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The optimal trading strategy graph shows the proportion of wealth that should be invested in the stock and the bond, respectively. The optimal performance function (also know as the optimal value function) is the maximum expected utility from terminal wealth starting with an initial endowment. The expected terminal wealth shows the expected wealth at the end of the investment horizon. A negative value means that the stock is sold short and the money is invested in the bond. A value greater than one means that the optimal portfolio is a leveraged portfolio for which money from the bank is borrowed (bond is short sold) and invested in the stock. The optimal strategy is defined as the proportion of wealth held in the stock, meaning the amount of money invested in the stock divided by the total amount of wealth.
The table shows the numerical results of the portfolio selection problem. In the case of a power or log utility, this parameter is equal to. The Arrow–Pratt index of risk aversion is defined by. The value represents log utility and represents a power utility function of the form. You can change the utility function using the risk aversion parameter. The first graph shows the utility function used.
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