1. A company has a $37 million stock portfolio with a beta of 1.2. The S&P index

Question

1. A company has a $37 million stock portfolio with a beta of 1.2. The S&P index futures price is currently standing at 1000. Futures contracts on $250 times the index can be traded. How many contracts is needed to reduce the beta to 0.8? If a short position is needed, report a negative number. (margin of error = +/- 1)

2. The price of a stock is $36 and the price of a three-month call option on the stock with a $36 strike is $3.60. Suppose a trader has $3,600 to invest and is trying to choose between buying 1,000 options (10 contracts) or 100 shares of stock. How high does the stock price have to rise for an investment in options to be as profitable as an investment in the stock?

3. A trader writes 100 European put options (1 contract) with a strike price of $50 and a time to maturity of six months. The price received for each option is $4. At expiration, the price of the underlying asset becomes $42. Calculate the trader's gain. If loss, report a negative number.

4. 3-yr interest rate is 5.9% and 4-yr interest rate is 6.2% (both continuously compounded). What is the forward rate (continuously compounded) for the fourth year (between yr-3 and yr-4)? Report in % and round the number to the nearest 2 decimal percentage points such as 5.78%. (margin of error = +/- 0.05%)

Explanation / Answer

1)

Let b* = desired beta

Let b = portfolio beta

Then N = (b* - b)(P/A)    (N < 0: sell)

N > 0: buy

Thus N= (0.8-1.2)*37m/(250*1000) = -59.2 or 59

Thus to reduce the beta to 0.8 we need to sell 59 Futures

2)

For the deal to be profitable,

Let the stock price be S

Thus profit on option strategy is = (S-36-3.6)*1000
Profit on stock = (S-36)*100

Equating the two will give S = 40

3)Since the strike price is more than Stock price , the buyer of the put option wil exercise it

Net position for the writer = (42-50)*100+ 400 = -400

Thus the writer is at $400 loss

4)

(1+S3)^3*(1+F4) = (1+S4)^4

S3=5.9%

S4=6.2%

Solving for F4 we have F4= 7.11%

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.