Forwards are traded in OTC markets, while Futures are traded in Exchanges.
2) In which strategy would you have to post more margin? I suggest that you go to MEFF margin calculator and input these strategies.
2.1) Buy a Future. As there is a potential loss, you would have to post a margin.
2.2) Buy a call option. No need to post any margin as there is no potential loss.
2.3) Buy a Future and sell a Put option at strike = price of the Future. You would have twice the potential loss of the Future. Aprox. twice the margin needed in the Future. This would be the correct answer.
2.4) Buy a put option. No need to post any margin as there is no potential loss
Probably you would also like to have a look at other strategies, like buying a Future and buying a Put option at strike = price of the Future (synthetic bought call ==> no margin) and selling an option (it does not matter if you sell a call or a put; as there would be a potential default risk, you would have to post margin).
3) A trader buys a European call and sells a European put. Both options have the same underlying asset, strike and expiry. Under what circumstances the price of the call will be the same as the price of the put?
If a trader buys a European call, he would have to pay the premium. Let's call it "c". If a trader sells a European put, he would receive a premium. Let's call it "p". So the net position would yield in p - c in the first day.
The question asks us to determine when p - c = 0 or p = c. If you make a chart of the strategy, you will notice that it is very similar to the payoff of a Forward. Remember, in a forward you do not have to anything upfront. The answer would be that only if the strike is equal to the price of the Forward for the same expiry the net premium would be zero.
Maybe you want to have a look at the options calculator. Price a 1 year forward (for example, S = 100, r = 5%, T = 1). Then calculate premiums for both call and put for Strike = Forward price. You will notice that the premium of the call is equal to the premium of the put. It does not depend on volatility.
4) A company goes long 2 orange juice Futures contracts. Each contract allows you to buy 15,000 pounds of orange juice for 160 cents/pound. Initial margin is USD 6,000 and maintenance margin is USD 4,500. What change in price will drive a margin call?
For a margin call ocurring, the margin account balance should be lower than USD 4,500; this means that the investor should suffer a loss of USD 1,500. To calculate the price at which the margin account balance would be lower than USD 4,500, we should solve the following equation:
(160 cents - Price)* 2 (# contracts) * 15,000 (pounds/contract) >= 1,500 (loss that would leave the balance at 4,500) ==> Price <= 160 cents - [1,500 / (2 * 15,000)] <= 155 cents. The answer, then, would be 6 cents (if the price reaches 155 there would be no margin call).
5) With the same hypothesis of the previous question, when will I be able to withdraw USD 2,000 from the margin account?
To withdraw USD 2,000, we will need to generate 2,000 above the initial margin (a 2,000 profit in the position).To calculate the price at which the margin account balance would reach USD 8,500, we should solve the following equation:
(Price- 160 cents)* 2 (# contracts) * 15,000 (pounds/contract) = 2,000 (profit that would leave the margin account balance at USD 8,500) ==>
Price = [2,000 / (2 * 15,000)] + 160 cents = 167 cents (rounded to the nearest integer).
6) A friend of yours wants to buy a portfolio of Energy stocks with a value of EUR 100,000; he is worried about the direction of the market and he is thinking about partially hedging his risk. IBEX-35 Futures contract is trading at 8900 and the beta of the portfolio is 1.75. What strategy would you recommend?
First of all, take into account that your friend is short the portfolio (he does not have it, he wants to buy it, if price goes up he will have to pay more). Then, to hedge this position we would have to go long the Future.
Given that the hedge will not be perfect (he will be hedging a portfolio of energy stocks with IBEX Futures) , your friend will have to apply a hedge ratio:
Number of contracts = Beta x (Portfolio value) / (Future x Multiplier).
As he has to hedge with IBEX Futures (multiplier = 10), he will have to buy:
1.75 x 100,000 / (8,900 x 10) = 1.97 (we would buy 2, the nearest integer)
What would happen if we wanted to hedge with Mini-IBEX Futures? Given that the multiplier for mini-IBEX Futures is 1, he would have to buy:
1.75 x 100,000 / (8,900 x 1) = 19.7 (we would buy 20, the nearest integer)
Try to check in the MEFF margin calculator if the margin required for both strategies would be the same.
7) A well diversified portfolio with Spanish stocks has a beta of 1.2. During the last days, IBEX has been coming down and the portfolio manager believes that there will be a rebound. How would you raise the beta to 1.5 to profit from this rebound? The portfolio has a value of EUR 5.000.000 and the mini-IBEX Futures contract (multiplier 1) with expiry in the next month is trading at 9,280. What would you recommend?
