Extreme dependence in the NASDAQ and S&P 500 composite indexes

Abstract

Dependence among large observations in equity markets is usually examined using secondmoment models such as those from the GARCH or SV classes. Such models treat the entire set of returns, and tend to produce very similar estimates on the major equity markets, with a sum of estimated GARCH parameters, for example, slightly below one. Using dependence measures from extreme value theory, however, it is possible to characterize dependence among only the largest (or largest negative) financial returns; these alternative characterizations of clustering have important applications in risk management. In this paper we compare the NASDAQ and S&P in this way, and implement tests which can be used for the null hypothesis of the same degree of extreme dependence. Although GARCH-type characterizations of second-moment dependence in the two markets produce similar results, the same is not true in the extremes: we find significantly more extreme dependence in the NASDAQ returns. More generally, the study of extreme dependence may reveal contrasts which are obscured when examining the conditional second moment.

On the Estimation of the Extremal Index Based on Scaling and Resampling

“…The 95% confidence interval based on (5.23) and scale j = 6 is (0.34, 0.49), and the one based on the pooled scales and (5.24) is (0.34, 0.50). Our results are in agreement with the Ferro-Segers and runs estimates (for 200 threshold exceedences therein) of θ loss reported in Figure 3b of Galbraith and Zernov (2006).…”

“…These values confirm the common observation that the tails of the losses are slightly heavier than the tails of the gains (see e.g. Table 1 in Galbraith and Zernov (2006)). The bottom two panels on Figure 7 show boxplots of resampled estimates of the extremal index θ as a function of the scale j.…”

“…The problem of estimating θ has also received some attention in the literature: Hsing (1993), Smith and Weissman (1994), Weissman and Novak (1998) and Ferro and Segers (2003). Applications of the extremal index in various scientific areas include its incorporation in calculations of the Value-at-Risk measure (Longin (2000) and Klüppelberg in Finkenstädt and Rootzén (2004)), in the study of the Nasdaq and S&P 500 indices (Galbraith and Zernov (2006)) and in the study of GARCH processes (Laurini (2004)). The estimation of the extremal index θ is an important practical problem with rapidly expanding areas of application to finance, insurance, hydrology and telecommunications, to name a few (for more details, see e.g.…”

Extreme return correlation and volatility: a two‐threshold approach

“…He finds that the return distributions exhibit longer and thicker (shorter and thinner) right (left) tails, thereby suggesting that boom and recessionary market conditions affect the extreme returns in an asymmetric manner. Galbraith and Zernov (2009) examine the extreme returns in the time‐series of returns from NASDAQ and S&P 500 indices. They use the tail index and the extremal index to characterize the tails[6].…”

“…The various financial markets where extreme value theory has been applied are; equity markets (Longin and Solnik, 2001; Kaizoji, 2006; LeBaron and Samanta, 2005; Longin, 1996; Galbraith and Zernov, 2009), futures markets (Cotter, 2001, 2004; Longin, 1999), and foreign exchange markets (Koedijk et al , 1990; Quintos et al , 2001). …”