Measuring large comovements in financial markets

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.     

Hedging Housing Risk*

An unusually rich source of data on housing prices in Stockholm is used to analyze the investment implications of housing choices. This empirical analysis derives market-wide price and return series for housing investment during a 13-year period, and it also provides estimates of the individual-specific, idiosyncratic, variation in housing returns. Because the idiosyncratic component follows an autocorrelated process, the analysis of portfolio choice is dependent upon the holding period. We analyze the composition of household investment portfolios containing housing, common stocks, stocks in real estate holding companies, bonds, and t-bills. For short holding periods, the efficient portfolio contains essentially no housing. For longer periods, low-risk portfolios contain 15 to 50 percent housing. These results suggest that there are large potential gains from policies or institutions that would permit households to hedge their lumpy investments in housing. We estimate the potential value of hedges in reducing risk to households, yet yielding the same investment returns. The value is surprisingly large, especially to poorer homeowners.     

A multivariate model of strategic asset allocation

We develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely long-lived investor with Epstein–Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Empirical estimates in long-run annual and post-war quarterly U.S. data suggest that the predictability of stock returns greatly increases the optimal demand for stocks. The role of nominal bonds in long-term portfolios depends on the importance of real interest rate risk relative to other sources of risk. Long-term inflation-indexed bonds greatly increase the utility of conservative investors.     

Which past returns affect trading volume?

Anecdotal evidence suggests and recent theoretical models argue that past stock returns affect subsequent stock trading volume. We study 3,000 individual investors over a 51 month period to test this apparent link between past returns and volume using several different panel regression models (linear panel regressions, negative binomial panel regressions, Tobit panel regressions). We find that both past market returns as well as past portfolio returns affect trading activity of individual investors (as measured by stock portfolio turnover, the number of stock transactions, and the propensity to trade stocks in a given month). After high portfolio returns, investors buy high risk stocks and reduce the number of stocks in their portfolio. High past market returns do not lead to higher risk taking or underdiversification. We argue that the only explanations for our findings are overconfidence theories based on biased self-attribution and differences of opinion explanations for high levels of trading activity.     

Model Misspecification and Underdiversification

In this paper, we study intertemporal portfolio choice when an investor accounts explicitly for model misspecification. We develop a framework that allows for ambiguity about not just the joint distribution of returns for all stocks in the portfolio, but also for different levels of ambiguity for the marginal distribution of returns for any subset of these stocks. We find that when the overall ambiguity about the joint distribution of returns is high, then small differences in ambiguity for the marginal return distribution will result in a portfolio that is significantly underdiversified relative to the standard mean‐variance portfolio.     

Delayed Reaction to Good News and the Cross-Autocorrelation of Portfolio Returns

We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross-autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross-sectional tests of the delay for individual securities suggest that existing explanations of the cross-autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time-varying risk premiums fail to capture the directional asymmetry in the data.     

Estimating the Value of Employee Stock Option Portfolios and Their Sensitivities to Price and Volatility

The costs associated with compiling data on employee stock option portfolios is a substantial obstacle in investigating the impact of stock options on managerial incentives, accounting choice, financing decisions, and the valuation of equity. We present an accurate method of estimating option portfolio value and the sensitivities of option portfolio value to stock price and stock-return volatility that is easily implemented using data from only the current year's proxy statement or annual report. This method can be applied to either executive stock option portfolios or to firm-wide option plans. In broad samples of actual and simulated CEO option portfolios, we show that these proxies capture more than 99% of the variation in option portfolio value and sensitivities. Sensitivity analysis indicates that the degree of bias in these proxies varies with option portfolio characteristics, and is most severe in samples of CEOs with a large proportion of out-of-the-money options. However, the proxies' explanatory power remains above 95% in all subsamples.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.     

When are contrarian profits due to stock market overreaction?

If returns on some stocks systematically lead or lag those ofothers, a portfolio strategy that sells 'winners' and buys 'losers'can produce positive expected returns, even if no stock's returnsare negatively autocorrelated as virtually all models of overreactionimply. Using a particular contrarian strategy we show that,despite negative autocorrelation in individual stock returns,weekly portfolio returns are strongly positively autocorrelatedand are the result of important cross-auto-correlations. Wefind that the returns of large stocks lead those of smallerstocks, and we present evidence against overreaction as theonly source of contrarian profits.     

Fundamental indexation via smoothed cap weights

If prices of individual stocks are unbiased but noisy approximations to fundamental values, there will be a gap in returns between the standard cap-weighted market portfolio and the one based on fundamentals. The discrepancy occurs because, relative to fundamentals, cap-weights are too large (small) for stocks with positive (negative) deviations from fundamental values. It follows that the usual cap-weighted portfolio will underperform relative to the fundamental-based portfolio as long as prices revert to fundamental values. This has led Arnott et al. to propose new market indices based on a firm’s fundamental size as measured by its revenues, number of employees, and so on. In this paper we follow the same principle but propose to estimate fundamental weights using a smoothed average of standard cap-weights. Since the putative excess returns of a fundamentals-weighted portfolio requires reversion to fundamental values, and because fundamental values are likely to change slowly, we can estimate current fundamentals by smoothing the time series of a stock’s noisy prices. The determination of fundamental size in terms of accounting data is thereby replaced by a simple estimate based on price history. We derive expressions for expected returns of the market capitalization-based and fundamentals-based portfolios under various assumptions about (i) the random deviations from fundamental values and (ii) the change in fundamentals over time. We present empirical comparisons between portfolios and find the returns of the fundamentals-based portfolios exceed the standard indices by an amount comparable to the prior estimates that used accounting data to determine size.     

