Background risk in generalized expected utility theory

Summary. In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion. Received: August 10, 2001; revised version: June 18, 2002 RID="*" ID="*"I thank Simon Grant and an anonymous referee for helpful comments and criticism. This research was supported by an Australian Research Council Senior Fellowship and Australian Research Council Large Grant A79800678.     

Optimal saving in the presence of two risks

We examine optimal saving in the presence of two small risks: income risk and a background risk. First, we compute the necessary and sufficient condition for a positive precautionary saving, showing that it depends on two terms capturing respectively the direct effect of income risk and the interaction between the two risks. Second, we examine the necessary and sufficient condition for a positive extra-saving due to the contemporaneous presence of the two risks. We show that this condition also depends on a term capturing the direct effect of background risk and that it can hold independently of the previous one.      

Precautionary saving in the presence of other risks: a comment

Courbage and Rey (Econ Theory 32:417–424 2007) analyse precautionary saving in the presence of a background risk under specific sets of assumptions on the form of income risk and background risk. Three cases are examined: the case of independent risks, the case of Bernoulli-distributed random variables and the case of risk first-degree stochastic. For each of these cases Courbage and Rey compute the specific sets of conditions related to precautionary saving. This comment shows that some of their conclusions are partially incorrect.      

On the utility premium of Friedman and Savage

We re-examine the utility premium of Friedman–Savage [Friedman, Milton and Savage, Leonard J., “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56, 1948, pp. 279–304.]. This measure is useful in understanding risky choices. For instance its reaction to an increased wealth equates to a precautionary demand for saving. We also analyze its two components.     

Risk aversion and risk loving in the small: a decomposition of the multivariate risk premium

This note proposes a decomposition of the familiar scalar multivariate risk premium into components which can be easily interpreted in the context of consumer theory. The premium under consideration is the standard one used to ascertain the impact of price and income risk on consumer welfare. This proposed premium decomposition allows for a more intuitive identification of the detrimental and beneficial effects that arise from income and price risk. As an illustrative example, this decomposition is used to ascertain the welfare effects arising from the price fluctuations experienced by UK households over the period 1963–97.     

Precautionary saving in the presence of other risks

Does the sign of the third derivative of the utility function with respect to wealth still govern precautionary saving motives in the presence of a background risk? This article shows that some other properties of the utility function have also to be considered depending on the serial correlation existing between the background risk and the future income risk.     

Money demand in the czech republic since transition

We analyse the demand for money since the “break up” of the Czech-Slovak Republics at the beginning of 1993 and for the aggregates M0, Ml, and M2 using monthly data. Due to the widespread use of foreign currency in formally centrally planned economies, we also investigate the issue of currency substitution. Because of our relatively small sample period the Johansen cointegration approach is not used and instead we use the general to specific methodology in a single equation framework. Previous empirical evidence on money demand in Eastern Europe, and specifically Czech Republic, has been mixed. Both graphical and empirical results suggest that any currency substitution was a one-off event due to increased uncertainty at the end of 1992 at the time of the monetary dissolution. Certainly, currency substitution in the Czech Republic is not as strong as has been found in other former centrally planned economies. However, our results do indicate that Czech National Bank may have to take account of foreign interest rates when interpreting movements in the monetary aggregates.     

The equilibrium manifold keeps the memory of individual demand functions

Summary. It is shown that the property that the equilibrium manifold keeps the memory of the individual demand functions holds true if every individual demand function satisfies the following three properties: 1) It is a function of commodity prices and of consumers income; 2) Consumption belongs to the nonnegative orthant of the commodity space; 3) Walras law. Neither differentiability nor continuity are necessary. In addition, the demand functions do not have to be utility maximizing subject to budget constraints.Received: 2 September 2003, Revised: 26 January 2004, JEL Classification Numbers: D50, D51.A preliminary version of this paper was released in October 1999 under the title Deriving individual demand functions from the equilibrium manifold. I wish to thank an anonymous referee for thoughtful comments.     

