random walk model is consistent with the dynamics of returns in most of the emerging markets analyzed, which contrasts many random walk test results documented with the use of single variance-ratio techniques. Further, a runs test suggests that most of the emerging markets are weak-form efficient. Overall, our results suggest that investors are unlikely to make systematic nonzero profit by using past information in many of the examined markets, thus, investors should predicate their investment strategies on the assumption of random walks. Additionally, our results suggest exchange rate matters in returns' dynamics determination for some of the emerging equity markets we analyzed.     

The Equity Market Risk Premium and the Valuation of Overseas Investments

There is little agreement among academics or practitioners about how to measure the size of the equity market risk premium, particularly when it relates to investments in emerging markets. Using monthly equity returns for 22 developed and 24 emerging markets covering the period 1976–2006, the authors find that developed capital markets have experienced significant increases in their degree of integration with the U.S. and world market indexes, while emerging markets remain at least partly segmented from those of the U.S. and the world. For countries that are reasonably well integrated into global capital markets, the authors suggest using the U.S.—based equity market risk premium. But when valuing investments in emerging markets, they recommend use of the Capital Asset Pricing Model adjusted for political risk and a measure of co‐movement between the foreign and U.S. stock markets. The authors also remind readers that the equity market risk premium is supposed to be a forward‐looking measure, and that the common practice of inferring the future from the past can be misleading, particularly in the case of rapidly developing emerging markets.