We know that if we wanted to hedge completely our portfolio, we would have to sell (remember, we are long the portfolio) the following number of contracts:
1.2 x 5,000,000 / (9,280 x 1) = 646.55
By selling 647 contracts we would completely hedge the portfolio. Consider the following scenarios:
Scenario 1 – IBEX up by 1%
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Scenario 2 – IBEX down by 1%
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Long portfolio
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5,000,000 x ( 1 + 0.01 x 1.2) = 5,060,000
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5,000,000 x ( 1 - 0.01 x 1.2) = 4,940,000
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Short 647Futures
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647 x (9280 – 9373) = -60,171
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647 x (9280 – 9187) = 60.171
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Net new portfolio
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Aprox. 5,000,000
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Aprox. 5,000,000
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* If IBEX goes up by 1%, the portfolio will go up by 1.2 x 1%, being beta = 1.2
If we take this approach, the value of the portfolio will not change, independently of how IBEX performs. Our beta will be equal to zero. So, to make our beta equal to zero, we had to short 647 contracts. If we short less contracts, our beta will decrease. If we buy some contracts, our beta will increase.
To determine hoy many contracts we should buy to increase the beta of the portfolio to 1.5 we should apply the following formula:
(New beta - Old beta) x (Portfolio value) / (Future x Multiplier).
In this case:
(1.5 - 1.2) x 5,000,000 / 9,280 x 1) = 161.64 (or 162 contracts, the nearest integer).
8) Brent is trading at 96.25 $/barrel and the 1 year risk free rate is r = 0.60%, if we know that the convenience yield is 0% and the 1 year Future is trading at 97.80 $/barrel. What should be the storage costs?
The formula we use to calculate the price of a commodity forward is:
F = S x e ^(r + u - y), where "u" are storage costs and "y" is convenience yield.
In this case:
F = 97.8 = 96.25 x e ^(0.6% + u - 0), so, to solve for "u" ==>
==> 97.8 / 96.25 = e ^(0.6% + u) ==> Ln (97.8 / 96.25) = 0.6% + u ==>
==> u = Ln (97.8 / 96.25) - 0.6% = 1%
9) A stock is expected to pay a dividend of USD1 per share in 2 months and in 5 months. The stock price is USD50, and the risk free rate is 8% per annum with cont. compounding for all maturities. What should be the 6 month forward price?
The formula we use to calculate the price of a forward of a stock that pays a discrete dividend is the following:
F = (S - I) x e^(r x T), where "I" is the present value of the dividends that are paid before the expiry of the forward.
In this case:
I = (1 x e^(-8% x 2/12) + 1 x e^(-8% x 5/12)) = 1.95
F = (50 - 1.95) x e^(8% x 6/12) = 50
10) We shorted the forward in the previous question. 3 months later, the price of the stock is USD48 and the risk free rate is still 8%. What is the value of the position?
To calculate the MTM (value), we simulate closing-out the position. Given that we shorted the forward, to close the position out, we would go long the forward. So we have to calculate the forward price:
I = (1 x e^(-8% x 2/12)) = 0.99
F = (48 - 0.99) x e^(8% x 3/12) = 47.96
Given we shorted the forward, we would receive at expiry the difference between both forwards (50 - 47.96). The MTM would be this amount brought to present value:
(50 - 47.96) x e^(-8% x 3/12) = 2
11) If the 6m rate is 5% and the 3m rate is 4%, what should be the forward rate 3m-6m? Assume cont. compounding
To avoid arbitrage opportunities, bringing an amount to present value from 6 months and bringing it from 6 months to 3 months and the to present value should be the same. In mathematical terms:
e^(-5% x 6/12) = e^(-r% x 3/12) x e^(-4% x 3/12)
Solving for "r" in the equation:
e^(-5% x 6/12) / e^(-4% x 3/12) = e^(-r% x 3/12) ==> Ln (0.9851) = -r% x 3/12 ==>
==> r% = - Ln (0.9851) x 12/3 = 6%
12) Given a plain vanilla call option and a whale option with the same strike and expiry: which one should be more expensive?
Plain vanilla should be more expensive. Whale option provides a similar payoff if underlying asset does not move a lot; however, plain vanilla will provide an infinite payoff if underlying asset moves a lot while the payoff for whale option is limited.
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