Wealth and the demand for money in the European Union

This study presents the results of an empirical analysis of the demand for money in the European Union as a whole over the period 1971–1995, with a particular focus on the impact of financial wealth. The empirical evidence shows a substantial impact of wealth on the demand for M2 and M3, whereas no influence of wealth on the demand for M1 is found. This finding may explain the remarkable increase of the broad monetary aggregates over the last decade or so. This means that taking into account the growth of wealth, the monetary expansion has been fairly modest. The evidence thus indicates that the strong increase of M2 and M3 should be attributed to portfolio investment considerations rather than to an expansionary monetary policy.Helpful comments by two anonymous referees, the participants in the Workshop on Money Demand at the Humboldt Universität and Hans Lunsing gratefully acknowledged.     

Stability of money demand in Switzerland: A comparison of the M2 and M3 cases

Long-run parameters of money demand functions for Switzerland's M2 and M3 aggregate are estimated and their stability investigated. For both aggregates a single stable cointegrating vector is found. Around these long-run relationships a single-equation model for m2 and a single-equation model for cpi is built respectively for M2 and M3, and both estimated models are found to be stable. Testing forecast performance, the cpi model seems to be superior to the m2 model, providing some positive signs that the M3 model is stable in the sense that it does not suffer from a structural break during the period of estimation.We would like to thank Jürgen Wolters and two anonymous referees for their comments and Neil Ericsson, David Hendry, Katarina Juselius, Helmut Lütkepohl, Grayham Mizon and the other participants of the Workshop on Money Demand in Europe, Berlin, October 10–11, 1997, where an earlier version of the paper was presented, for their suggestions. The data may be obtained from the internet, http://wotan.wiwi.hu-berlin.de/oekonometrie/engl/data.html. The views expressed here are those of the authors and do not reflect the views of the Swiss National Bank.     

The impact of the correlation between health expenditure and survival probability on the demand for insurance

This paper studies the effects of health shocks on the demand for health insurance and annuities, along with precautionary saving in a dynamic life-cycle model. I argue that when the health shock can simultaneously increase health expenses and reduce longevity, rational agents would neither fully insure their uncertain health expenses nor fully annuitize their wealth because the correlation between health expenses and longevity provides a self-insurance channel for both uncertainties. That is, when the agent is hit by a health shock (which simultaneously increases health expenses and reduces longevity), she can use the resources originally saved for consumption in the reduced period of life to pay for the increased health expenses. Since the two uncertainties partially offset each other, the precautionary saving generated in the model should be smaller than in a standard model without the correlation between health expenses and longevity. In a quantitative life-cycle model calibrated using the Medical Expenditure Panel Survey dataset, I find that the health expenses are highly correlated with the survival probabilities, and this correlation significantly reduces the demand for actuarially fair health insurance, while its impact on the demand for annuities and precautionary saving is relatively small.     

Decreasing absolute prudence: Characterization and applications to second-best risk sharing

In this paper, we provide two basic properties of utility functions u which exhibit decreasing absolute prudence i.e. (− u/u″)′ ≤ 0. These properties are used to examine the allocation of risks in an economy when some agents bear non-transferable risks. We show that it is fair Pareto-efficient to let those with a non-transferable risk bear relatively less of the transferable risk in the economy if and only if absolute prudence is decreasing. In another model, there is a complete set of contingent markets, but some agents have no direct access to them. We examine the fair efficient allocation of risk in a pool gathering a trader and a non-trader. Decreasing absolute prudence provides an upper bound to the share of the pool's risk that should be borne by the trader.     

