LRT with many assets: separation. Show that if the investor has a power or a logarithmic utility function the proportions of wealth invested in the risky assets are independent of her initial wealth....

LRT with many assets: separation. Show that if the investor has a power or a logarithmic utility function the proportions of wealth invested in the risky assets are independent of her initial wealth. (Hint: it is best to work with choice variables c and δ j where c is the amount invested in the safe asset and δ j is the proportion of the remaining funds w′  (w  c) invested in the jth risky asset.