Suppose that you can invest in the Timer fund, an investment fund whose managers can infallibly predict whether the S&P 529 index will have a rate of return over the next year which will be greater than or equal to the riskless rate of interest over this same period. The Timer fund is not allowed to sell short or borrow money. If the fund predicts that the index return will be more than the interest rate, it secretly invests all of its money in an S&P 529 index fund. On the other hand, if the fund predicts that the S&P 529 index return will be less than the interest rate, it secretly invests all its money in riskless bonds maturing in a year.
Note that the way the investment strategy works, each year an investor will receive the higher of the riskless rate and the market return or, equiv- alently, the payoff is max((1 + rf ), ST /S0), where rf is the riskless rate, ST is the value of the index in one year’s time, and S0 is the value of the index today.
The S&P 529 index is currently trading for 1300 and riskless rates over any horizon are 4% (i.e., assume that the term structure of interest rates is flat). The volatility of the S&P 529 index is 22% per year.
If you had $1m to invest, how much would you be willing to pay (in terms of fees) for the service offered by the Timer fund?