An investor is allocating her wealth between a risk-free asset and a risky asset. The risk-free asset has a rate of return equal to 3%. The risky asset has an expected return equal to 18% and a standard deviation of returns equal to 28%. The investors utility from holding a total portfolio C is given by:

UC=C3C2,

where C is the expected return of her portfolio and C is the return standard deviation of her portfolio.

Which fraction of her wealth should the investor invest in the risky asset?