If you start with income y, and buy z units of an asset with price one, mean return 1+r and variance o your income have a mean value of y+rz and a variance of 2202 SoE((x)=y+rz-.5B(y+r)2-.5B32a2 In this case, the optimal choice of the risky asset gives us: r-B(+rz)r-Bz02=0 orz= (1-By) BO What happens if there are multiple independent assets? Another way to think about it is that there is fixed amount of risky asset to be allocated-this implies an r, which is increasing in risk and decreasing in wealthIf you start with income y, and buy z units of an asset with price one, mean return 1r and variance 2, your income have a mean value of yrz and a variance of z22 So Eux  y  rz . 5y  rz2 . 5z22 In this case, the optimal choice of the risky asset gives us: r  y  rzr  z2  0 or z  r1y 2r2 What happens if there are multiple independent assets? Another way to think about it is that there is fixed amount of risky asset to be allocated– this implies an r, which is increasing in risk and decreasing in wealth