Consider an investor with initial wealth of W0 = 10000. He/she has the opportunity to invest in a risk-free account yielding 4% p.a. or in a stock index account with an expected rate of return of 10% p.a. and respective standard deviation of 25% p.a. The expected utility function, defined over final wealth is given by E[U(W1)] = E[(W1)(a/2)Var(W1). The risk aversion parameter has value a = 0.00025.

a) State the decision problem in terms of expected wealth and the variance of the expected wealth as a function of the portfolio weights (w for the risk-free asset and (1 w) for the risky asset).

b) Depict the decision problem in a -diagram.