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182CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCYYou can see that σ µ < σ r for values of γ below 30. This means ⇐(115)that exchange rate payoffs are too volatile relative to the fundamentals(the intertemporal marginal rate of substitution) over this range of γ.Note how the GMM estimate of γ = 48 obtained earlier in this chapteris consistent with this result. In order to explain the data, the Lucasmodel with CRRA utility requires people to be very risk averse. Manypeople feel that the degree of risk aversion associated with γ =48isunrealistically high and would rule out many observed risky gamblesundertaken by economic agents.0.70.60.5C =60C =5 0IMRSV o la tility0.40.3C =4 0Lower Volatility Bound0.2C =3 0C =2 00.1C =1 0C =4C =200.86 0.88 0.9 0.92 0.94 0.96 0.98 1MeanFigure 6.2: Mean and volatility estimates of the intertemporal marginalrate of substitution (IMRS) with β =0.99 and alternative values of γunder constant relative risk aversion utility and lower bound implied byforward exchange payoffs of the pound, deutschemark, and yen, 1973.1to 1997.1.(116)⇒The mean and volatility of the intertemporal marginal rate of substitution(θ µ , σ µ ) for alternative values of γ and the lower volatility bound(σ r =0.309θ µ ) implied by the data are illustrated in Figure 6.2. 7