On the way to recovery: A nonparametric bias free estimation of recovery rate densities

In this paper we analyse recovery rates on defaulted bonds using the Standard & Poor's/PMD database for the years 1981–1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.     

Credit rating dynamics and Markov mixture models

Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence, we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm’s ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical current credit ratings can have substantially different transition probability vectors. We also find that conditioning on the state of the business cycle or industry group does not remove the heterogeneity with respect to the rate of movement. We go on to compare the performance of mixture and Markov chain using out-of-sample predictions.     

A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model

We consider the problem of pricing European exotic path-dependent derivatives on an underlying described by the Heston stochastic volatility model. Lipton has found a closed form integral representation of the joint transition probability density function of underlying price and variance in the Heston model. We give a convenient numerical approximation of this formula and we use the obtained approximated transition probability density function to price discrete path-dependent options as discounted expectations. The expected value of the payoff is calculated evaluating an integral with the Monte Carlo method using a variance reduction technique based on a suitable approximation of the transition probability density function of the Heston model. As a test case, we evaluate the price of a discrete arithmetic average Asian option, when the average over n = 12 prices is considered, that is when the integral to evaluate is a 2n = 24 dimensional integral. We show that the method proposed is computationally efficient and gives accurate results.     

Empirical risk aversion functions-estimates and assessment of their reliability

In this paper, we examine investor's risk preferences implied by option prices. In order to derive these preferences, we specify the functional form of a pricing kernel and then shift its parameters until realized returns are best explained by the subjective probability density function, which consists of the ratio of the risk-neutral probability density function and the pricing kernel. We examine, alternatively, pricing kernels of power, exponential, and higher order polynomial forms. Using S&P 500 index options, we find surprising evidence of risk neutrality, instead of risk aversion, in both the power and exponential cases. When extending the underlying assumption on the specification of the pricing kernel to one of higher order polynomial functions, we obtain functions exhibiting ‘monotonically decreasing’ relative risk aversion (DRRA) and anomalous ‘inverted U-shaped’ relative risk aversion. We find, however, that only the DRRA function is robust to variation in sample characteristics, and is statistically significant. Finally, we also find that most of our empirical results are consistent, even when taking into account market imperfections such as illiquidity.     

The determinants of bank loan recovery rates

Using Moody’s Ultimate Recovery Database, we estimate a model for bank loan recoveries using variables reflecting loan and borrower characteristics, industry and macroeconomic conditions, and several recovery process variables. We find that loan characteristics are more significant determinants of recovery rates than are borrower characteristics prior to default. Industry and macroeconomic conditions are relevant, as are prepackaged bankruptcy arrangements. We examine whether a commonly used proxy for recovery rates, the 30-day post-default trading price of the loan, represents an efficient estimate of actual recoveries and find that such a proxy is biased and inefficient.     

An improved estimation method and empirical properties of the probability of informed trading

We report evidence that boundary solutions can cause a bias in the estimate of the probability of informed trading (PIN). We develop an algorithm to overcome this bias and use it to estimate PIN for nearly 80,000 stock-quarters between 1993 and 2004. We obtain two sets of PIN estimates by using the factorized likelihood functions in both [Easley et al., 2010] and [Lin and Ke, 2011], respectively. We find that the estimate based on the EHO factorization is systematically smaller than the estimate based on the LK factorization, meaning that there is a downward bias associated with the EHO factorization. In addition, we find that boundary solutions appear with a very high frequency when the LK factorization is used. Thus it is necessary to use the LK factorization together with the algorithm in this paper. At last, we document several interesting empirical properties of PIN.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

The intertemporal relation between expected returns and risk

This paper explores the time-series relation between expected returns and risk for a large cross section of industry and size/book-to-market portfolios. I use a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model to estimate a portfolio's conditional covariance with the market and then test whether the conditional covariance predicts time–variation in the portfolio's expected return. Restricting the slope to be the same across assets, the risk-return coefficient is highly significant with a risk–aversion coefficient (slope) between one and five. The results are robust to different portfolio formations, alternative GARCH specifications, additional state variables, and small sample biases. When conditional covariances are replaced by conditional betas, the risk premium on beta is estimated to be in the range of 3% to 5% per annum and is statistically significant.     

Disentangling the effect of jumps on systematic risk using a new estimator of integrated co-volatility

We propose a new threshold–pre-averaging realized estimator for the integrated co-volatility of two assets using non-synchronous observations with the simultaneous presence of microstructure noise and jumps. We derive a noise-robust Hayashi–Yoshida estimator that allows for very general structure of jumps in the underlying process. Based on the new estimator, different aspects and components of co-volatility are compared to examine the effect of jumps on systematic risk using tick-by-tick data from the Chinese stock market during 2009–2011. We find controlling for jumps contributes significantly to the beta estimation and common jumps mostly dominate the jump’s effect, but there is also evidence that idiosyncratic jumps may lead to significant deviation. We also find that not controlling for noise and jumps in previous realized beta estimations tend to considerably underestimate the systematic risk.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

Volatility and covariation of financial assets: A high-frequency analysis

Using high frequency data for the price dynamics of equities we measure the impact that market microstructure noise has on estimates of the: (i) volatility of returns; and (ii) variance–covariance matrix of n assets. We propose a Kalman-filter-based methodology that allows us to deconstruct price series into the true efficient price and the microstructure noise. This approach allows us to employ volatility estimators that achieve very low Root Mean Squared Errors (RMSEs) compared to other estimators that have been proposed to deal with market microstructure noise at high frequencies. Furthermore, this price series decomposition allows us to estimate the variance covariance matrix of n assets in a more efficient way than the methods so far proposed in the literature. We illustrate our results by calculating how microstructure noise affects portfolio decisions and calculations of the equity beta in a CAPM setting.     

