ass issues in finance a simple manipulation of the basic pricing formula can gives a lot of intuition about classic issues in finance--including determinants of the interest rate risk corrections, idiosyncratic versus syncratic risk, beta pricing model, mean variance variance frontiers, the slope of mean- variance frontier, time -varying expected returns, and present value relations
Class issues in finance • A simple manipulation of the basic pricing formula can gives a lot of intuition about classic issues in finance—including determinants of the interest rate, risk corrections, idiosyncratic versus syncratic risk, beta pricing model, mean variancevariance frontiers, the slope of meanvariance frontier, time-varying expected returns, and present value relations
Risk- free rate a bond pay I rmb at t+l. its value today is E、( m The return of the bond is risk-free rate R=r+l R,=1/E(m1 If a risk-free asset is not traded, we can define l/e, (m, as"shadow risk-free rate. sometimes it is also called"zero-beta rate Use power utility u'(c=c? by turning of uncertainty we obtain R we see three effects right away 1. Real interest rates are high when people are impatient, i.e., when B is low. If everyone wants to consume now. it takes a high interest rate to convince them to save 2. Real interest rates are high when consumption growth is high. High interes rates lower the level of consumption now, while raising its growth rate from today to tomorrow 3 real interest rate are more sensitive to consumption growth if the power parameter yis large. When r is large, the utility is highly curved
Risk-free rate • A bond pay 1 RMB at t+1, its value today is • The return of the bond is risk-free rate • So • If a risk-free asset is not traded, we can define as “shadow” risk-free rate, sometimes it is also called “zero-beta” rate. • Use power utility • By turning of uncertainty, we obtain • we see three effects right away: • 1. Real interest rates are high when people are impatient, i.e., when • is low. If everyone wants to consume now, it takes a high interest rate to convince them to save; • 2. Real interest rates are high when consumption growth is high. High interest rates lower the level of consumption now, while raising its growth rate from today to tomorrow. • 3 real interest rate are more sensitive to consumption growth if the power parameter is large. When is large, the utility is highly curved • Rf = rf +1 ( ) pt = Et mt+1 1/ ( ) Rf = Et mt+1 1/ ( ) Et mt+1 −γ u'(c) = c γ β ⎟⎟⎠⎞ ⎜⎜⎝⎛ = +t f tcc R 1 1 β γ γ