Risk evaluations with robust approximate factor models

Approximate factor models and their extensions are widely used in economic analysis and forecasting due to their ability to extracting useful information from a large number of relevant variables. In these models, candidate predictors are typically subject to some common components. In this paper we propose a new method for robustly estimating the approximate factor models and use it in risk assessments. We consider a class of approximate factor models in which the candidate predictors are additionally subject to idiosyncratic large uncommon components such as jumps or outliers. By assuming that occurrences of the uncommon components are rare, we develop an estimation procedure to simultaneously disentangle and estimate the common and uncommon components. We then use the proposed method to investigate whether risks from the latent factors are priced for expected returns of Fama and French 100 size and book-to-market ratio portfolios. We find that while the risk from the common factor is priced for the 100 portfolios, the risks from the idiosyncratic factors are not. However, we find that model uncertainty risks of the idiosyncratic factors are priced, suggesting that with effective diversifications, only the predictable idiosyncratic risks can be reduced, but the unpredictable ones may still exist. We also illustrate how the proposed method can be adopted on evaluating value at risk (VaR) and find it can delivery comparable results as the conventional methods on VaR evaluations.     

Risk factor contributions in portfolio credit risk models

Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate extension of techniques for position contributions, since the portfolio loss is a nonlinear function of the risk factors. We employ the Hoeffding decomposition of the portfolio loss into a sum of terms depending on the factors. This decomposition restores linearity, but includes terms arising from joint effects of groups of factors. These cross-factor terms provide information to risk managers, since they can be viewed as best hedges of the portfolio loss involving instruments of increasing complexity. We illustrate the technique on multi-factor portfolio credit risk models, where systematic factors represent industries, geographical sectors, etc.     

Testing conditional factor models

Using nonparametric techniques, we develop a methodology for estimating and testing conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The estimators and tests can be implemented for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As applications of the methodology, we estimate conditional CAPM and multifactor models on book-to-market and momentum decile portfolios. We reject the null that long-run alphas are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios.     

联行业务存在的风险因素与整改措施

中央银行会计集中核算系统(ABS)上线后，联行柜作为核算中心的一个重要职能部门，是ABS系统内部支付信息的收发中心，也是系统处理联行往来业务的中继站，地位非常重要。联行柜的职责是负责全辖电子联行往来账、手工联行往来账处理、对账及查询查复事项等。从联行业务运行情况看，该系统也存在着一定的风险因素，影响了资金运转速度，带来一定的资金风险。     

Risk analysis for accounting models: A spreadsheet simulation approach

Risk analysis can be performed on accounting models using spreadsheet add-ins having statistical forecasting and simulation capabilities. Modeling uncertainty, performing a simulation, and viewing probability distributions of key output variables present to students the risk within a modeled relationship. This use of technology for accounting instruction is presented for capital budgeting, budgeted cash flow, and a budgeted income statement.     

The Risk Map: A new tool for validating risk models

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.     

A general framework for the derivation of asset price bounds: an application to stochastic volatility option models

We present a generalization of Cochrane and Saá-Requejo’s good-deal bounds which allows to include in a flexible way the implications of a given stochastic discount factor model. Furthermore, a useful application to stochastic volatility models of option pricing is provided where closed-form solutions for the bounds are obtained. A calibration exercise demonstrates that our benchmark good-deal pricing results in much tighter bounds. Finally, a discussion of methodological and economic issues is also provided.      

Notes on dynamic factor pricing models

These notes discuss three aspects of dynamic factor pricing (i.e., APT) models. First, the diversifiable component of returns is unpredictable in a no-arbitrage world. Second, conditional factor loadings or betas have an unconditional factor structure when returns follow an unconditional factor structure, which provides a link between conditional and unconditional factor pricing models. Third, the estimation of dynamic factor pricing models is easily simplified in large cross sections when returns follow an unconditional factor structure. These results aid in the interpretation of existing applications and identify some of the issues in the formulation and estimation of dynamic factor pricing models.     

Price discovery and common factor models

If a financial asset is traded in more than one market, common factor models may be used to measure the contribution of these markets to the price discovery process. We examine the relationship between the Hasbrouck (J. Finance (50) (1995) 1175) and Gonzalo and Granger (J. Bus. Econ. Stat. 13 (1995) 27) common factor models. These two models complement each other and provide different views of the price discovery process between markets. The Gonzalo and Granger model focuses on the components of the common factor and the error correction process, while the Hasbrouck model considers each market's contribution to the variance of the innovations to the common factor. We show that the two models are directly related and provide similar results if the residuals are uncorrelated between markets. However, if substantive correlation exists, they typically provide different results. We illustrate these differences using analytic examples plus a real world example consisting of electronic communications networks (ECNs) and other Nasdaq market makers.     

Macroeconomic risks and characteristic-based factor models

We show that book-to-market, size, and momentum capture cross-sectional variation in exposures to a broad set of macroeconomic factors identified in the prior literature as potentially important for pricing equities. The factors considered include innovations in economic growth expectations, inflation, the aggregate survival probability, the term structure of interest rates, and the exchange rate. Factor mimicking portfolios constructed on the basis of book-to-market, size, and momentum therefore, serve as proxy composite macroeconomic risk factors. Conditional and unconditional cross-sectional asset pricing tests indicate that most of the macroeconomic factors considered are priced. The performance of an asset pricing model based on the macroeconomic factors is comparable to the performance of the Fama and French (1993) model. However, the momentum factor is found to contain incremental information for asset pricing.     

