10. Assume that a discrete time process St satisfies t In(St) = ln(So) +at+Ei, t = 1, 2,..., (1) i=1 where the i are independent and identically distributed (i.i.d.) with expec- tation 0, and a is a constant. Let r > 0 be the risk-free rate. Use a property of conditional expectations (that if the value of a random variable is known at time t it is regarded as a constant in a conditional expectation), to show that the discounted process e-rt St (wherer > 0 is the risk-free rate) is a martingale iff (if and only if) the returns, defined by Rt+1 = ln(St+1/St), (2) 3 satisfy EleRt) = e", (3) or, equivalently, if E(St/St-1) = e". Thus, the price-relatives are expected to grow at the risk-free rate under the martingale model. 10. Assume that a discrete time process St satisfies t In(St) = ln(So) +at+Ei, t = 1, 2,..., (1) i=1 where the i are independent and identically distributed (i.i.d.) with expec- tation 0, and a is a constant. Let r > 0 be the risk-free rate. Use a property of conditional expectations (that if the value of a random variable is known at time t it is regarded as a constant in a conditional expectation), to show that the discounted process e-rt St (wherer > 0 is the risk-free rate) is a martingale iff (if and only if) the returns, defined by Rt+1 = ln(St+1/St), (2) 3 satisfy EleRt) = e", (3) or, equivalently, if E(St/St-1) = e". Thus, the price-relatives are expected to grow at the risk-free rate under the martingale model