Practical methods for measuring and managing operational risk in the financial sector: A clinical study

This paper analyzes the implications of the advanced measurement approach (AMA) for the assessment of operational risk. Through a clinical case study on a matrix of two selected business lines and two event types of a large financial institution, we develop a procedure that addresses the major issues faced by banks in the implementation of the AMA. For each cell, we calibrate two truncated distributions functions, one for “normal” losses and the other for the “extreme” losses. In addition, we propose a method to include external data in the framework. We then estimate the impact of operational risk management on bank profitability, through an adapted measure of RAROC. The results suggest that substantial savings can be achieved through active management techniques.     

Maximum likelihood estimation of non-affine volatility processes

In this paper we develop a new estimation method for extracting non-affine latent stochastic volatility and risk premia from measures of model-free realized and risk-neutral integrated volatility. We estimate non-affine models with nonlinear drift and constant elasticity of variance and we compare them to the popular square-root stochastic volatility model. Our empirical findings are: (1) the square-root model is misspecified; (2) the inclusion of constant elasticity of variance and nonlinear drift captures stylized facts of volatility dynamics and (3) the square-root stochastic volatility model is explosive under the risk-neutral probability measure.     

Forecasting the performance of hedge fund styles

This article predicts the relative performance of hedge fund investment styles using time-varying conditional stochastic dominance tests. These tests allow for the construction of dynamic trading strategies based on nonparametric density forecasts of hedge fund returns. During the recent financial turmoil, our tests predict a superior performance for the Global Macro investment style compared with the other strategies of ‘Directional Traders’. The Dedicated Short Bias investment style is stochastically dominated by the other directional styles. These results are confirmed by simple nonparametric tests constructed from realized excess returns. Further, by utilizing a cross-validation method for optimal bandwidth parameter selection, we discover the factors that have predictive power regarding the density of hedge fund returns. We observe that different factors have forecasting power for different regions of the returns distribution and, more importantly, that the Fung and Hsieh factors have power not only for describing the risk premium but also, if appropriately exploited, for density forecasting.     

Cyclicality in catastrophic and operational risk measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973–2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the generalized Pareto distribution and the skewed generalized error distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.     

Correlation dynamics in equity markets: evidence from India

This study is aimed at understanding the correlation dynamics of the equity markets from a developing country perspective using daily data from July 1997 to August 2006. A simple unconditional correlation estimate and dynamic time varying correlation estimate from a DCC-MVGARCH of Engle and Sheppard (2001) are derived for S&P CNX Nifty and other 10 world indices that includes four developed and six Asian country indices. The results show low correlation across S&P CNX Nifty with both Asian and developed nations. In addition a Logistic Smooth Transition Regression (LSTR) model is implemented and finds that the S&P CNX Nifty index is moving towards a better integration with other world markets but not at a very noteworthy phase. The low correlation provides space for the global funds to diversify risk in Indian markets.     

Identification of speculative bubbles using state-space models with Markov-switching

In this paper we use a state-space model with Markov-switching to detect speculative bubbles in stock-price data. To this end we express a present-value stock-price model in state-space form which we estimate using the Kalman filter. This procedure enables us to estimate a two-regime Markov-switching specification of the unobservable bubble process. The respective Markov-regimes represent two distinct phases in the bubble process, namely one in which the bubble survives and one in which it collapses. We ultimately identify bursting stock-price bubbles by statistically separating both Markov-regimes from each other. In an empirical analysis we apply our methodology to a plethora of artificial and real-world data sets. Our study has two major findings. First, we find significant Markov-switching structures in real-world stock-price bubbles. Second, in the stock markets considered our identification procedure correctly detects most speculative periods which have been classified as such by economic historians.     

Saving-based asset-pricing

This paper explores the implications of a novel class of preferences for the behavior of asset prices. Following a suggestion by Marshall (1920), we entertain the possibility that people derive utility not only from consumption, but also from the very act of saving. These “saving-based” preferences are related to models of habit formation and the spirit of capitalism, but incorporate the feature that people have anticipatory habits because they care about the future accumulation of wealth. We derive the Euler equations for these preferences and estimate them with GMM. Our estimates suggest that the preference for saving is economically significant.     

OLIVE: A SIMPLE METHOD FOR ESTIMATING BETAS WHEN FACTORS ARE MEASURED WITH ERROR

We propose a simple and intuitive method for estimating betas when factors are measured with error: ordinary least squares instrumental variable estimator (OLIVE). OLIVE performs well when the number of instruments becomes large, whereas the performance of conventional instrumental variable methods becomes poor or even infeasible. In an empirical application, OLIVE beta estimates improve R² significantly. More important, our results help resolve two puzzling findings in the prior literature: first, the sign of average risk premium on the beta for market return changes from negative to positive; second, the estimated value of average zero‐beta rate is no longer too high.