Pricing Two Heterogeneous Trees

2011 ◽  
Vol 46 (5) ◽  
pp. 1437-1462 ◽  
Author(s):  
Nicole Branger ◽  
Christian Schlag ◽  
Lue Wu
Keyword(s):  
Growth Rate ◽  
Risk Aversion ◽  
Information Structure ◽  
Exchange Economy ◽  
Equilibrium Price ◽  
Expected Returns ◽  
Risk Averse ◽  
Relative Risk Aversion ◽  
Rate Process ◽  
Current Value

AbstractWe consider a Lucas-type exchange economy with two heterogeneous stocks (trees) and a representative investor with constant relative risk aversion. The dividend process for one stock follows a geometric Brownian motion with constant and known parameters. The expected dividend growth rate for the other tree is stochastic and in general unobservable, although there may be a signal from which the investor can learn about its current value. We find that the equilibrium quantities in our model significantly depend on the information structure and on the level of risk aversion. While an observable stochastic drift mainly makes the economy more risky, a latent expected growth rate process with learning significantly changes the equilibrium price-dividend ratios, price reactions to dividend and drift innovations, expected returns, volatilities, correlations, and differences between the stocks. These effects are the more pronounced the more risk averse the representative investor.

scholarly journals FALSE CONSCIOUSNESS IN FINANCIAL MARKETS: OR IS IT IN IVORY TOWERS?

2013 ◽  
Vol 4 (1) ◽  
pp. 19-30
Author(s):  
Adi Schnytzer ◽  
Sara Westreich
Keyword(s):  
Risk Aversion ◽  
Financial Markets ◽  
Risk Index ◽  
Recent Model ◽  
Economic Index ◽  
Expected Returns ◽  
False Consciousness ◽  
Risk Averse ◽  
Different Levels ◽  
Negative Expectations

In general, models in finance assume that investors are risk averse. An example of such a recent model is the pioneering work of Aumann and Serrano, which presents an economic index of riskiness of gambles which is independent of wealth and holds (as might be understood from the adjective “economic”) for exclusively risk averse investors. In their paper, they discuss gambles with positive expected returns which will be accepted or rejected by agents which different levels of risk aversion. The question never asked by the authors (and in most of the finance literature) is: Who is offering these attractive gambles? To arrive at an answer, we extend the Aumann-Serrano risk index in such a way that it accommodates gambles with either positive or negative expectations and is thus suitable for both the risk averse and risk lovers.  Once we allow for the existence of risk lovers, it may be shown that in financial markets, many gambles with negative expectations are taken either knowingly or unknowingly so that there are always people that act as if they are risk lovers. The paper concludes with a brief discussion of the implications of our result, in particular that gambling is by no means restricted to the casino or the track.

Variable annuities and aggregate mortality risk

2016 ◽  
Vol 237 ◽  
pp. R55-R61 ◽  
Author(s):  
Martin Weale ◽  
Justin van de Ven
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Mortality Risk ◽  
Mortality Rates ◽  
Risk Averse ◽  
Actual Cost ◽  
Relative Risk Aversion ◽  
Variable Annuities ◽  
Actual Mortality ◽  
Specific Mortality

This paper explores the extent to which annuitants might be prepared to pay for protection against cohort-specific mortality risk, by comparing traditional indexed annuities with annuities whose payout rates are revised in response to differences between expected and actual mortality rates of the cohort in question. It finds that a man aged 65 with a coefficient of relative risk aversion of two would be prepared to pay 75p per £100 annuitised for protection against aggregate mortality risk while a man with risk aversion of twenty would be prepared to pay £5.75 per £100; studies put the actual cost at £2.70–£7 per £100, suggesting that unless annuitants are very risk averse it is likely that existing products tend to over-insure against cohort mortality risk.

scholarly journals Rare Disasters, Asset Prices, and Welfare Costs

2009 ◽  
Vol 99 (1) ◽  
pp. 243-264 ◽  
Author(s):  
Robert J Barro
Keyword(s):  
Growth Rate ◽  
Relative Risk ◽  
Risk Aversion ◽  
Asset Prices ◽  
Welfare Cost ◽  
Elasticity Of Substitution ◽  
Relative Risk Aversion ◽  
Rare Disasters ◽  
Representative Consumer ◽  
Consumer Model

