Question

# As a stock portfolio manager, you have investments in many U.S. stocks and plan to hold...

1. As a stock portfolio manager, you have investments in many U.S. stocks and plan to hold these stocks over a long-term period. However, you are concerned that the stock market may experience a temporary decline over the next three months, and that your stock portfolio will probably decline by about the same degree as the market. You are aware that options on S&P 500 index futures are available. The following options on S&P 500 index futures are available and have an expiration date about three months from now:

1372                       40                       24

1428                       24                       40

The options on S&P 500 index futures are priced at \$250 times the quoted premium. Currently, the S&P 500 index level is 1400. The strike price of 1372 represents a 2 percent decline from the prevailing index level, and the strike price of 1428 represents an increase of 2 percent above the prevailing index level.

1. Assume that you wanted to take an options position to hedge your entire portfolio, which is currently valued at about \$700,000. How many index option contracts should you take a position in to hedge your entire portfolio?2.5 MARKS
2. Assume that you want to create a hedge so that your portfolio will lose no more than 2 percent from its present value. How could you take a position in options on index futures to achieve this goal? What is the cost to you as a result of creating this hedge? 2.5 MARKS

a) the options carry notional value with \$100 multiplier. So, no. opf contracts needed = portfolio/(index level * multiplier)

= 700000/(1400*100) = 5

b) To cover downside risk of 2%, we will go long on put options with strike price of 1372, which is 2% lower than current level. This way, if index decline exceed 2% ie.e if index goes below 1372, the losses on our portfolio will be offset by gains on our index put option.

As calculated above we'll buy 5 contracts of S&P put options with strike price of 1372.

Cost of hedge = premium paid for buying the contracts = 24*100*5 = \$12000

If index falls 2% or by 28 opints, then our 5 put contracts will be worth (28*5*100) or \$14000, which will more than offset the cost of the contracts.

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