Non-parametric method for European option bounds

There is much research whose efforts have been devoted to discovering the distributional defects in the Black–Scholes model, which are known to cause severe biases. However, with a free specification for the distribution, one can only find upper and lower bounds for option prices. In this paper, we derive a new non-parametric lower bound and provide an alternative interpretation of Ritchken’s (J Finance 40:1219–1233, 1985) upper bound to the price of the European option. In a series of numerical examples, our new lower bound is substantially tighter than previous lower bounds. This is prevalent especially for out of the money options where the previous lower bounds perform badly. Moreover, we present how our bounds can be derived from histograms which are completely non-parametric in an empirical study. We discover violations in our lower bound and show that those violations present arbitrage profits. In particular, our empirical results show that out of the money calls are substantially overpriced (violate the lower bound).     

Portfolio efficiency and discount factor bounds with conditioning information: An empirical study

Stochastic discount factor bounds provide a useful diagnostic tool for testing asset pricing models by specifying a lower bound on the variance of any admissible discount factor. In this paper, we provide a unified derivation of such bounds in the presence of conditioning information, which allows us to compare their theoretical and empirical properties. We find that, while the location of the ‘unconditionally efficient (UE)’ bounds of [Ferson, W., Siegel, A., 2001. The efficient use of conditioning information in portfolios. Journal of Finance 56 (3), 967–982] is statistically indistinguishable from the (theoretically) optimal bounds of [Gallant, R., Hansen, L., Tauchen, G., 1990. Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution. Journal of Econometrics 45 (1), 141–179] (GHT), the former exhibit better sampling properties. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the efficient return weights underlying their construction.     

A comparison of single factor Markov-functional and multi factor market models

We compare single factor Markov-functional and multi factor market models and the impact of their correlation structures on the hedging performance of Bermudan swaptions. We show that hedging performance of both models is comparable, thereby supporting the claim that Bermudan swaptions can be adequately risk-managed with single factor models. Moreover, we show that the impact of smile can be much larger than the impact of correlation. We use the constant exercise method for calculating risk sensitivities of callable products in market models, which is a modification of the least-squares Monte Carlo method. The hedge results show the constant exercise method enables proper functioning of market models as risk-management tools.     

Bond portfolio optimization using dynamic factor models

A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a duration-constrained mean-variance optimization, which can be used to improve bond indexing. An empirical application involving two large data sets of U.S. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve strategies used in bond desks. Additionally, we propose a dynamic rule to switch among alternative bond investment strategies, and find that the benefits of such dynamic rule are even more pronounced when the set of available policies is augmented with the proposed mean-variance portfolios.     

Risk and ambiguity in models of business cycles

We inject aggregate uncertainty — risk and ambiguity — into an otherwise standard business cycle model and describe its consequences. We find that increases in uncertainty generally reduce consumption, but they do not account, in this model, for either the magnitude or the persistence of the most recent recession. We speculate about extensions that might do better along one or both dimensions.     

Analytical bounds for Treasury bond futures prices

The pricing of delivery options, particularly timing options, in Treasury bond futures is prohibitively expensive. Recursive use of the lattice model is unavoidable for valuing such options, as Boyle in J Finance 14(1):101?C113, (1989) demonstrates. As a result, the main purpose of this study is to derive upper bounds and lower bounds for Treasury bond futures prices. This study first shows that the popular preference-free, closed form cost of carry model is an upper bound for the Treasury bond futures price. Then, the next step is to derive analytical lower bounds for the futures price under one and two-factor Cox-Ingersoll-Ross models of the term structure. The bound under the two-factor Cox-Ingersoll-Ross model is then tested empirically using weekly futures prices from January 1987 to December 2000.     

Forecasting the yield curve with linear factor models

In this work we compare the interest rate forecasting performance of a broad class of linear models. The models are estimated through a MCMC procedure with data from the US and Brazilian markets. We show that a simple parametric specification has the best predictive power, but it does not outperform the random walk. We also find that macroeconomic variables and no-arbitrage conditions have little effect to improve the out-of-sample fit, while a financial variable (Stock Index) increases the forecasting accuracy.     

Testing conditional factor models: A nonparametric approach

Some recent studies of conditional factor models do not specify conditioning information but use data from small windows to estimate the time series of conditional alphas and betas. In this paper, we propose a nonparametric method using an optimal window to estimate time-varying coefficients. In addition, we offer two empirical tests of a conditional factor model. Using our new method, we examine the performance of the conditional CAPM and the conditional Fama-French three-factor model in explaining the return variations of portfolios sorted by size, book-to-market ratios, and past returns, for which recent literature has generated controversial results. We find that, although in general the conditional FF model outperforms the conditional CAPM, both models fail to explain well-known asset-pricing anomalies. Moreover, for both models, the failure is more pronounced for the equally-weighted portfolios than for the value-weighted ones.