The division has $6 million of capital, which is split into two parts. The first part is the reserve capital needed to pay claims over the next year. The remainder is invested in short-term bonds, which provide a random return, equally likely to be any value between 5% and 8%. If the reserve capital turns out to be less than the total value of claims for the year, the division has to borrow enough money, at a cost of 10% of the amount borrowed, to make up the difference.
The firm would like to find an capital allocation that maximizes the
expected amount of cash they have left at the end of the year. Suppose
they have narrowed down their choice to the following possible amounts
of reserve capital: $4.7 million, $4.8 million, $4.9 million, $5.0
million, and $5.1 million. Based on 1000 simulation trials each,
which option is the best?