Estimating the performance attributes of Australian multi-sector managed funds within a dynamic Kalman filter framework

This paper examines the impact of Kalman filtering as a technique for modeling the risk levels of managed funds. Using a sample of Australian Multi-sector trusts we examine selectivity and market timing performance using conventional performance models alongside Kalman filter models that allow beta to vary via a random walk. Further, we consider the stability and asymmetry of these performance measures together with a measure of volatility timing arising from a cubic model of fund performance. We find that the positive selectivity (negative market timing) that stems from the conventional models is not present with the Kalman filter model. The Kalman filter model tends to show neutral performance for both. However, both models confirm a strong tendency toward negative volatility timing.     

Estimating the Dynamics of Mutual Fund Alphas and Betas

This article develops a Kalman filter model to track dynamicmutual fund factor loadings. It then uses the estimates to analyzewhether managers with market-timing ability can be identifiedex ante. The primary findings are as follows: (i) Ordinary leastsquares (OLS) timing models produce false positives (nonzeroalphas) at too high a rate with either daily or monthly data.In contrast, the Kalman filter model produces them at approximatelythe correct rate with monthly data; (ii) In monthly data, thoughthe OLS models fail to detect any timing among fund managers,the Kalman filter does; (iii) The alpha and beta forecasts fromthe Kalman model are more accurate than those from the OLS timingmodels; (iv) The Kalman filter model tracks most fund alphasand betas better than OLS models that employ macroeconomic variablesin addition to fund returns.     

An alternative method to estimate parameters in modelling the behaviour of commodity prices

Measuring the risk of investment projects involving commodities and modelling its price dynamics behaviour is usually implemented with Kalman filtering techniques. However, because the use of these techniques has high implementation requirements, recent literature has employed approximate models. This paper proposes a new and simpler spreadsheet implementation procedure which presents lower implementation requirements than the widely used Kalman filtering estimation procedure. The proposal needs to estimate fewer parameters than usual and does not directly estimate sequences but considers the relationship between the states implicitly when defining the regression matrices. This translates into a significant reduction in processing time. We apply the proposal to estimate the parameters of a 4-factor model for four commercial commodities: crude oil, heating oil, unleaded gasoline and natural gas; we then compare the accuracy with results using the Kalman filter method. Results indicate that error measurements are approximately equal for the actual model and the approximation proposed in this paper, for both the in- and out-of-sample data-sets.     

Are the Fama–French factors proxying news related to GDP growth? The Australian evidence

Inspired by Vassalou (J Financ Econ 68:47–73, 2003), we investigate the contention that the Fama and French (J Financ Econ 33:3–56, 1993) model’s ability to explain the cross sectional variation in equity returns is because the Fama–French factors are proxying for risk associated with future GDP growth in the Australian equities market. To assess the validity of Vassalou’s findings, we augment the CAPM and the Fama–French model with a GDP growth factor and run system regressions of the GDP-enhanced models using the GMM approach. Our results suggest that news about future GDP growth is not priced in equity returns and that any ability that SMB and HML exhibit in explaining equity returns is not because they contain information about future GDP growth.

Robustness of the estimates of the hybrid New Keynesian Phillips curve

Galí and Gertler [1999. Inflation dynamics: a structural econometric approach. Journal of Monetary Eonomics 44(2), 195-222] developed a hybrid variant of the New Keynesian Phillips curve that relates inflation to real marginal cost, expected future inflation and lagged inflation. GMM estimates of the model suggest that forward-looking behavior is dominant: the coefficient on expected future inflation substantially exceeds the coefficient on lagged inflation. While the latter differs significantly from zero, it is quantitatively modest. Several authors have suggested that our results are the product of specification bias or suspect estimation methods. Here we show that these claims are incorrect, and that our results are robust to a variety of estimation procedures, including GMM estimation of the closed form, and nonlinear instrumental variables. Also, as we discuss, many others have obtained very similar results to ours using a systems approach, including FIML techniques. Hence, the conclusions of GG and others regarding the importance of forward-looking behavior remain robust.     

