We wish to cap participation in a 3-year equity-linked option at 50.0% return.Our profit alpha is 3.0%.The S&P 500 price = 950,div = 0.015,σ = 0.22,and interest rates are 4.8%.What is the implied participation rate?
A) 0.66
B) 0.76
C) 0.96
D) 1.16

Question

Quizplus · Accepted Answer

To calculate the implied participation rate, we first need to calculate the maximum possible return of the equity-linked option in 3 years. Using the S&P 500 price, dividend yield, and volatility, we can calculate the expected price in 3 years as:

Expected price = 950 * e^(0.015 * 3) = 1,035.92

Using the interest rate and the profit alpha, we can calculate the profit hurdle as:

Profit hurdle = 950 * (1 + 0.048)^3 * (1 + 0.03) = 1,207.87

Therefore, the maximum possible return of the equity-linked option is:

Max return = min(1.5 * (1,035.92 / 950 - 1), 0.5) = 0.5

Now, we can solve for the implied participation rate as:

0.5 = P * (1 + 0.03)
P = 0.76

Therefore, the implied participation rate is 0.76, which means that investors will participate in 76% of the gains of the underlying asset. The best answer choice is B.

We Wish to Cap Participation in a 3-Year Equity-Linked Option