Term premium and equity premium in economies with habit formation

In this paper we investigate the size of the risk premium and the term premium in an representative agent exchange model economy where households preferences are subject to habit formation. As a novel feature, we develop theoretical measures for risk premium and term premium that can be used even when the consumption growth process is serially autocorrelated. We find that habit formation increases risk aversion significantly but increases much more the aversion to variations of consumption across dates. This induces a substantial increase in the precautionary demand of short term assets and a significant fall in the precautionary demand of long term assets. As a result, the term premium increases substantially with habit formation. Next we calibrate our model economy and examine the quantitative predictions of our theoretical measures of equity premium, risk premium and term premium. In line with previous literature, we show that it is possible to find a reasonable calibration for which the equity premium is that observed in the data. However, we find that around 70 percent of the equity premium is just term premium. That is, a very large fraction of the increase in the equity premium is due to the asymmetric effect that habit formation has on the precautionary demand of an asset depending on its maturity

Behavioral Finance

Behavioral finance as a subdiscipline of behavioral economics is finance incorporating findings from psychology and sociology into its theories. Behavioral finance models are usually developed to explain investor behavior or market anomalies when rational models provide no sufficient explanations. To understand the research agenda, methodology, and contributions, this survey reviews traditional finance theory first. Then, this survey shows how modifications (e.g. incorporating market frictions) can rationally explain observed individual or market behavior. In the second section, the survey will explain the behavioral finance research methodology -how biases are modeled, incorporated into traditional finance theories, and tested empirically and experimentally- using one specific subset of the behavioral finance literature, the overconfidence literature.

Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets

The authors use the efficient hedging methodology for optimal pricing and hedging of equitylinked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, they consider a policy that pays the maximum of the values of n risky assets at some maturity date T , provided that the policyholder survives to T . Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. The authors show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. They also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are derived for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.Financial markets;

ASSET PRICING, GROWTH, AND THE BUSINESS CYCLE WITH IRREVERSIBLE INVESTMENT

This paper advances a simple model that emphasizes the diversity of capital types, some of these types are long lived, while others are highly specific. This modeling of capital implies that irreversibility constraints may be strongly binding, thus generating sizable capital losses, even with moderate shocks and positive aggregate investment. The resulting riskiness of investing in capital has consequences for growth, the business cycle, and asset returns. Growth is affected as the representative consumer invests a larger portion of output as a form of self-insurance. The business cycle is affected as consumption becomes more variable. The asset returns are affected as the added risk raises its premium, specially in recessions. The focus of the paper is to evaluate the quantitative importance of these effects. When evaluated, the model is capable of matching the most prominent characteristics of U.S. output, consumption, and asset returns, including a wide equity premium. However, this is not a resolution to the equity premium puzzle as the paper does not address why the representative consumer has the high risk aversion necessary to match these observed time series.

The Behavior of Savings and Asset Prices When Preferences and Beliefs Are Heterogeneous

Movements in asset prices are a major risk confronting individuals. This paper establishes new asset pricing results when agents differ in risk preference, time preference and/or expectations. It shows that risk tolerance is a critical concept driving savings decisions, consumption allocations, prices and return volatilities. Surprisingly, due to the equilibrium risk sharing, the precautionary savings motive in the aggregate can vastly exceed that of even the most prudent actual agent in the economy. Consequently, a low real interest rate, resulting from large aggregate savings, can prevail with reasonable risk aversions for all agents. One downside of a large aggregate savings motive is that savings rates become extremely sensitive to output fluctuation. Thus, the same mechanism that produces realistically low interest rates tends to make them unrealistically volatile. A powerful isomorphism allows differences in time preference and expectations to be swept away in the analysis, yielding an equivalent economy whose agents differ merely in risk aversion. These results hold great potential to simplify the analysis of heterogeneous-agent economies, as we demonstrate in quantifying how asset prices move and bounding their volatilities. All results are obtained in closed form for any number of agents possessing additively separable preferences in an endowment economy.

