Optimal Portfolio Choice with Bid-Ask Spreads

A climate charity invests its cash reserves for one year, splitting the money between a risk-free account paying rf% and exactly one of four funds of the same kind as a clean-energy stock fund. For each fund, the expected one-year return, its standard deviation and the round-trip bid-ask spread paid to buy the fund and sell it at the end of the year (as a percentage of the amount invested, deducted from the return) are: table. Whichever fund the climate charity picks, the climate charity chooses the share w of the cash reserves in the fund to maximize the mean-variance utility U = E[r] - (A/2) Var(r) of the portfolio's one-year return r (returns measured as decimals), with risk aversion A = aversion, and w must be between 0 and 1 (no borrowing or short sales). Which fund gives it the highest utility?