A representative-consumer model with Epstein-Zin-Weil preferences and i.i.d. shocks, including rare disasters, accords with observed equity premia and risk-free rates if the coefficient of relative risk aversion equals 3–4. If the intertemporal elasticity of substitution exceeds one, an increase in uncertainty lowers the price-dividend ratio for equity, and a rise in the expected growth rate raises this ratio. Calibrations indicate that society would willingly reduce GDP by around 20 percent each year to eliminate rare disasters. The welfare cost from usual economic fluctuations is much smaller, though still important, corresponding to lowering GDP by about 1.5 percent each year. (JEL E13, E21, E22, E32)

Relative Risk Aversion and Portfolio Choice

2005 ◽  
Author(s):  
Pablo Muñoz Ceballos ◽  
Esteban Flores Díaz
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Relative Risk Aversion

Eliciting Risk Preferences and Elasticity of Substitution

2020 ◽  
Vol 17 (4) ◽  
pp. 314-329
Author(s):  
Johan Burgaard ◽  
Mogens Steffensen
Keyword(s):  
Risk Aversion ◽  
Discount Rate ◽  
Predictive Power ◽  
Recursive Utility ◽  
Risk Averse ◽  
Indirect Utility ◽  
Consistent Estimation ◽  
On Certainty ◽  
Certainty Equivalents ◽  
Elasticity Of Intertemporal Substitution

Risk aversion and elasticity of intertemporal substitution (EIS) are separated via the celebrated recursive utility building on certainty equivalents of indirect utility. Based on an alternative separation method, we formulate a questionnaire for simultaneous and consistent estimation of risk aversion, subjective discount rate, and EIS. From a representative group of 1,153 respondents, we estimate parameters for these preferences and their variability within the population. Risk aversion and the subjective discount rate are found to be in the orders of 2 and 0, respectively, not diverging far away from results from other studies. Our estimate of EIS in the order of 10 is larger than often reported. Background variables like age and income have little predictive power for the three estimates. Only gender has a significant influence on risk aversion in the usually perceived direction that females are more risk-averse than males. Using individual estimates of preference parameters, we find covariance between preferences toward risk and EIS. We present the background reasoning on objectives, the questionnaire, a statistical analysis of the results, and economic interpretations of these, including relations to the literature.

scholarly journals Relative risk aversion models: How plausible are their assumptions?

2021 ◽  
pp. 104346312199408
Author(s):  
Carlo Barone ◽  
Katherin Barg ◽  
Mathieu Ichou
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Loss Aversion ◽  
Educational Inequality ◽  
Risky Choice ◽  
Relative Risk Aversion ◽  
Downward Mobility ◽  
Educational Decisions ◽  
Empirically Supported ◽  
Occupational Risks

This work examines the validity of the two main assumptions of relative risk-aversion models of educational inequality. We compare the Breen-Goldthorpe (BG) and the Breen-Yaish (BY) models in terms of their assumptions about status maintenance motives and beliefs about the occupational risks associated with educational decisions. Concerning the first assumption, our contribution is threefold. First, we criticise the assumption of the BG model that families aim only at avoiding downward mobility and are insensitive to the prospects of upward mobility. We argue that the loss-aversion assumption proposed by BY is a more realistic formulation of status-maintenance motives. Second, we propose and implement a novel empirical approach to assess the validity of the loss-aversion assumption. Third, we present empirical results based on a sample of families of lower secondary school leavers indicating that families are sensitive to the prospects of both upward and downward mobility, and that the loss-aversion hypothesis of BY is empirically supported. As regards the risky choice assumption, we argue that families may not believe that more ambitious educational options entail occupational risks relative to less ambitious ones. We present empirical evidence indicating that, in France, the academic path is not perceived as a risky option. We conclude that, if the restrictive assumptions of the BG model are removed, relative-risk aversion needs not drive educational inequalities.

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