Plz explain how I should begin the solution to this, In a one step binomial tree, with one step period dt, if p is the real world probability and q is the risk neutral probabbility, (u and d rep the usual proportions), Show that p > q iff (1+theta) > exp(rd t) and interpret this result, where theta is the expected real rate of return).
Start with : 1. (1+theta) > exp(rd t) 2. Add to both sides -d => (1+theta) -d > exp(rd t) -d 3. Divide by (u-d) => ((1+theta) -d)/(u-d) > (exp(rd t) -d)/(u-d) 4. The above is actually p>q This inequality implies that real world expected returns are greater than risk free interest rate. This is true when the real returns include risk premium (CAPM) and positivelt correlated with market returns.
Intuitively, p ought to be bigger than q because the underlying risky asset ought to yield a higher expected return than the risk-free rate, precisely because it is a risky asset. In fact, the expected return can be thought of as being equal to the risk-free rate plus a suitable risk premium, which represents the reward for accepting the additional risk. In a binomial tree, a higher expected return corresponds to a higher weight on up-branches than down-branches. Consequently, in a sensible tree model, p must be higher than q, so as to place a higher weight on the up-branches.