On the estimation and comparison of short-rate models using the generalised method of moments

Subsequent to the influential paper of [Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.B., 1992. An empirical comparison of alternative models of the short-term interest rate. Journal of Finance 47, 1209–1227], the generalised method of moments (GMM) has been a popular technique for estimation and inference relating to continuous-time models of the short-term interest rate. GMM has been widely employed to estimate model parameters and to assess the goodness-of-fit of competing short-rate specifications. The current paper conducts a series of simulation experiments to document the bias and precision of GMM estimates of short-rate parameters, as well as the size and power of [Hansen, L.P., 1982. Large sample properties of generalised method of moments estimators. Econometrica 50, 1029–1054], J-test of over-identifying restrictions. While the J-test appears to have appropriate size and good power in sample sizes commonly encountered in the short-rate literature, GMM estimates of the speed of mean reversion are shown to be severely biased. Consequently, it is dangerous to draw strong conclusions about the strength of mean reversion using GMM. In contrast, the parameter capturing the levels effect, which is important in differentiating between competing short-rate specifications, is estimated with little bias.     

Unbiasedness of the Forward Exchange Rates

This paper derives an error correction model under the assumption that the spot and the forward rates are cointegrated, the first difference of forward rates is stationary, and the first order autocorrelation in the forecast error is allowed. When tests of the unbiasedness hypothesis are conducted with an error correction model using generalized methods of moments [GMM], the unbiasedness hypothesis cannot be rejected. Furthermore, the multivariate GMM estimation supports the hypothesis of unbiasedness of the forward exchange rates and the absence of a risk premium in the foreign exchange markets.     

Interacting particle systems for the computation of rare credit portfolio losses

In this paper, we introduce the use of interacting particle systems in the computation of probabilities of simultaneous defaults in large credit portfolios. The method can be applied to compute small historical as well as risk-neutral probabilities. It only requires that the model be based on a background Markov chain for which a simulation algorithm is available. We use the strategy developed by Del Moral and Garnier in (Ann. Appl. Probab. 15:2496–2534, 2005) for the estimation of random walk rare events probabilities. For the purpose of illustration, we consider a discrete-time version of a first passage model for default. We use a structural model with stochastic volatility, and we demonstrate the efficiency of our method in situations where importance sampling is not possible or numerically unstable.      

On the Efficiency of Conditional Heteroskedasticity Models

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.     

The Return Performance of Cubic Market Model: An Application to Emerging Markets

This article studies the performance of the high-order moment capital asset pricing model (CAPM) market models in emerging markets. We apply the cubic market model (4-moment CAPM) to 16 emerging market stock indices ranging from January 2010 to September 2015. Performance of the model is evaluated through the Fama and MacBeth’s two-step regression and through different corrections proposed in the literature, as well as generalized method of moments (GMM) estimation. According to Fama–MacBeth’s procedure, CAPM, the quadratic and cubic market models seem to be insignificant for the analyzed sample; however, the GMM estimation shows that quadratic model is valid for Indian, Polish, and Thai country indices, whereas cubic market model is accurate for Indian country index.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Modeling and forecasting stock return volatility using a random level shift model

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 ? α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of daily absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-of-sample forecasts of squared returns. In most cases, our simple random level shift model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.     

Calibration risk: Illustrating the impact of calibration risk under the Heston model

It is already well documented that model risk is an important issue regarding the pricing of exotics (see Schoutens et al., in A perfect calibration! Now what?, Wilmott Magazine, March 2004: pp 66–78, 2004). Arguments have been made to put this into the perspective of bid-ask pricing using the theory of conic finance and pricing to acceptability (Cherny and Madan Review of Financial Studies, 22: 2571–2606, 2009). In this paper we show also the presence and importance of calibration risk. More particularly, we point out that a variety of plausible calibration methods lead again to serious price differences for exotics and different distributions of the P&L of the delta-hedging strategy. This is illustrated under the popular Heston stochastic volatility model, which is used among practitioners to price all kinds of exotic and structured products. This paper shows that it is prudent to take some additional safety margin into account for the pricing of these structured notes.     

