You have an equity portfolio valued at $1.22 million that has a beta of .98. You have decided to hedge this portfolio using SPX call option contracts. The S&P 500 index is currently 3,092. The option delta is .639. How many option contracts must you write to effectively hedge your portfolio?

Question

Quizplus · Accepted Answer

To hedge the portfolio, we need to calculate the number of contracts needed to offset the portfolio's beta risk.

First, we need to calculate the notional value of the portfolio:

Notional value = Portfolio value / index level
Notional value = $1,220,000 / 3,092
Notional value = $394,278.35

Next, we need to calculate the number of contracts needed:

Contracts = (Notional value x Portfolio beta) / (Option delta x Index level)
Contracts = ($394,278.35 x 0.98) / (0.639 x 3,092)
Contracts = 6.03

Since we cannot trade fractional contracts, we round up to the nearest whole number, which is 6. Therefore, we need to write 6 SPX call option contracts to effectively hedge our portfolio.

You Have an Equity Portfolio Valued at $1