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:

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   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.
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   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.
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   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.

     

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.     

Stock market liberalization and international risk sharing

This paper empirically examines what macroeconomic risks are shared (or not shared) internationally after stock market liberalization in several developing countries. To address this issue, we incorporate an international asset pricing model into a non-linear structural vector autoregression (VAR) system that identifies various sources of macroeconomic risks. We find that most of the risks corresponding to exogenous financial market shocks are surprisingly well shared, although other macroeconomic risks associated with exogenous shocks to output, inflation and monetary policies are not fully shared across countries. Our results suggest that one of the main benefits from stock market liberalization is to allow the countries studied in this paper to better hedge against exogenous and idiosyncratic financial market risks, and stock market liberalization needs to be accompanied by other measures of economic integration in order to achieve the full benefits of international risk sharing.     

Identifying VARS based on high frequency futures data

Using the prices of federal funds futures contracts, we measure the impact of the surprise component of Federal Reserve policy decisions on the expected future trajectory of interest rates. We show how this information can be used to identify the effects of a monetary policy shock in a standard VAR. This alternative approach to identification is quite different, and, we argue, more plausible, than the conventional identifying restrictions. We find that a usual recursive identification of the model is rejected, as is any identification that insists on a monetary policy shock having an exactly zero effect on prices contemporaneously. We nevertheless agree with the conclusion of much of the VAR literature that only a small fraction of the variance of output can be attributed to monetary policy shocks.     

The stability of short-term interest rates pass-through in the euro area during the financial market and sovereign debt crises

We analyse the dynamics of the pass-through of banks’ marginal cost to bank lending rates over the 2008 crisis and the euro area sovereign debt crisis in France, Germany, Greece, Italy, Portugal and Spain. We measure banks’ marginal cost by their rate on new deposits, contrary to the literature that focuses on money market rates. This allows us to account for banks’ risks. We focus on the interest rate on new short-term loans granted to non-financial corporations in these countries. Our analysis is based on an error-correction approach that we extend to handle the time-varying long-run relationship between banks’ lending rates and banks’ marginal cost, as well as stochastic volatility. Our application is based on a harmonised monthly database from January 2003 to October 2014. We estimate the model within a Bayesian framework, using Markov Chain Monte Carlo methods (MCMC).We reject the view that the transmission mechanism is permanent over time. The long-run relationship moved with the sovereign debt crises to a new one, with a slower pass-through and higher bank lending rates. Its developments are heterogeneous from one country to the other. Impediments to the transmission of monetary rates depend on the heterogeneity in banks marginal costs and therefore, its risks. We also find that rates to small firms increase compared to large firms in a few countries. Using a VAR model, we show that overall, the effect of a shock on the rate of new deposits on the unexpected variances of new loans has been less important since 2010. These results confirm the slowdown in the transmission mechanism.     

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.     

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) .     

The fed and the term structure: Addressing simultaneity within a structural VAR model

This paper applies a new identification approach to estimate the contemporaneous relation between the term structure and monetary policy within a VAR framework. To achieve identification, we combine high-frequency Treasury futures and fed funds futures data with the VAR methodology. Results indicate that policy actions have a slope effect in the yield curve. We also find that the Fed responds to Treasury yields and that this response is stronger for the short and intermediate rates and less aggressive for long-yields. All estimated parameters are significant and robust to various model specifications.     

中国金融状况指数的构建及其时间演化特征

通过选取利率、汇率、房价和股价等方面的指标,利用VAR广义脉冲响应模型赋权来构建中国金融状况指数,并运用马尔科夫区制转移模型对其进行时间演化特征分析。结果表明:中国金融状况指数具有非线性、周期性和两阶段动态变化特征,且在扩张阶段和紧缩阶段表现出相互变迁的结构性突变。同时,中国金融状况指数在各区制内的平滑概率值较大,均接近于1,说明各区制具有一定的持续性。     

Forecasting the Term Structure of South African Government Bond Yields

This article uses the parsimonious dynamic Nelson–Siegel model to fit the yields of South African government bonds. We find that the dynamic Nelson–Siegel model has good fitting abilities for all maturities. We further forecast the term structure by seven different dynamic Nelson–Siegel models with time series models. We find that the DNS–VAR–GARCH model is useful for forecasting the short-term rates, the DNS–VAR best predicts the medium-term rates, and the DNS–RW best predicts the long-term rates. In addition, the dynamic Nelson–Siegel models provide better forecasts of yield data than a random walk model, especially for the 12-month forecasting horizons.     

