Paul Kofman

Increased correlation in bear markets

A number of studies have provided evidence of increased correlations in global financial market returns during bear markets. Other studies, however, have shown that some of this evidence may be biased. We derive an alternative to previous estimators for implied correlation that is based on measures of portfolio downside risk and that does not suffer from bias. The unbiased quantile correlation estimates are directly applicable to portfolio optimization and to risk management techniques in general. This simple and practical method captures the increasing correlation in extreme market conditions while providing a pragmatic approach to understanding correlation structure in multivariate return distributions. Based on data for international equity markets, we found evidence of significant increased correlation in international equity returns in bear markets. This finding proves the importance of providing a tail-adjusted mean–variance covariance matrix. A generally accepted concept today is that, over time, returns when the markets are experiencing large negative movements are more highly correlated than returns during more normal times. If true, this phenomenon has serious implications for portfolio and risk management because it means that the benefits of diversification are curtailed precisely when investors most need them. The correlation, however, depends on how the returns are conditioned on the size of the returns. Previous studies have provided alternative correlation structures with which to compare conditional empirical correlations, but these estimates have upward or downward biases that need to be corrected. In this article, we provide a quantile correlation approach that is not biased by the size of the return distribution. The result is a simple and pragmatic approach to estimating correlations conditional on the size of the returns. Based on empirical data, we show how the correlation estimates can be used directly in portfolio and risk management. We derive a conditional correlation structure based on the quantile of the joint return distribution; that is, correlation is conditioned on the size of the return distribution. In a bivariate framework, the correlation is estimated by using those observations that fall below the portfolio return of the two assets. The approach is thus in line with current correlation measures used in Markowitz-style portfolio analysis and in current risk management techniques. The quantile correlation structure is determined by the weights of the assets in the portfolio and the quantile estimates of the distribution of returns on the two assets and of the portfolio return. When the distribution is normal, the conditional correlation structure is constant; hence, the conditional quantile correlation will equal the unconditional correlation. Therefore, because the correlation structure is constant over the distribution for normality, one can easily compare empirical estimates of conditional correlation with their theoretical values under conditions of normal distribution. We examine a variety of daily returns from international stock market indexes for the period May 1990 through December 1999 to establish, first, their unconditional correlations. For example, this procedure produced a correlation between the U.S. market (S&P 500 Index) and the U.K. market (the FTSE 100 Index) of 0.349. Assuming bivariate normality for the whole distribution, we would expect the quantile conditional correlation also to be 0.349. For quantiles up to the 95 percent level, we found that the assumption of normality cannot be rejected at the 95 percent confidence level for all the series. For higher quantiles, however—that is, large negative returns in the bivariate return distribution—the conditional correlation structure increased the correlations; in the case of the U.S. and U.K. markets, the correlation increased to 0.457. The effect on mean–variance portfolio optimization is a reduction in the recommended weight of the risky assets held in the portfolio. These results imply that the gains from diversification are not reaped in periods when diversification benefits are most crucial from a mean–variance perspective—in bear markets. Practitioners, therefore, need to know what sort of model is generating the correlations they are relying on. If the underlying model assumed normality, then the correlation estimates used in the model need to be adjusted to incorporate the bear markets higher-than-normal correlation structure.

A threshold error-correction model for intraday futures and index returns

Index-futures arbitragers only enter into the market if the deviation from the arbitrage relation is sufficiently large to compensate for transaction costs and associated interest rate and dividend risks. We estimate the band around the theoretical futures price within which arbitrage is not profitable for most arbitragers, using a threshold autoregression model. Combining these thresholds with an error-correction model, we show that the impact of the mispricing error is increasing with the magnitude of that error and that the information effect of lagged futures returns on index returns is significantly larger when the mispricing error is negative.

