This year Dumbledore is worth $122,941. He now wants to allocate his wealth between the Vanguard S&P 500 ETF (VOO) and a risk-free bond. Suppose he has a mean-variance utility which is defined as U=E[rp]−1/2*A*σ^2*p where E[rp] and σP are the expected return and standard deviation of his complete portfolio, respectively. A is a measure of his risk aversion, which is A=6.

Suppose VOO has an expected return E[rV]=0.13 per year and volatility σV=0.16 per year, and a risk-free bond yields 0.06 per year.

What is the fraction Dumbledore should invest in VOO in order to maximize his expected utility?