Forecasting the weekly time-varying beta of UK firms: GARCH models vs. Kalman filter method

This paper investigates the forecasting ability of three different Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models and the Kalman filter method. The three GARCH models applied are: bivariate GARCH, BEKK GARCH, and GARCH-GJR. Forecast errors based on 20 UK company's weekly stock return (based on time-varying beta) forecasts are employed to evaluate the out-of-sample forecasting ability of both the GARCH models and the Kalman method. Measures of forecast errors overwhelmingly support the Kalman filter approach. Among the GARCH models, GJR appears to provide somewhat more accurate forecasts than the two other GARCH models.     

Boom–Bust Cycles and the Forecasting Performance of Linear and Non-Linear Models of House Prices

The tremendous rise in house prices over the last decade has been both a national and a global phenomenon. The growth of secondary mortgage holdings and the increased impact of house prices on consumption and other components of economic activity imply ever-greater importance for accurate forecasts of home price changes. Given the boom–bust nature of housing markets, nonlinear techniques seem intuitively very well suited to forecasting prices, and better, for volatile markets, than linear models which impose symmetry of adjustment in both rising and falling price periods. Accordingly, Crawford and Fratantoni (Real Estate Economics 31:223–243, 2003) apply a Markov-switching model to U.S. home prices, and compare the performance with autoregressive-moving average (ARMA) and generalized autoregressive conditional heteroscedastic (GARCH) models. While the switching model shows great promise with excellent in-sample fit, its out-of-sample forecasts are generally inferior to more standard forecasting techniques. Since these results were published, some researchers have discovered that the Markov-switching model is particularly ill-suited for forecasting. We thus consider other non-linear models besides the Markov switching, and after evaluating alternatives, employ the generalized autoregressive (GAR) model. We find the GAR does a better job at out-of-sample forecasting than ARMA and GARCH models in many cases, especially in those markets traditionally associated with high home-price volatility.     

GARCH vs. stochastic volatility: Option pricing and risk management

In this paper we compare the out-of-sample performance of two common extensions of the Black–Scholes option pricing model, namely GARCH and stochastic volatility (SV). We calibrate the three models to intraday FTSE 100 option prices and apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk (VaR) oriented measures. When we analyze the fit to observed prices, GARCH clearly dominates both SV and the benchmark Black–Scholes model. However, the predictions of the market risk from hypothetical derivative positions show sizable errors. The fit to the realized profits and losses is poor and there are no notable differences between the models. Overall, we therefore observe that the more complex option pricing models can improve on the Black–Scholes methodology only for the purpose of pricing, but not for the VaR forecasts.     

Empirical Analysis of Business Cycle Synchronization and Shock Similarity Between Romania and the Eurozone

This study investigates benefits from a trading strategy based on the spillovers from international stock markets to the Polish emerging stock market. The analysis is conducted within the framework of factor and predictive generalized autoregressive conditional heteroskedasticity (GARCH) models of the Warsaw Stock Exchange main index, WIG. We apply an approach in which the mean equation of the GARCH model includes a deterministic part incorporating cross-markets linkages. Both in-sample and out-of-sample forecasts from the estimated models are calculated. The trading strategy is based on signals from the out-of-sample predictions. The models' performance and benefits from adopting such a strategy are evaluated using direction quality measures. Our results suggest that predictive models using cross-market linkages can produce superior out-of-sample forecasts compared to benchmarks.     

GARCH option pricing models with Meixner innovations

The paper presents GARCH option pricing models with Meixner-distributed innovations. The risk-neutral dynamics are derived by means of the conditional Esscher transform. Assessing the option pricing performance both in-sample and out-of-sample, we find that the models compare favorably against the benchmark models. Simulations suggest that the driver of these results is the impact of conditional skewness and conditional excess kurtosis on option prices.     

Asymmetric effect of basis on dynamic futures hedging: Empirical evidence from commodity markets

The dynamic minimum variance hedge ratios (MVHRs) have been commonly estimated using the Bivariate GARCH model that overlooks the basis effect on the time-varying variance–covariance of spot and futures returns. This paper proposes an alternative specification of the BGARCH model in which the effect is incorporated for estimating MVHRs. Empirical investigation in commodity markets suggests that the basis effect is asymmetric, i.e., the positive basis has greater impact than the negative basis on the variance and covariance structure. Both in-sample and out-of-sample comparisons of the MVHR performance reveal that the model with the asymmetric effect provides greater risk reduction than the conventional models, illustrating importance of the asymmetric effect when modeling the joint dynamics of spot and futures returns and hence estimating hedging strategies.     