Volatility spillovers and the price of risk: Evidence from the Swiss stock market

This paper investigates the behavior of the risk premium on the Swiss stock market. The risk premium consists of two components, which are estimated separately: the amount of volatility and the unit price of risk. By estimating a bivariate GARCH-M model the volatility of the Swiss market is found to be strongly exposed to spillovers from the other major financial markets. To estimate the unit price of risk a Kalman filter procedure is employed, which allows for variability in this variable. Investors place a high price on risk, when the market is considered `expensive'. First version received: March 1998/final version received: July 1998     

Investor sentiment,variance risk premium and delta-hedged gains

Delta-hedged gains are supposed to be negative and represent a volatility risk premium. Using a sample of Standard & Poor 500 index options from 2006 to 2009, this study documents two anomalies that cannot be explained by the volatility risk premium. First, delta-hedged gains are more negative for out-of-money options than for at-the-money options. Second, delta-hedged gains are significantly positive during financial crisis period. We propose a behavioural explanation in which both option prices and stock prices are affected by investor’s sentiment, but pessimistic sentiment has a greater impact on stock market than option market. This asymmetric response to pessimistic mood in turn affects the relative expensiveness of option prices.     

Global risk and demand for gold by central banks

This article examines the influence of global risk on the holding of gold by central banks based on annual data for 100 countries during 1990–2015. We use a dynamic panel generalized method of moments model to estimate this effect, controlling for a variety of domestic factors. Consistent with portfolio diversification and perception of gold as a safe asset, we find that the gold holdings of central banks increase in response to higher global risk. This effect varies based on the levels of capital account openness, reserve adequacy, income status and currency regimes. These findings suggest that central banks adjust their gold holdings in response to changes in global risk conditions, with the magnitude of response depending on country-specific vulnerabilities.     

Time-varying uncertainty and variance risk premium

This paper extends the AK production model in Pindyck and Wang (2013) into a more general setting in which the volatility of capital stock is stochastic and driven by shocks. After solving the equilibrium, the fundamental shocks are embedded into the stock price and the leverage effect is contributed from three distinct channels. As an application, we employ our extended AK production model to match well the negative variance risk premium.     

Revisiting the risk-return relation in the Chinese stock market: Decomposition of risk premium and volatility feedback effect

The empirical results of the risk-return relationship are mixed for both mature and merging markets. In this paper, we develop a new volatility model to revisit the risk-return relation of the aggregate stock market index by extending the Realized GARCH model of Hansen et al. (2012) with the Wang and Yang (2013) framework, in which the overall risk-return relation is decomposed into a risk premium and a volatility feedback effect. An empirical analysis of three major Chinese stock indices reveals positive risk premium and negative volatility feedback effect, and those findings are stable across different markets and sub-samples. However, their relative magnitudes differ between markets and varies through time.     

Loan price modelling for local governments using risk premium analysis

Previous studies have highlighted the question of government loan interest as one of great current importance. Government borrowing levels are high, and reducing interest payments would generate savings to meet other spending needs and/or to lower taxation, thus supporting the sustainability of public finances. However, no previous study has presented a method for a local government to calculate its own credit risk and thus be in a position to negotiate lower interest rates on its borrowing. This article defines a financial model that enables local governments to estimate the interest rate payable on a bank loan, based on their credit risk premium, in accordance with the Basel II rules and the findings of our empirical study of large local governments.     

On the accuracy of Blue Chip forecasts of interest rates and country risk premiums

We examine the accuracy of Blue Chip forecasts of short- and long-term interest rates and country risk premiums for the Eurozone and six other industrial countries for 1999–2008. In so doing, we utilize comparable random walk forecasts as benchmarks. Consistent with the efficient market hypothesis, the long-term interest rate forecasts fail to outperform the random walk. Our findings on the accuracy of short-term interest rate forecasts are, however, mixed. Further results reveal that Blue Chip is more (less) accurate in predicting country risk premiums associated with short-term (long-term) interest rates. Such evidence is reasonable since the short-term country risk premiums contain only the perceived default risk, while the long-term risk premiums, in addition, can contain the perceived inflation and exchange rate differentials.