Semi-parametric estimation of joint large movements of risky assets

The classical approach to modelling the occurrence of joint large movements of asset returns is to assume multivariate normality for the distribution of asset returns. This implies independence between large returns. However, it is now recognised by both academics and practitioners that large movements of assets returns do not occur independently. This fact encourages the modelling joint large movements of asset returns as non-normal, a non trivial task mainly due to the natural scarcity of such extreme events. This paper shows how to estimate the probability of joint large movements of asset prices using a semi-parametric approach borrowed from extreme value theory (EVT). It helps to understand the contribution of individual assets to large portfolio losses in terms of joint large movements. The advantages of this approach are that it does not require the assumption of a specific parametric form for the dependence structure of the joint large movements, avoiding the model misspecification; it addresses specifically the scarcity of data which is a problem for the reliable fitting of fully parametric models; and it is applicable to portfolios of many assets: there is no dimension explosion. The paper includes an empirical analysis of international equity data showing how to implement semi-parametric EVT modelling and how to exploit its strengths to help understand the probability of joint large movements. We estimate the probability of joint large losses in a portfolio composed of the FTSE 100, Nikkei 250 and S&P 500 indices. Each of the index returns is found to be heavy tailed. The S&P 500 index has a much stronger effect on large portfolio losses than the FTSE 100, although having similar univariate tail heaviness

Habit formation: implications for the wealth distribution

In this paper we study the role of habit formation in shaping the wealth distribution in an otherwise standard heterogeneous agents model economy with idiosyncratic uncertainty. We compare the inplications for precautionary savings and for wealth concentration between economies that only differ in the role played by habit formation. Once preferences are properly adjusted so that the Intertemporal Elasticity of Substituion is the same in all model economies studied, we find that habit formation brings a hefty increase in precautionary savings and very mild reductions in the coefficient of variation and in the Gini index of wealth. We also find that the reductions in these measures of inequality also hold when we adjust our economy so that aggregate savings are the same as in the economy without habit formation. These findings hold for both persistent and non persistent habits although for the former the quantitative size of the effects is much larger. We conclude that habit formation, while being a mechanism that increases the amount of precautionary savings generated in a model, does not change the implications for wealth inequality that arise from standard models

TERM PREMIUM AND EQUITY PREMIUM IN ECONOMIES WITH HABIT FORMATION

In this paper we investigate the size of the risk premium and the term premium in an representative agent exchange model economy where households preferences are subject to habit formation. As a novel feature, we develop theoretical measures for risk premium and term premium that can be used even when the consumption growth process is serially autocorrelated. We find that habit formation increases risk aversion significantly but increases much more the aversion to variations of consumption across dates. This induces a substantial increase in the precautionary demand of short term assets and a significant fall in the precautionary demand of long term assets. As a result, the term premium increases substantially with habit formation. Next we calibrate our model economy and examine the quantitative predictions of our theoretical measures of equity premium, risk premium and term premium. In line with previous literature, we show that it is possible to find a reasonable calibration for which the equity premium is that observed in the data. However, we find that around 70 percent of the equity premium is just term premium. That is, a very large fraction of the increase in the equity premium is due to the asymmetric effect that habit formation has on the precautionary demand of an asset depending on its maturity.

Information Exchange and the Limits of Arbitrage

Evidence suggests that arbitragers exchange investment ideas. We analyze why and under what circumstances sharing occurs. Our model suggests that sharing ideas will lead to the following: more efficient asset prices, larger arbitrager profits, and correlated arbitrager returns. We predict that arbitragers will exchange ideas in markets where arbitragers are capital constrained, noise trader influence is high, and arbitrage investors are more loss averse. We also predict that arbitrage networks can lead to crowded trades, which can create systematic risk in extreme market circumstances.Arbitrage, hedge funds, market efficiency, information exchange, loss aversion, crowded trades