Causal Relations Among Stock Returns,Interest Rates,Real Activity,and Inflation

Using a multivariate vector-autoregression (VAR) approach, this paper investigates causal relations and dynamic interactions among asset returns, real activity, and inflation in the postwar United States. Major findings are (1) stock returns appear Granger-causally prior and help explain real activity, (2) with interest rates in the VAR, stock returns explain little variation in inflation, although interest rates explain a substantial fraction of the variation in inflation, and (3) inflation explains little variation in real activity. These findings seem more compatible with Fama (1981) than with Geske and Roll (1983) or with Ram and Spencer (1983) .     

Vector autoregressions and reduced form representations of DSGE models

The performance of dynamic stochastic general equilibrium models is often tested against estimated VARs. This requires that the data-generating process consistent with the DSGE theoretical model has a finite order VAR representation. This paper discusses the assumptions needed for a finite order VAR(p) representation of a DSGE model to exist. When a VAR(p) is only an approximation to the exact infinite order VAR, the truncated VAR(p) may return largely incorrect estimates of the impulse response function. The results do not hinge on small-sample bias or on incorrect identification assumptions. But the bias introduced by truncation can lead to bias in the identification of the structural shocks. Identification strategies that work in the exact VAR representation perform poorly in the truncated VAR.     

A Reexamination of Real Stock Returns,Real Interest Rates,Real Activity,and Inflation: Evidence from a Large Data Set

Using the informational sufficiency procedure from Forni and Gambetti (2014) along with data from McCracken and Ng (2014), we update the results of Lee (1992) and find that his vector autoregression (VAR) is informationally deficient. To correct this problem, we estimate a factor augmented VAR (FAVAR) and analyze the differences once informational deficiency is corrected with an emphasis on the relationship between real stock returns and inflation. In particular, we examine Modigliani and Cohn's (1979) inflation illusion hypothesis, Fama's (1983) proxy hypothesis, and the “anticipated policy hypothesis.”     

Pitfalls in VAR based return decompositions: A clarification

We analyze the pitfalls involved in VAR based return decompositions. First, we show that recent criticism of such decompositions is misplaced and builds on invalid VAR models and erroneous interpretations. Second, we derive the requirements needed for VAR decompositions to be valid. A crucial – but often neglected – requirement is that the asset price needs to be included as a state variable in the VAR. In equity return decompositions this requirement is equivalent to including the dividend–price ratio in the VAR. Finally, we clarify the intriguing issue of the role of the residual component in return decompositions. In a properly specified first-order VAR, it makes no difference whether cash flow news or discount rate news is backed out residually, and it makes no difference whether both news components are computed directly or one of them is backed out residually.     

Cash-flow or return predictability at long horizons? The case of earnings yield

We examine the predictive ability of the aggregate earnings yield for both market returns and earnings growth by estimating variance decompositions at multiple horizons. Based on weighted long-horizon regressions, we find that most of the variation in the earnings yield is due to return predictability, with earnings growth predictability assuming a minor role. However, by using implied estimates from a first-order restricted VAR, we find an opposite predictability mix. The inconsistency in results stems from a misspecification of the restricted VAR. Using an unrestricted first-order VAR estimated by OLS, or alternatively, estimating the restricted VAR by the Projection Minimum Distance method, produces long-run variance decompositions that are substantially more similar to the decomposition obtained under the direct method. Hence, earnings yield is not fundamentally different from the dividend yield. These results suggest that the practice of analyzing long-run return and cash-flow predictability from a restricted VAR can be quite misleading.     

VALUE AT RISK: USES AND ABUSES

Value at risk (or "VAR") is a method of measuring the financial risk of an asset, portfolio, or exposure over some specified period of time. By facilitating the consistent measurement of risk across different assets and activities, VAR allows companies to monitor, report, and control their risks in a manner that efficiently relates risk control to desired and actual economic exposures.
Nevertheless, reliance on VAR can result in serious problems when improperly used, and would-be users of VAR are advised to consider the following three pieces of advice:

• ▪

   First, VAR is a tool for firms engaged in total value risk management. Companies concerned not with the value of a stock of assets and liabilities over a specific time horizon, but rather with the volatility of a flow of funds, are often better off eschewing VAR altogether in favor of a measure of cash flow volatility.
• ▪

