The futures price, also known as the 'locked-in price', is paid at the end when the futures contract matures. The buyer (who is long the future) pays the futures price to the seller (who is short the future) at maturity in exchange for the underlying asset if the future is physically settled. If the contract is cash-settled then the loser will pay the difference between the underlying asset's value and the strike price to the winner.
Confusingly, the 'futures price' is more similar to the 'option strike price' (also called the exercise price) than the 'option price', since the strike price is paid at the end, while the option price is paid at the start.
Which of the below formulas gives the payoff at maturity ##(f_T)## from being long a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
No explanation provided.
Which of the following statements about futures is NOT correct?
Futures prices can be calculated based on the spot price of the underlying asset compounded forward at the total opportunity cost of capital, plus any storage costs and minus any income yields such as dividends.
###F_T = S_0.e^{(r_\text{total} - r_\text{income} + r_\text{storage costs}).T}###Which of the below formulas gives the payoff at maturity ##(f_T)## from being short a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
No explanation provided.
A trader buys one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. If the trader doesn’t close out her contract before expiry then in one year she will have the:
No explanation provided.
A trader sells one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:
No explanation provided.
In general, stock prices tend to rise. What does this mean for futures on equity?
Equity futures prices ##(F_T=E(P_T))## do tend to be higher than spot prices ##(P_0)##, and this is called contango ##(F_T > P_0)##. The opposite is called backwardation ##(F_T < P_0)##.
Contango does not imply that equities or futures are mis-priced. The fact that spot prices are usually less than futures prices is due to the appreciation of equity prices over time, also called the expected capital yield. A stock's spot price ##(P_0)## is usually expected to grow higher in the future when there is a positive expected capital return. This higher expected price will be reflected in the futures price. This relationship is given below where the expected continuously compounded capital return is given by ##r_\text{cc, capital}##.
###F_T = E(P_T) = P_0.e^{r_\text{cc, capital}.T}###Therefore when ##r_\text{cc, capital} > 0##, then ##F_T>P_0## which is contango.
Which of the following statements about futures contracts on shares is NOT correct, assuming that markets are efficient?
When an equity future is first negotiated (at t=0):
In an efficient market where stocks are fairly priced, the value of a future to both the long and short traders should be zero, or else one party would be agreeing to a bad deal. However, while the initial value of the future is zero, the futures price quote will not be zero. The futures price quote should reflect the market's prediction of the underlying asset price at the maturity of the futures contract. Note that shares have no storage costs.
Which of the following statements about futures is NOT correct?
Buyers of futures pay the futures price at the maturity of the futures contract when they buy the underlying asset. They do not pay the futures price at the start. They only pay the initial margin to their futures broker at the start.
The reason why the futures are not paid for at the start is because futures actually have a zero value at the start when they're first agreed to. This is because the futures price paid at the end must be 'fair', it's the market's best prediction of the underlying asset price at maturity, or else the buyer or seller wouldn't agree on the futures price. This is unlike options which actually have a non-zero value at the start and therefore have an option price or premium which is paid at the start by the option buyer. The equivalent of the futures price for an option is the option strike price which is paid at the end.
The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.
What should be the 3 year gold futures price?
Storage costs disadvantage the holder of gold, the underlying asset. The returns on the underlying asset should compensate them for this, so storage costs should be added to the required total return.
Another way to think of storage costs is that they're like negative dividends, so instead of being subtracted from the total required return, they should be added to the total required return.
###F_T = S_0.e^{(r_\text{total} + r_\text{costs}).T}### ###\begin{aligned} F_3 &= S_0.e^{(r_\text{total} + r_\text{costs}) \times 3} \\ &= 700 \times e^{(0.1 + 0.02) \times 3} \\ &= 1,003.33059 \\ \end{aligned}###