You have just been appointed manager of the equity portfolio of a large pension plan. The portfolio has a current value of $100 billion and is well diversified; consequently, it has a beta close to one. The trustees of the pension plan are very risk averse, and in order to prevent you from taking on too much risk, they have structured your compensation as follows: if the value of the fund drops below $90 billion in one year, you will be fired with no severance pay.
If the fund is between $90 billion and $120 billion, you will be paid $2 million + 0.01 percent of the difference between the fund value and $90 billion (i.e., if the fund is worth $95 billion in one year, you will be paid $2 million + $500,000 = $2.5 million). If the fund is worth more than $120 billion, your salary will be capped at $5 million. You are allowed to invest in options on the S&P/TSX. The current value of the S&P/TSX is 1,000, and there are puts and calls traded that expire in one year. The puts and calls both have multipliers of $100. The standard deviation of returns on the S&P/TSX is 10 percent per year, and the risk-free rate is 3 percent per year. Assume that there are no dividends for either the portfolio or the S&P/TSX and that the options are European.
a. Describe how you can best protect your personal interests.
b. How much will these actions cost the portfolio?