Are RiskMetrics forecasts good enough? Evidence from 31 stock markets

Academic research has highlighted the inherent flaws within the RiskMetrics model and demonstrated the superiority of the GARCH approach in-sample. However, these results do not necessarily extend to forecasting performance. This paper seeks answer to the question of whether RiskMetrics volatility forecasts are adequate in comparison to those obtained from GARCH models. To answer the question stock index data is taken from 31 international markets and subjected to two exercises, a straightforward volatility forecasting exercise and a Value-at-Risk exceptions forecasting competition. Our results provide some simple answers to the above question. When forecasting volatility of the G7 stock markets the APARCH model, in particular, provides superior forecasts that are significantly different from the RiskMetrics models in over half the cases. This result also extends to the European markets with the APARCH model typically preferred. For the Asian markets the RiskMetrics model performs well, and is only significantly dominated by the GARCH models for one market, although there is evidence that the APARCH model provides a better forecast for the larger Asian markets. Regarding the Value-at-Risk exercise, when forecasting the 1% VaR the RiskMetrics model does a poor job and is typically the worst performing model, again the APARCH model does well. However, forecasting the 5% VaR then the RiskMetrics model does provide an adequate performance. In short, the RiskMetrics model only performs well in forecasting the volatility of small emerging markets and for broader VaR measures.     

The information content of option-implied information for volatility forecasting with investor sentiment

This study explores the effect of investor sentiment on the volatility forecasting power of option-implied information. We find that the risk-neutral skewness has the explanatory power regarding future volatility only during high sentiment periods. Furthermore, the implied volatility has varying volatility forecasting ability depending on the level of investor sentiment. Our findings suggest that the effectiveness of volatility forecasting models based on option-implied information varies over time with the level of investor sentiment. We confirm the important role of investor sentiment in volatility forecasting models exploiting option-implied information with strong evidence from in-sample and out-of-sample analyses. We also present improvements in the accuracy of volatility forecasts from volatility forecasting models derived by incorporating investor sentiment in these models.     

Limits to mutual funds' ability to rely on mean/variance optimization

Our evidence suggests that estimation error in the required statistics is an important factor inhibiting investors' ability to rely on mean/variance analysis. We compare the returns reported by mutual funds to the returns obtained from a mean/variance optimized portfolio of fund holdings. The results suggest that funds tend to outperform the optimized portfolio out-of-sample (when means/variances/covariances are unknown), but under-perform in-sample (when the required statistics in the optimization are known). Therefore, a popular assumption in asset pricing models that investors rely on a basic mean/variance analysis with known underlying statistics is likely to be grossly violated in the case of mutual funds.     

Forecasting Intraday Volatility and Value-at-Risk with High-Frequency Data

In this paper, we develop modeling tools to forecast Value-at-Risk and volatility with investment horizons of less than one day. We quantify the market risk based on the study at a 30-min time horizon using modified GARCH models. The evaluation of intraday market risk can be useful to market participants (day traders and market makers) involved in frequent trading. As expected, the volatility features a significant intraday seasonality, which motivates us to include the intraday seasonal indexes in the GARCH models. We also incorporate realized variance (RV) and time-varying degrees of freedom in the GARCH models to capture more intraday information on the volatile market. The intrinsic tail risk index is introduced to assist with understanding the inherent risk level in each trading time interval. The proposed models are evaluated based on their forecasting performance of one-period-ahead volatility and Intraday Value-at-Risk (IVaR) with application to the 30 constituent stocks. We find that models with seasonal indexes generally outperform those without; RV can improve the out-of-sample forecasts of IVaR; student GARCH models with time-varying degrees of freedom perform best at 0.5 and 1 % IVaR, while normal GARCH models excel for 2.5 and 5 % IVaR. The results show that RV and seasonal indexes are useful to forecasting intraday volatility and Intraday VaR.     

The predictability of aggregate returns on commodity futures

This paper provides evidence that aggregate returns on commodity futures (without the returns on collateral) are predictable, both in-sample and out-of-sample, by various lagged variables from the stock market, bond market, macroeconomics, and the commodity market. Out of the 32 candidate predictors we consider, we find that investor sentiment is the best in-sample predictor of short-horizon returns, whereas the level and slope of the yield curve have much in-sample predictive power for long-horizon returns. We find that it is possible to forecast aggregate returns on commodity futures out-of-sample through several combination forecasts (the out-of-sample return forecasting R² is up to 1.65% at the monthly frequency).     