人民币国际化对中国金融风险的影响

本文运用VAR模型实证分析人民币国际化对中国金融风险的影响,结果表明,总体上人民币国际化过程中的货币交易媒介职能会促进中国金融风险的增长,人民币计价单位职能则使金融风险能得到一定抑制,而人民币价值储藏职能会降低中国金融风险。因此,中国应进一步推进人民币对外直接投资,加大人民币债券发行规模,稳步、有序推进资本账户和金融的对外开放,同时进一步完善汇率形成机制和外汇管理政策,构建货币政策与宏观审慎政策双支柱的调控框架,增强对金融风险的预警功能和干预职能。     

Unconventional monetary policy and the spillovers to emerging markets

Unconventional monetary policy such as Quantitative Easing (QE) is often considered to have considerable spillover effects on emerging market economies (EME). Aims at quantifying these effects so far mostly use high-frequency data around announcement dates, panels or VAR models. This paper proposes an alternative way to estimate the effects of QE on emerging markets that allows us to include macroeconomic, i.e. low-frequency, data together with announcement dates. A Qual VAR is estimated that integrates binary information of QE announcements with an otherwise standard VAR, including US and emerging market variables. A key advantage is that the model accounts for the endogeneity and forecastability of QE announcements. The model uncovers the Fed's latent, unobservable propensity for QE and generates impulse responses for EME variables to QE shocks. The results suggest that QE has significant effects on EME's financial conditions and plays a sizable role in explaining capital inflows, equity prices and exchange rates.     

When units roots matter: excess volatility and excess smoothness of long-term interest rates

This paper re-examines volatility tests of the expectations model of the term structure of interest rates. In a multivariate vector autoregression (VAR) including interest rates, prices, money and output, we find that the long-term interest rate overreacts to all transitory shocks, and underreacts to all permanent shocks, irrespective of the number of unit roots and the cointegration structure in the system.     

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.     

What Drives Firm‐Level Stock Returns?

I use a vector autoregressive model (VAR) to decompose an individual firm's stock return into two components: changes in cash-flow expectations (i.e., cash-flow news) and changes in discount rates (i.e., expected-return news). The VAR yields three main results. First, firm-level stock returns are mainly driven by cash-flow news. For a typical stock, the variance of cash-flow news is more than twice that of expected-return news. Second, shocks to expected returns and cash flows are positively correlated for a typical small stock. Third, expected-return-news series are highly correlated across firms, while cash-flow news can largely be diversified away in aggregate portfolios.     

A Bayesian analysis of a variance decomposition for stock returns

We apply Bayesian methods to study a common vector autoregression (VAR)-based approach for decomposing the variance of excess stock returns into components reflecting news about future excess stock returns, future real interest rates, and future dividends. We develop a new prior elicitation strategy, which involves expressing beliefs about the components of the variance decomposition. Previous Bayesian work elicited priors from the difficult-to-interpret parameters of the VAR. With a commonly used data set, we find that the posterior standard deviations for the variance decomposition based on these previously used priors, including “non-informative” limiting cases, are much larger than classical standard errors based on asymptotic approximations. Therefore, the non-informative researcher remains relatively uninformed about the variance decomposition after observing the data. We show the large posterior standard deviations arise because the “non-informative” prior is implicitly very informative in a highly undesirable way. However, reasonably informative priors using our elicitation method allow for much more precise inference about components of the variance decomposition.     

Reconsidering the role of money for output, prices and interest rates

New Keynesian models of monetary policy downplay the role of monetary aggregates, in the sense that the level of output, prices, and interest rates can be determined without knowledge of the quantity of money. This paper evaluates the empirical validity of this prediction by studying the effects of shocks to monetary aggregates using a vector autoregression (VAR). Shocks to monetary aggregates are identified by the restrictions suggested by New Keynesian monetary models. Contrary to the theoretical predictions, shocks to broad monetary aggregates have substantial and persistent effects on output, prices and interest rates.     

External shocks and the non-linear dynamics of Brady bond spreads in a regime-switching VAR

This paper analyzes the response of interest rate differentials between yields on Brady bonds and risk-less bonds to shocks in US interest rates and to conditions in global emerging bond markets. The effect of those shocks is likely to be non-linear. To capture this non-linear propagation, the reaction of refinancing conditions to shocks is investigated within a Markov-switching VAR framework that endogenously separates a crisis regime from a no-crisis regime. Regime-dependent impulse response functions reveal the non-linear response to external shocks. In periods of financial turbulences the positive impact of US rates breaks down. Likewise, shocks to other emerging markets are contagious in the sense that their negative impact is much more pronounced during times of financial distress.     

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.     

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.