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Although compound rates of interest (or yields) are quoted in the markets, we often find it more convenient to express bond prices in terms of continuously compounded spot interest rates/yields. If the continuously compounded spot yield is rnt , then a coupon-paying bond may be considered as a portfolio of ‘zeros’, and the price is (see Cuthbertson and Nitzsche 2001a) n Pnt = Ck e−rkt k + Mn e−rnt n = k=1 n Pkt∗ + Pnt∗ (43) k=1 where Pk∗ = Ck e−rk k and Pn∗ are the prices of zero coupon bonds paying Ck at time t + k and Mn at time t + n, respectively.

Do the entrepreneurs have to know the preferences of individual consumers in order to choose the optimum level of physical investment? g. stock markets) ensure that funds are channelled to the most efficient investment projects? Questions of the interaction between ‘finance’ and real investment decisions lie at the heart of the market system. The full answer to these questions involves complex issues. e. e. we assume zero price inflation). We shall see that under these assumptions, a separation principle applies.

18 CHAPTER 1 / BASIC CONCEPTS IN FINANCE Power (Constant Relative Risk Aversion) With an initial (safe) level of wealth W0 , a utility function, which relative to the starting point has the property U (W )/U (W0 ) = f (W/W0 ) so that utility reacts to the relative difference in wealth, is of the relative risk aversion type. The latter condition is met by power utility, where the response of utility to W/W0 is constant, hence the equivalent term constant relative risk aversion CRRA utility function: U (W ) = W (1−γ ) 1−γ γ > 0, γ = 1 U (W ) = W −γ RA (W ) = γ /W U (W ) = −γ W −γ −1 and RR (W ) = γ (a constant) (63) Since ln [U (W )] = −γ ln W , then γ is also the elasticity of marginal utility with respect to wealth.