Question

The followings are the information related to S&P index option

•      SP500 index (ticker symbol SPX) = 2500

•      SP500 Dec call with an exercise price 2450 = $70

•      SP500 Dec put with an exercise price 2450 = $12

•      Each option has a multiplier of $100 (or each contract has a multiplier of $100)

Jenny Smith is a money manager. Her portfolio of stocks tracks S&P500 index. The market value of the portfolio is $300 million. While not sure, Jenny expects a 10% drop in stock market in a month. She decides to go for an index put option portfolio insurance strategy. These contracts will mature in a month.

How many put option contracts does she need?

a. 1200

b. 1000

c. 1400

d. 1600

Assume the cost of buying the put option is equivalent to 576 units of S&P500 index. One month later, Jenny is wrong. The S&P500 index rises to 2800. What is the value of Jenny’s portfolio?

a. 334.39 million

b. 335.00 million

c. 335.79 million

d. 336.00 million

Assume the cost of buying the put option is equivalent to 576 units of S&P500 index. One month later, Jenny is correct. The S&P500 index drops to 2200. What is her portfolio value (stocks plus put option gain)?

a. 292.73 Million

b. 264.00 million

c. 262.73 million

d. 254.73 million

Answer 1

1.) how many contracts she needs?

Her portfolio value = $300 miillion

Value of S&P= 2500

300000000/2500 = 120000

While one contract =100

So, 120000 / 100 = 1200 contracts she will need.

2.) S&P goes 2800 from 2500.

So, a 12% increase from the current price.

Her portfolio is $300 million

300 million + 12% of 300 million = $336 million

3.) S&P goes to 2200 means 12% down.

Her portfolio is $300 million

300 million - 12% of 300 million = $264 million.

Gain on the put option is the strike price minus current price multiplied by contract size...

1200*(2450 - 2200)*100 = 30 Million

However, She paid some premium

576 * 1200 = 691,200

So portfolio value =

264,000,000 + 30,000,000 - 691,200

$293.3088 million which Is correct answer.

However correct answer is nearest to 292.73 million. So, we chose 292.73 million.