   Second, VAR should be applied very carefully to companies that practice "selective" risk management those firms that choose to take certain risks as a part of their primary business. When VAR is reported in such situations without estimates of corresponding expected profits, the information conveyed by the VAR estimate can be extremely misleading.
• ▪

   Third, as a number of recent derivatives disasters are used to illustrate, no form of risk measurement including VAR–is a substitute for good management. Risk management as a process encompasses much more than just risk measurement. Indeed, risk measurement (whether using VAR or some of the alternatives proposed in this article) is pointless without a well-developed organizational infrastructure and IT system capable of supporting the complex and dynamic process of risk taking and risk control.

     

The Danish stock and bond markets: comovement,return predictability and variance decomposition

VAR models of the kind developed by Shiller and Beltratti [J. Monetary Econ. 30 (1992) 25] and Campbell and Ammer [J. Finance 48 (1993) 3] are used to analyze the Danish stock and bond markets and their comovement. In contrast to these papers, however, VAR parameter estimates are bias-adjusted and VAR generated statistics, including their standard errors and confidence intervals, are computed using bootstrap simulation. In addition, we modify the Campbell–Ammer variance decomposition such that it can handle returns from a long-term coupon bond. Some parts of the results for the Danish stock and bond markets are quite similar to the US results reported by Shiller and Beltratti and Campbell and Ammer, but other parts stand in sharp contrast to the results for the US. The most important differences between the US and Denmark are that in Denmark news about higher future inflation lead to an increase in expected future stock returns, and that excess stock return news and excess bond return news are negatively correlated.     

Consumption-smoothing in a small, cyclically volatile open economy: Evidence from New Zealand

New Zealand's current account of the balance of payments has been persistently in deficit since the early 1970s and increased markedly during the late 1990s. Should this cause significant concern, for such a small, cyclically volatile open economy? Our results show that VAR1 and VAR2 forms of the traditional intertemporal consumption-smoothing model reflect very satisfactorily the volatile directions and turning points observed, that the data are not consistent with consumption-tilting to the present, and that New Zealand has had considerable success to date in consumption-smoothing around its average 5% current account deficit. Perhaps more unexpectedly, a Bergin–Sheffrin-type model of a small open economy with variable interest rates and exchange rates has not performed noticeably better.     

Evaluating Value at Risk Methodologies: Accuracy versus Computational Time

Recent research has shown that different methods of computing Value at Risk (VAR) generate widely varying results, suggesting the choice of VAR method is very important. This article examines six VAR methods, and compares their computational time requirements and their accuracy when the sole source of inaccuracy is errors in approximating nonlinearity. Simulations using portfolios of foreign exchange options showed fairly wide variation in accuracy and unsurprisingly wide variation in computational time. When the computational time and accuracy of the methods were examined together, four methods were superior to the others. The article also presents a new method for using order statistics to create confidence intervals for the errors and errors as a per cent of true value at risk for each VAR method. This makes it possible to easily interpret the implications of VAR errors for the size of shortfalls or surpluses in a firm's risk-based capital.     

VALUE-AT-RISK AND CORPORATE VALUATION

Although first used mainly by financial institutions to evaluate their trading risks, Value-at-Risk (VAR) can also be used to enhance an industrial corporation's understanding and management of its market risks. To illustrate this broader application of VAR analysis, the authors present a simple example focusing on the valuation of a closely held company. In this case, VAR is used to analyze the sensitivity of the firm's value to movements in uncertain exchange rates, commodity prices, and interest rates.     

Sufficient information in structural VARs

Necessary and sufficient conditions under which a VAR contains sufficient information to estimate the structural shocks are derived. On the basis of this theoretical result we propose two simple tests to detect informational deficiency and a procedure to amend a deficient VAR. A simulation based on a DSGE model with fiscal foresight suggests that our method correctly identifies and fixes the informational problem. In an empirical application, we show that a bivariate VAR including unemployment and labor productivity is informationally deficient. Once the relevant information is included into the model, technology shocks appear to be contractionary.     