Value-at-Risk analysis for long-term interest rate futures: Fat-tail and long memory in return innovations

This article uses the FIGARCH(1,d,1) models to calculate daily Value-at-Risk (VaR) for T-bond interest rate futures returns of long and short trading positions based on the normal, Student-t, and skewed Student-t innovations distributions. The empirical results show that based on Kupiec LR failure rate tests, in-sample and out-of-sample VaR values calculated using FIGARCH(1,d,1) model with skewed Student-t innovations are more accurate than those generated using traditional GARCH(1,1) models. Moreover, we find that the in-sample values of VaR are subject to a significant positive bias, as pointed out by Inui et al. [Inui, K., Kijima, M., Kitano, A., 2003. VaR is subject to a significant positive bias, working paper].     

Predicting the equity premium with dividend ratios: Reconciling the evidence

This paper evaluates the ability of dividend ratios to predict the equity premium. We conduct an in and out-of-sample comparative study and apply the Goyal and Welch (2003) graphical method to equity premia derived from the UK FTSE All-Share and the S&P 500 indices. Preliminary in-sample univariate regressions reveal that in both markets the equity premium contains an element of predictability. However, the considered out-of-sample models outperform the historical moving average only in the UK context. This is confirmed by the graphical diagnostic which further indicates that dividend ratios are useful predictors of UK excess returns. Our paper provides a possible explanation of why dividend ratios might be more informative in the UK market by linking these findings to the disappearing dividend phenomenon. Finally, Campbell and Shiller (1988) identities are employed to account for the time-varying properties of the dividend ratio and dividend growth processes. It is shown that by instrumenting the models with the identities, forecasting ability can be further improved.     

In-sample vs. out-of-sample tests of stock return predictability in the context of data mining

We undertake an extensive analysis of in-sample and out-of-sample tests of stock return predictability in an effort to better understand the nature of the empirical evidence on return predictability. We find that a number of financial variables appearing in the literature display both in-sample and out-of-sample predictive ability with respect to stock returns in annual data covering most of the twentieth century. In contrast to the extant literature, we demonstrate that there is little discrepancy between in-sample and out-of-sample test results once we employ out-of-sample tests with good power. While conventional wisdom holds that out-of-sample tests help guard against data mining, Inoue and Kilian [Inoue, A., Kilian, L., 2004. In-sample or out-of-sample tests of predictability: which one should we use? Econometric Reviews 23, 371–402.] recently argue that in-sample and out-of-sample tests are equally susceptible to data mining biases. Using a bootstrap procedure that explicitly accounts for data mining, we still find that certain financial variables display significant in-sample and out-of-sample predictive ability with respect to stock returns.     

Forecasting stock market volatility and the informational efficiency of the DAX-index options market

Alternative strategies for predicting stock market volatility are examined. In out-of-sample forecasting experiments implied-volatility information, derived from contemporaneously observed option prices or history-based volatility predictors, such as GARCH models, are investigated to determine if they are more appropriate for predicting future return volatility. Employing German DAX-index return data it is found that past returns do not contain useful information beyond the volatility expectations already reflected in option prices. This supports the efficient market hypothesis for the DAX-index options market.     

Bivariate mixed normal GARCH models and out-of-sample hedge performances

This study compares bivariate mixed normal GARCH models with standard bivariate GARCH models in terms of the percentage variance reduction of the out-of-sample hedged portfolio and also statistical significance tests of performance improvements using Superior Predictive Ability statistics. All competing models are applied to corn and wheat futures and empirical results demonstrate that the standard BEKK-GARCH model significantly outperforms the other competing GARCH models at shorter horizons. However, as the hedge horizon is extended to longer than 10 days, it is evident that the mixed normal BEKK-GARCH model is the best at the usual significance level of 5%.     

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.     

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.     

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.     

Predicting the bear stock market: Macroeconomic variables as leading indicators

This paper investigates whether macroeconomic variables can predict recessions in the stock market, i.e., bear markets. Series such as interest rate spreads, inflation rates, money stocks, aggregate output, unemployment rates, federal funds rates, federal government debt, and nominal exchange rates are evaluated. After using parametric and nonparametric approaches to identify recession periods in the stock market, we consider both in-sample and out-of-sample tests of the variables’ predictive ability. Empirical evidence from monthly data on the Standard & Poor’s S&P 500 price index suggests that among the macroeconomic variables we have evaluated, yield curve spreads and inflation rates are the most useful predictors of recessions in the US stock market, according to both in-sample and out-of-sample forecasting performance. Moreover, comparing the bear market prediction to the stock return predictability has shown that it is easier to predict bear markets using macroeconomic variables.