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- A portfolio of derivatives on a stock has a delta of 2400 and a gamma of –10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? Long/Short and how many options and why?Futures price of a commodity is currently trading at 100. By delivery date, futures price can either rise to 140 or drop to 70. The put option has K =90. To create a hedge portfolio with one put and some futures, we need to ______ futures contract for one put option we long. A. short .25 B. short .35 C. short .28 D. long .35 E. long .28Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.
- Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option XProblem 1: Hedging market risk using S&P500 index futures Assume you have a portfolio worth currently $5,000,000. Let portfolio beta be ß, = 2. Assume you want to hedge market risk until 3 months from now.' Current value of S&P500 index futures 3 month from now is 3,900.00. You are using mini futures i.e. $50 per point. a) If you want to completely remove market risk without using futures. What would you do? b) If you use S&P500 mini futures, how many futures you would buy to completely hedge your exposure to market risk. c) What would be the value of your new (i.e. hedged) portfolio when S&P500 goes up by 2% 3 months from now? d) What would be the value of your new portfolio when S&P500 declines by 3% 3 months from now. e) What should you do in a) if you want to change the ß of your portfolio approximately to ß = 1? f) What should you do in b) if you want to change the ß of your portfolio approximately to B = 1?Under the current market conditions Bond 1 has a price of 90 and a Mccauley duration of 10, and Bond 2 has a price of 110 and Macauley duration of 15. A portfolio is created with a combination of face amount F₁ of Bond 1 and F2 of Bond 2. The combined face amount of the portfolio is F1+F2= 100, and the Macauley duration of the portfolio is 12.5. Set up the equations for finding the portfolio value X. (a) 15X9F1 + 16.5(100-F₁), X=9F₁+1.1(100-F₁) (b) 12.5X9F1 +15(100-F₁), X= .9F₁ + 1.1(100-F₁) (c) 12.5X = 9F₁ + 16.5(100-F₁), X= .9F₁+1.1(100-F₁) (d) 12.5X = 10F₁ +16.5(100-F₁), X = .9F₁+1.1(100-F₁) (e) none of these
- You are planning to make a hedging. The standard deviation of semiannual changes in a futures price on the gold is $0.96. The standard deviation of semiannual changes of the gold price is $0.87 and the coefficient of correlation between the two changes is 0.9. What is the optimal hedge ratio for a 6-month contract? Choose correct answer: a. The optimal hedge ratio is 0.8352 b. The optimal hedge ratio is 0.1 c. The optimal hedge ratio is 0.9931 d. The optimal hedge ratio is 0.8156Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800. Explain how a put option on the index with a strike of 700 can be used to provide portfolio insurance.
- Write the equation of the Security Market Line (SML). Compute and draw theSML when the expected return of the NASDAQ index (market portfolio) is17% and the return to the risk-free asset is 7%You BUY a futures contract with the characteristics below. Assuming the S&P500 contract suddenly RISES by 12.00 points, what is your profit or loss as a return on the initial margin? S&P500 e-mini contract Futures (FO) 2,646.000 Initial margin 5420 Maint margin 4610 O 9.68% O 11.07% 10.15% 11.49% O 10.61%Consider the following portfolio: Long 0 calls with strike price 77.0 Short 1 calls with strike price 77.0 Long 1 calls with strike price 102.0 Short 0 calls with strike price 102.0 Complete the following payoff table. What choice corresponds to the last row of the table? Position ST ≤ 77.0 77.0 < ST ≤ 102.0 ST > 102.0 portfolio