Labor-supply shifts and economic fluctuations

We propose a new VAR identification scheme that distinguishes shifts of and movements along the labor demand schedule to identify labor-supply shocks. According to our VAR analysis of post-war US data, labor-supply shifts account for about 30 percent of the variation in hours and about 15 percent of the output fluctuations at business cycle frequencies. To assess the role of labor-supply shifts in a more structural framework, estimates from a dynamic general equilibrium model with stochastic variation in home production technology are compared to those from the VAR.     

Monetary policy shocks, Choleski identification, and DNK models

A popular identifying assumption in structural VAR studies is that the monetary policy shock does not affect macroeconomic variables contemporaneously. We examine the consequences of using this identification strategy when the data-generating process is a basic Dynamic New Keynesian (DNK) model but without these assumed time delays. The principle conclusion is that the standard Choleski assumption can severely distort the impulse response functions, producing price puzzles and muted responses of inflation and the output gap to monetary shocks.     

Estimation of a rational expectations model of the term structure

This paper shows how to represent a vector autoregression (VAR) in terms of the eigenvalues and eigenvectors of its companion matrix. This representation is used to impose the exact restrictions implied by the expectations hypothesis on the VAR for short and long term interest rates and to calculate the restricted maximum likelihood estimates. The first difference representation for short and long rates used by Sargent (1979) is shown to be inconsistent with the expectations hypothesis, but a VAR with two unit roots is constructed that satisfies the exact restrictions and leads to similar restricted estimates.     

Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model

Within a VAR based intertemporal asset allocation model we explore the effects on return predictability and optimal asset allocation of adjusting VAR parameter estimates for small-sample bias. We apply a simple and easy-to-use analytical bias formula instead of bootstrap or Monte Carlo bias-adjustment. Regarding return predictability we show that bias-adjustment in the multivariate setup can yield very different results than in the univariate case. Furthermore, bias-correcting the VAR parameters has both quantitatively and qualitatively important effects on the optimal portfolio choice. For intermediate values of risk-aversion, the intertemporal hedging demand for bonds and stocks is heavily affected by the bias-correction. Utility calculations also show large effects of bias-adjustment, both in-sample and out-of-sample.     

Technology shocks and labor market dynamics: Some evidence and theory

A positive technology shock may lead to a rise or a fall in per capita hours, depending on how hours enter the empirical VAR model. We provide evidence that, independent of how hours enter the VAR, a positive technology shock leads to a weak response in nominal wage inflation, a modest decline in price inflation, and a modest rise in the real wage in the short-run and a permanent rise in the long-run. We then examine the ability of several competing theories to account for this VAR evidence. Our preferred model features sticky prices, sticky nominal wages, and habit formation. The same model also does well in accounting for the labor market evidence in the post-Volcker period.     

Consumption,government spending,and the real exchange rate

Using panel structural VAR analysis and quarterly data from four industrialized countries, we document that an increase in government purchases raises output and private consumption, deteriorates the trade balance, and depreciates the real exchange rate. This pattern of comovement poses a puzzle for both neoclassical and Keynesian models. An explanation based on the deep-habit mechanism is proposed. An estimated two-country model with deep-habits is shown to replicate well the observed responses of output, consumption, and the trade balance, and the initial response of the real exchange rate to an estimated government spending shock.     

Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach)

The approach to modelling uncertainty of the international index portfolio by the value at risk (VAR) methodology under soft conditions by fuzzy-stochastic methodology is described in the paper. The generalised term uncertainty is understood to have two aspects: risk modelled by probability (stochastic methodology) and vagueness sometimes called impreciseness, ambiguity, softness is modelled by fuzzy methodology. Thus, hybrid model is called fuzzy-stochastic model. Input data for a stochastic model are unique distribution functions and crisp (real) data. Input data for fuzzy model are fuzzy numbers and crisp (real) data. Input data for hybrid model are fuzzy probability distribution functions, unique distribution functions, and crisp (real) data. Softly defined VAR model is constructed as hybrid model because it is supposed that the input data are difficult to determine as crisp numbers or as some unique distribution functions. Risk is modelled by stochastic methodology on the VAR basis and vagueness is modelled through the fuzzy numbers. The analytical delta normal VAR methodology for international index portfolio under soft conditions is described including illustrative example. It is shown, that methodology described could be considered to be generalised sensitivity analysis.