Mo Chaudhury

A Review of the Key Issues in Operational Risk Capital Modeling

In an effort to bolster soundness standards in banking, the 2006 international regulatory agreement of Basel II requires globally active banks to include operational risk in estimating regulatory and economic capital to be held against major types of risk. This paper discusses practical issues faced by a bank in designing and implementing an operational risk capital model. Focusing on the use of the Loss Distribution Approach (LDA) in the context of the Basel Advanced Measurement Approach (AMA), pertinent topics of future research are suggested.

Price Clustering in the CAC 40 Index Options Market

We examine in details the pattern and systematic tendencies of clustering in CAC 40 index option transaction prices during the period 1997 to 1999. Similar to extant studies in many financial markets, there is evidence of strong clustering at full index points and option prices are 90% more likely to end with the digit 0 (multiples of 10) than with the digit 5. While the 1999 contract downsizing led to some reduction in clustering at full index point, the basic pattern of clustering remains intact. The pattern of clustering rejects the attraction theory, but is consistent with the notion of cost recovery by market makers. We find important drivers for CAC 40 index option price clustering, namely, the level of option premium, option volume and underlying asset volatility. Higher premium level, higher asset volatility and lower volume are seen to increase option price clustering. We also observe a U-shaped pattern of clustering on an intra-day and intra-year basis. The option premium and volatility effects are consistent with a price level effect. The volatility effect also lends support to the notion of cost recovery by market makers. The volume effect likely represents a liquidity effect and is consistent with the Price Precision Hypothesis.

Functional Form of Stock Return Model: Some International Evidence

A Linear (loglinear) empirical return model is rejected for more than half (one-third) of an international sample of 425 stocks. A generalized functional form improves explanatory power and enhances the role of a global index in the stock return model. Additionally, the inclusion of a lagged dependent variable seems desirable for many stocks to allow incomplete price response to domestic and global market variations.

How Did the Financial Crisis Affect the Daily Stock Returns

In this paper, we investigate the effect of the recent financial crisis on the behavior of stock prices using the daily returns of thirty one major US stocks and the S&P 500 over the 2007/08 period. Unconditional mean daily returns fell to negative levels, unconditional volatility surged more than two hundred percent, correlation between stocks weakened and the risk reduction benefit of portfolio diversification rose. Beta risk increased significantly for financial stocks and the importance of market risk for them dropped, but the financial stocks still turned up a stellar alpha performance. Conditional variance persistence increased and leverage effect became stronger, but negative skewness of the unconditional distribution weakened. The unconditional kurtosis effect is mixed for stocks but dropped for the S&P 500. Despite a weaker negative skew and a lower kurtosis of returns, the S&P 500 implied volatility skew (tail asymmetry) effect strengthened sharply and the smile (fatter tail) effect was somewhat stronger too. But when scaled by the implied volatility average, the strengthening effects disappeared. Empirical one tail 99% Value at Risk for stock portfolios shot up more than two hundred percent, driven mainly by surging volatilities. Dominant thread among many of the effects or lack thereof is the surging unconditional volatility. Using this intuition, we propose an extended Value at Risk measure based on Normal distribution that is transparent and easy to implement.

Seasonal variations in the U.S. Stock Market returns: 1927–1984

When the seasonal components of the monthly returns as opposed to the returns themselves, are examined over the 1927–1984 period, the Standard & Poors 500 Composite Index (S&P 500) and the Center for Research in Security Prices (CRSP) value-weighted portfolio exhibit significant seasonality. Their seasonal behavior is quite similar to that of the smallest quintile of New York Stock Exchange (NYSE) stocks and the CRSP equally weighted portfolio during March through October. While January is strong for the two latter portfolios, December, November, and January appear to be consistently strong for the two former portfolios. The seasonal pattern has, however, changed substantially over time. While June and July returns experienced a significant drop in seasonal strength, March and April returns gained seasonal strength for all four portfolios from 1927–1958 to 1959–1984. These changes coincide in an inverse fashion with the shifts in interest rate seasonality.

Stock Overreaction to Extreme Market Events

In this paper we find that stocks overreact to both positive and negative extreme daily movements of the broader market, but more intensely in the latter case. The overreaction is even more pronounced when the market exhibits clustered extreme swings, indicating that the overreaction is related to market volatility. Indeed, a contrarian investment strategy earns a significant Fama-French daily alpha of 0.34% (85.68% annualized) with a Sharpe ratio of 5.23 in highly volatile circumstances. Stock overreaction appears to be driven by the loser stocks that revert more strongly, even as they exhibit a lower market beta than the winners.

Overreaction to extreme market events and investor sentiment

ABSTRACT This article investigates the role of investor psychology, captured here by investor sentiment index, in driving individual stock price reactions to extreme movements in the broader market. In addition to confirming prior evidence of overreaction, we find much stronger overreaction when investor sentiment is low rather than high. This is consistent with the role of the contrast dimension of an uncommon event, suggested in the psychology literature, over and above the emotion of surprise it brings about. In a low sentiment environment, the contrast is sharper and hence leads to stronger overreaction.

Volatility and Expected Option Returns: A Note

Are options on more volatile assets expected to provide higher or lower return? Using analytics, we show the ambiguous nature of the answer when the volatility differential is due to the systematic/priced risk. Here the difference in the expected return of the assets also matters and has an effect on expected option return that is opposite to the case of idiosyncratic/unpriced risk. Our numerical results, based on more than 13 million parameter combinations, elaborate how the direction and magnitude of the net effect depends on the levels of asset beta and volatility and the moneyness and maturity of options. Accordingly, in analyzing the cross-section of returns on traded options, securities with embedded options, and other nonlinear derivatives, one should pay attention to the source of volatility differential, and the sample range/mix of betas, volatilities, and option moneyness and maturity.

The Financial Crisis and the Behavior of S&P 500 Index Option Prices

Stronger volatility skew and smile effects accompanied by a risk-neutral distribution that is closer to the Normal seem unconventional at first thought. But that is what we find during the financial crisis, with the unconventionally high risk-neutral volatility level playing a major role. Additionally, the term structure of implied volatility became inverted (negatively sloped) during the crisis, driven by the inversion of the term structure of risk-neutral volatility and by the rise in the shorter term unconditional volatility. The term structures of risk-neutral skewness and kurtosis appear relatively flat with only negligible change during the crisis. The scale and its term structure rather than the shape factors of the unconditional risk neutral distribution to maturity thus appear more important for the structure of crisis time option prices.

Why Basel II Market Risk VaR is Too Conservative

This article argues that the 2009 Basel II market risk Value at Risk (VaR), which adds a stress VaR component, is overly conservative and that it is the failure to model extreme surges in volatility rather than any restrictions imposed by the VaR framework or the normality assumption that caused capital inadequacy during the financial crisis. This hypothesis is supported by comparing the pre-2009 VaR and the new 2009 VaR of Basel II and Extended Value at Risk (EVaR) for the S&P 500. EVaR is based on a market responsive composite volatility measure developed in this article and the popular normal distribution.