The effect of estimation risk on optimal portfolio choice

This paper determines the effect of estimation risk on optimal portfolio choice under uncertainty. In most realistic problems, the parameters of return distributions are unknown and are estimated using available economic data. Traditional analysis neglects estimation risk by treating the estimated parameters as if they were the true parameters to determine the optimal choice under uncertainty. We show that for normally distributed returns and ‘non-informative’ or ‘invariant’ priors, the admissible set of portfolios taking the estimation uncertainty into account is identical to that given by traditional analysis. However, as a result of estimation risk, the optimal portfolio choice differs from that obtained by traditional analysis. For other plausible priors, the admissible set, and consequently the optimal choice, is shown to differ from that in traditional analysis.     

WINDOW DRESSING IN BOND MUTUAL FUNDS

We examine portfolio credit quality holding and daily return patterns in a large sample of bond mutual funds and document evidence of window dressing. Using portfolio credit quality holdings data, we find that bond funds on average hold significantly more government bonds during disclosure than nondisclosure, presumably to present a safer portfolio to shareholders. Multiple‐index market models estimated with daily returns data corroborate these findings. We detect differences in factor loadings on days surrounding disclosure dates that indicate systematic tilting of the portfolio toward higher quality instruments.     

Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints

We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of state variables. By suitably embedding the constrained problem in an appropriate family of unconstrained ones, we provide some equivalent optimality conditions for the indirect value function and optimal portfolio weights. These results simplify and help to solve the constrained optimal portfolio choice problem in jump-diffusion models. Finally, we apply our theoretical results to several examples, to examine the impact of no-short-selling and/or no-borrowing constraints on the performance of optimal portfolio strategies.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

The wealth effects of portfolio rebalancing in emerging equity markets

This paper analyzes the wealth effects of alternative portfolio rebalancing strategies for equity investments in nine emerging markets for the period from 1976 to 1998. The choice of rebalancing intervals has a large effect on wealth accumulation and the geometric mean return. The difference between no rebalancing and semi-annual rebalancing is 5.87 percentage points per year. Surprisingly, semi-annual rebalancing, which was optimal for this data set, was also 2.62 percentage points per year better than monthly rebalancing. Positive first- and second-degree autocorrelation among the monthly returns appears to account for the decrease in returns for rebalancing more frequently than semi-annually.     

Linear predictability vs. bull and bear market models in strategic asset allocation decisions: evidence from UK data

Most papers in the portfolio choice literature have examined linear predictability frameworks based on the idea that simple but flexible Vector Autoregressive (VAR) models can be expanded to produce portfolio allocations that hedge against the bull and bear dynamics typical of financial markets through careful selection of predictor variables that capture business cycles and market sentiment. Yet, a distinct literature exists that shows that non-linear econometric frameworks, such as Markov switching, are also natural tools to compute optimal portfolios arising from the existence of good and bad market states. This paper examines whether and how simple VARs can produce portfolio rules similar to those obtained under a simple Markov switching, by studying the effects of expanding both the order of the VAR and the number/selection of predictor variables included. In a typical stock-bond strategic asset allocation problem for UK data, we compute the out-of-sample certainty equivalent returns for a wide range of VARs and compare these measures of performance with those of non-linear models. We conclude that most VARs cannot produce portfolio rules, hedging demands or (net of transaction costs) out-of-sample performances that approximate those obtained from simple non-linear frameworks.     

Modeling asymmetric comovements of asset returns

Existing time-varying covariance models usually impose strongrestrictions on how past shocks affect the forecasted covariancematrix. In this article we compare the restrictions imposedby the four most popular multivariate GARCH models, and introducea set of robust conditional moment tests to detect misspecification.We demonstrate that the choice of a multivariate volatilitymodel can lead to substantially different conclusions in anyapplication that involves forecasting dynamic covariance matrices(like estimating the optimal hedge ratio or deriving the riskminimizing portfolio). We therefore introduce a general modelwhich nests these four models and their natural 'asymmetric'extensions. The new model is applied to study the dynamic relationbetween large and small firm returns.     

Are Momentum Profits Robust to Trading Costs?

We test whether momentum strategies remain profitable after considering market frictions induced by trading. Intraday data are used to estimate alternative measures of proportional and non-proportional (price impact) trading costs. The price impact models imply that abnormal returns to portfolio strategies decline with portfolio size. We calculate break-even fund sizes that lead to zero abnormal returns. In addition to equal- and value-weighted momentum strategies, we derive a liquidity-weighted strategy designed to reduce the cost of trades. Equal-weighted strategies perform the best before trading costs and the worst after trading costs. Liquidity-weighted and hybrid liquidity/value-weighted strategies have the largest break-even fund sizes: $5 billion or more (relative to December 1999 market capitalization) may be invested in these momentum strategies before the apparent profit opportunities vanish.