Spreads, information flows and transparency across trading systems

This paper analyses the relative merits of an automated versus an open outcry trading system for a derivatives contract which is traded simultaneously at two competing exchanges. The only characterizing difference between these exchanges is the mode of operation. The domestic exchange (listing the underlying asset) operates by automated trading, the foreign exchange uses open outcry. Investigations are made to determine whether this operational competition supports a trading system segmentation hypothesis. First, quote setting is investigated to determine whether or not it is related to the transparency of the trading system. Second, analysis is carried out to determine whether the transparency of the trading system influences the lead/lag relationship in returns and volatility between the two markets. Both hypotheses are empirically tested for the Bund futures contract as it is traded in London (LIFFE) and Frankfurt (DTB).

Increased Correlation in Bear Markets: A Downside Risk Perspective

A number of studies have provided evidence of increased correlations in global financial market returns during bear markets. Other studies, however, have shown that some of this evidence may be biased. We derive an alternative to previous estimators for implied correlation that is based on measures of portfolio downside risk and that does not suffer from bias. The unbiased quantile correlation estimates are directly applicable to portfolio optimization and to risk management techniques in general. This simple and practical method captures the increasing correlation in extreme market conditions while providing a pragmatic approach to understanding correlation structure in multivariate return distributions. Based on data for international equity markets, we found evidence of significant increased correlation in international equity returns in bear markets. This finding proves the importance of providing a tail-adjusted mean–variance covariance matrix. A generally accepted concept today is that, over time, returns when the markets are experiencing large negative movements are more highly correlated than returns during more normal times. If true, this phenomenon has serious implications for portfolio and risk management because it means that the benefits of diversification are curtailed precisely when investors most need them. The correlation, however, depends on how the returns are conditioned on the size of the returns. Previous studies have provided alternative correlation structures with which to compare conditional empirical correlations, but these estimates have upward or downward biases that need to be corrected. In this article, we provide a quantile correlation approach that is not biased by the size of the return distribution. The result is a simple and pragmatic approach to estimating correlations conditional on the size of the returns. Based on empirical data, we show how the correlation estimates can be used directly in portfolio and risk management. We derive a conditional correlation structure based on the quantile of the joint return distribution; that is, correlation is conditioned on the size of the return distribution. In a bivariate framework, the correlation is estimated by using those observations that fall below the portfolio return of the two assets. The approach is thus in line with current correlation measures used in Markowitz-style portfolio analysis and in current risk management techniques. The quantile correlation structure is determined by the weights of the assets in the portfolio and the quantile estimates of the distribution of returns on the two assets and of the portfolio return. When the distribution is normal, the conditional correlation structure is constant; hence, the conditional quantile correlation will equal the unconditional correlation. Therefore, because the correlation structure is constant over the distribution for normality, one can easily compare empirical estimates of conditional correlation with their theoretical values under conditions of normal distribution. We examine a variety of daily returns from international stock market indexes for the period May 1990 through December 1999 to establish, first, their unconditional correlations. For example, this procedure produced a correlation between the U.S. market (S&P 500 Index) and the U.K. market (the FTSE 100 Index) of 0.349. Assuming bivariate normality for the whole distribution, we would expect the quantile conditional correlation also to be 0.349. For quantiles up to the 95 percent level, we found that the assumption of normality cannot be rejected at the 95 percent confidence level for all the series. For higher quantiles, however—that is, large negative returns in the bivariate return distribution—the conditional correlation structure increased the correlations; in the case of the U.S. and U.K. markets, the correlation increased to 0.457. The effect on mean–variance portfolio optimization is a reduction in the recommended weight of the risky assets held in the portfolio. These results imply that the gains from diversification are not reaped in periods when diversification benefits are most crucial from a mean–variance perspective—in bear markets. Practitioners, therefore, need to know what sort of model is generating the correlations they are relying on. If the underlying model assumed normality, then the correlation estimates used in the model need to be adjusted to incorporate the bear markets higher-than-normal correlation structure.

Interaction between stock markets: an analysis of the common trading hours at the London and New York stock exchange

Abstract This paper examines the spill-overs in both returns and volatility between the London and New York stock markets during overlapping trading hours. Using high-frequency data for the FTSE and S&P stock index futures, we estimate the seasonal patterns in volatility using a Flexible Fourier Form specification. The estimated seasonals are used to adjust the returns before conducting the lead-lag analysis. The results indicate that both markets influence each other, although the impact of the USA on the UK is clearly stronger.

The inefficiency of Reuters foreign exchange quotes

Abstract Reuters foreign exchange (FXFX) page is the world wide predominant information source to foreign exchange traders. In this study we compare the indicative spot exchange rate quotes from Reuters with their matching futures exchange rates from the Chicago Mercantile Exchange. We find that the indicative quotes on Reuters FXFX page are inefficient and could be improved by incorporating information from the futures market. This casts doubt on the way banks determine these quotes, as well as on the informational content of these quotes as an indicator of the current exchange rate.

Tracking Error and Active Portfolio Management

Persistent bear market conditions have led to a shift of focus in the tracking error literature. Until recently the portfolio allocation literature focused on tracking error minimization as a consequence of passive benchmark management under portfolio weights, transaction costs and short selling constraints. Abysmal benchmark performance shifted the literatures focus towards active portfolio strategies that aim at beating the benchmark while keeping tracking error within acceptable bounds. We investigate an active (dynamic) portfolio allocation strategy that exploits the predictability in the conditional variance-covariance matrix of asset returns. To illustrate our procedure we use Jorions (2002) tracking error frontier methodology. We apply our model to a representative portfolio of Australian stocks over the period January 1999 through November 2002.

Is Default Risk Priced in Australian Equity? Exploring the Role of the Business Cycle

Using an extensive Australian sample, we explore two related issues in the context of a default risk asset-pricing factor (DEF) over the business cycle: (a) whether a DEF can explain the size premium in the three-factor Fama–French (FF) model; and (b) whether a DEF has a separate role itself in a four-factor version of the FF model. While we find that the default factor does not explain the success of size, our evidence shows it has a complementary role to small minus big and high minus low. Notably, subgroups of test portfolios likely to seriously challenge any asset-pricing model show evidence that the four-factor model is not perfect. Finally, while we find that conditioning on the business cycle itself has little impact, when we condition on a leading indicator, it has a positive (negative) effect on the estimated default (market) risk premium.

Mixtures of tails in clustered automobile collision claims

Abstract Knowledge of the tail shape of claim distributions provides important actuarial information. This paper discusses how two techniques commonly used in assessing the most appropriate underlying distribution can be usefully combined. The maximum likelihood approach is theoretically appealing since it is preferable to many other estimators in the sense of best asymptotic normality. Likelihood based tests are, however, not always capable to discriminate among non-nested classes of distributions. Extremal value theory offers an attractive tool to overcome this problem. It shows that a much larger set of distributions is nested in their tails by the so-called tail parameter. This paper shows that both estimation strategies can be usefully combined when the data generating process is characterized by strong clustering in time and size. We find that the extreme value theory is a useful starting point in detecting the appropriate distribution class. Once that has been achieved, the likelihood-based EM-algorithm is proposed to capture the clustering phenomena. Clustering is particularly pervasive in actuarial data. An empirical application to a four-year data set of Dutch automobile collision claims is therefore used to illustrate the approach.

Reversing the lead, or a series of unfortunate events? NYMEX, ICE and Amaranth

A number of studies compare the efficiency and transparency of floor trading with automated/electronic trading systems in the competition for order flow. Although most of these studies find that electronic systems lead price discovery, a few studies highlight the weaknesses of electronic trading in highly volatile market conditions. A series of unusual events in 2006, sparking extreme volatility in natural gas futures trading, provide an ideal setting to revisit the resilience of trading system price leadership in the face of high volatility. We estimate time‐varying Hasbrouck‐style information shares to investigate the intertemporal and cross‐sectional dynamics in price discovery. The results strongly suggest that the information share is time‐dependent and contract‐dependent. Floor trading dominates price discovery in the less liquid longer‐maturity contracts, whereas electronic trading dominates price discovery in the most liquid spot‐month contract. We find that the floor trading information share increases significantly with realized volatility.