Hyperbolic Discounting and Consumer Patience: The Case of Korea

ABSTRACT

In this article, we test whether the consumption pattern in Korea exhibits a time-inconsistent discounting behavior compared to the conventional exponential discounting. We derive the quasi-hyperbolic Euler equation and estimate it using the generalized method of moments (GMM). The estimation results show that Korean consumers exhibit a time-inconsistent quasi-hyperbolic discounting behavior in general, but the pattern of inconsistency in consumption behavior, in particular the degree of impatience, depends on the estimation period, in particular whether it includes financial crisis periods in 1997–98 and 2008–11.     

Theory of Storage and the Pricing of Commodity Claims

We extend the literature on commodity pricing by incorporating a link between the spread of forward prices and spot price volatility suggested by the theory of storage. Our model has closed form solutions that are generalizations of the two-factor model of Gibson–Schwartz (1990). We estimate the model on daily copper spot and forward prices using the Kalman filter methodology. Our findings confirm the link between the forward spread and volatility, but also show that the Gibson–Schwartz (1990) model prices forward contracts almost as well. In the pricing of option contracts, however, there are significant differences between the models.     

Marketing Period Risk in a Portfolio Context: Theory and Empirical Estimates from the UK Commercial Real Estate Market

The role of selling (or marketing) period uncertainty in understanding risk associated with property investment is examined in this paper. Using an approach developed by Lin (2004), and Lin and Vandell (2001, 2005), combined with a statistical model of UK commercial property transactions, we show that the ex ante level of risk exposure for a commercial real estate investor is around one and a half times that obtained from historical statistics. The risk related to marketing time uncertainty can be reduced by constructing a portfolio. We find that at least ten properties are necessary to reduce this risk, assuming independence between marketing period risk and price risk. These findings have important implications for mixed-asset portfolio allocation decisions.      

Pricing credit card loans with default risks: a discrete-time approach

The main purpose of this paper is to modify the Jarrow and van Deventer model by using Das and Sundaram (Manag Sci 46:46–62, 2000) model to extend the Heath–Jarrow–Morton (J Finan Quant Anal 25:419–440, 1990) term-structure model to facilitate the consideration of default risks for pricing credit card loans. Furthermore, we derive closed-form solutions within a continuous-time framework. In addition, we also provide a numerical method for the evaluation of credit card loans within a discrete-time framework. Using the market segmentation argument to describe the characteristics of the credit card industry, our simulation results show that the shapes of the forward rate and forward spread (default risk premium) term structures play extremely important roles in determining the value of credit card loans.     

Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?

Abstract:  We show in a theoretical model that the expected excess return on any asset depends on its covariance not only with the market portfolio, but also with changes in the representative agent's estimate. We test our model using GMM and compare it to the CAPM. The results suggest that adding an 'estimation factor' to the CAPM helps explain cross-sectional returns and that, unconditionally, this estimation factor carries a negative risk premium.     

“Extended Black” term structure models

This paper examines “Extended Black” term structure models (EBTSM), which are multi-factor extensions of the one-factor Black model (Black, F., 1995. Interest rates as options. Journal of Finance 50, 1371-1376). EBTSM are not affected by the admissibility restrictions that plague canonical affine models. EBTSM encompass quadratic models, but unlike in quadratic models bond yields are sufficient statistics to infer the latent factors driving the short interest rate. EBTSM are amenable to econometric estimation despite the need to solve bond pricing equations through finite difference numerical methods. Estimation through the Iterated Extended Kalman filter reveals that a two-factor EBTSM fit well the observed cross section and time series of Japanese Government bond yields. A three-factor EBTSM is also proposed.     

Second-order Bayesian revision of a generalised linear model

It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned.