A $1 billion mutual fund tracking the s&p 500 index. the index currently trades

Question

A $1 billion mutual fund tracking the s&p 500 index. the index currently trades at 2000. In oder to protect the fund against an index decline beyond 10% in a year. ie, the value of the fund in a year mush be above 900m. Q:1. What forward or option position would you take. specify long or short, expiration date, strike price and qualtity. ( for example, a put option for a year, with a certain strike price?) 2. Using the table below calculate the cost of your protection in dollars and in percentage of fund value.

Instrument Expiration Strike Premium Forward 6 months 2025 0 Call 6 months 1500 495.27 Call 1 Year 1700 332.47 Call 1 Year 1800 262.26 Call 6 months 1900 162.84 Call 1 Year 2000 152.47 Forward 1 Year 2050 0 Put 6 months 2000 115.42 Put 1 Year 1900 114.43 Put 6 months 1800 36.65 Put 1 Year 1800 74.79 Put 1 Year 2000 164.39

Explanation / Answer

In order to protect against more than 10% decline of index value over 1 year, the fund should hedge using:

Long Put option @ 1 year expiration strike price @ 2000 * 0.9 = 1800

Quantity = 1,000,000,000/(2000 * 100) = 5000 contracts (note: 100 is the contract multiplier)

Cost of protection = premium * no. of contracts * contract multiplier = 74.79 * 5000 * 100 = $ 37,395,000

As a percentage of fund - (37,395,000/1,000,000,000) * 100 = 3.7395%

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