Fig 1.
The optimal asset allocation between the S&P500 index and a risk-free asset as a function of the risk-free interest rate rf.
The empirical S&P500 annual returns during 1997–2016 are employed. The bold line shows the optimal allocation to the stock index for a PT investor with the parameters in [23]: α = β = 0.88, λ = 2.25 given by Eq 5. The optimal allocation to the stock index drops dramatically from 100% to 0% once the risk-free rate reaches 0.035. In contrast, for an investor with a logarithmic utility function (thin line) the optimal allocation to the stock decreases gradually with the risk-free rate (note that the allocation is bounded between 0% and 100%, as no borrowing or short-selling are allowed).
Table 1.
The three tasks in the experiment are given below.
In each task the subject is asked to allocate his investment between the stock and the risk-free bond. Note that the return distributions and risk-free rates in Tasks 2 and 3 are the 2-period and 3-period distributions implied by the 1-period distribution and risk-free rate of Task 1, under the assumption of i.i.d. returns. The detailed experimental procedure is provided below.
Table 2.
Optimal investment proportion in the stock for PT preferences with reference point at the future value of current wealth (W0Rf).
Table 3.
The optimal allocation to the stock in the three tasks for CRRA investors.
Table 4.
The portfolio rate of return distribution for a 2-period horizon, with and without revision of the portfolio weights after the first period.
Table 5.
Asset allocation patterns observed in the experiment.