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Econ 333 Spring 081Portfolio Tools 2“A bird in the hand is worth two in the bush”Danthine and Donaldson, p. 83
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Econ 333 Spring 082Portfolio Tools 2: A brief revue of conceptsIn individual’s attitude toward risk can be measured in two ways:–The Arrow-Pratt measure of absolute risk aversion: Ra (w) = - U’’(w) / U’(w) –The Arrow-Pratt measure of relative risk-aversion: Rr (w) = - w U’’(w) / U’(w)•The sign of these measures immediately tells us the basic attitude toward risk–For a risk-averse individual U’’< 0 (strictly concave), so Ra > 0 and Rr > 0 are positive–For risk-neutral individual U’’= 0 (linear), so Ra = Rr =0–For risk-lovers U’’> 0 (strictly convex), so Ra <0 and Rr <0.•Ra (w) is clearly a local measure of risk aversion, i.e. it need not be the same at every level of wealth•The Von Newman Morgensten (VNM) utility of an individual is said to display:–Constant Absolute Risk Aversion (CARA) if Ra (w) remains constant with an increase in wealth–Decreasing Absolute Risk Aversion (DARA) if Ra (w) decreases with an increase in wealth–Increasing Absolute Risk Aversion (IARA) if Ra (w) increases with an increase in wealth