\(\gamma\)
4.0
Risk aversion
\(p(B)\)
0.25
Probability of bad state
\(C(B)\)
0.90
Consumption if bad
\(X(B)\)
0.50
Asset payoff if bad
Fixed parameters
\(C_0 = 1\)
\(C(G) = 1.05\)
\(X(G) = 1\)
\(\delta = 0.98\)
Physical vs. risk-neutral probabilities
States with high marginal utility get more weight under \(q\) than under \(p\).
Pricing a risky asset
The asset pays 1 in the good state and 0.50 in the bad state.
\(\psi(G) = p(G)\cdot M(G) = \) 0.75 \(\cdot\) 0.81\(\, = \,\)0.60
\(\psi(B) = p(B)\cdot M(B) = \) 0.25 \(\cdot\) 1.49\(\, = \,\)0.37
\(P = \psi(G)\cdot X(G) + \psi(B)\cdot X(B)\)
\(\phantom{P}= \) 0.60 \(\cdot\) 1\(\, +\, \)0.37 \(\cdot\) 0.50
\(\phantom{P}= \) 0.79
Expected return \(\mu = E[X]/P - 1 = \) 10.56%
Risk-free rate \(r^f = 1/E[M] - 1 = \) 2.24%
Risk premium \(\mu - r^f\)
8.32%