Forwards and futures - Commodities, financial

Question 1

Define a commodity

Answer 1

A commodity is characterized by its physical characteristics and properties, the date of its availability, the location.

Question 2

elaborate on the price of a commodity

Answer 2

The price of a commodity is the price that must be payed NOW to get the commodity in the future.

Question 3

corn in differnet months, same commodity or not?

Answer 3

Not. Different unit

Question 4

why do we differ between commodities of the same item from different months?

Answer 4

Because commodities has the issue or storage and transportation and other costs that occur in real life. These are not subject to financial forwards, but only commodities.

Question 5

give the forward price on a financial asset

Answer 5

F_{0,T} = S_0 e^{(r-l)t}

Euler term is a multiplicative constant resulting from continuous compounding. Accurate representation of the time value of money. r is the rate, l is the dividend (assuming continuous etc), and t is the time in years or whatver r and l are given as.

Question 6

Why use euler for the interest term?

Answer 6

Allows each sub-period interval of any size to be equal to each other in regards to the interest rate received.

Intersting to consider what happens if the process was linear. If so, the gain early on in absolute points is the same as later. Therefore, the percentage gain is largest early on. Therefore, it is better to invest early. But this doesnt make any sense. We know from before that timing doesnt matter. Cash flows and all that matter, and time horizon does not.

As a result, we want a measure that always gives the same rate of return for a X-sized interval.

To get this, we consider:

(r-l)t = ln(x)
r-l = 1/t ln(x)
if no dividends:

r = 1/t ln(x), where x is the factor. This gives a return that is proportional to the size of the time period we’re looking at.

An alternative way of finding this result, is considering what happens if we consider annual rate of return x, and make it smaller and smaller and apply it at each small time step.
(1+r/n)^(nt). In the limit, this reach e etc

Question 7

do we expect the forward price of commodities to be the same as for financial forwards?

Answer 7

No. mainyl due to other costs.

Seasonality

Storage costs

Many different aspects of commodities makes prices not follow the standard forward price formula that govern financial forwards.

Question 8

the 4 important aspects of commodities in regards to forwards?

Answer 8

1) Storage costs. Includes deterioration

2) Carry markets. markets that compensate the holder for holding the hsit.

3) Lease rate

4) Convenience yield. For instance, having gold in a safe for you to look at might have convenience yield. Having something ready at hand might have convience yield.

Question 9

what is contango

Answer 9

forward curve is sloping upwards

Question 10

what is backwardation

Answer 10

forward curve is sloping downwards

Question 11

elaborate on backwardation

Answer 11

short term supply pressure.

Question 12

what is prepaid forward price

Answer 12

Prepaid forward price is the price we pay today for receiving an asset in the future. Therefore, it is typically just the present value of the commoditiy on the future date.

PrepaidForward = e^(-at) E_0[S_T]

Take the expected value of the asset at time t=T, and discount it using the appropriate rate.

Question 13

what is the relationship between forward price and prepaid forward price

Answer 13

The forward price is equal to the prepaid forward, but after applying the future value operation.

Notice that both prepaid forwards and forward contracts does not reap the rewards of dividends of other benefits associated with holdign the asset.

Question 14

what is the formula for forward price when considering the prepaid price

Answer 14

the risk premium battle against the rate.

Question 15

why do we use differnet rates for discounting the expected value of the future asset price level, and for the computation of the future value?

Answer 15

r is for risk free shit only.
We must use alpha for the commodity because it is risky, and therefore has a risk premium associated with it.
On the other hand, when we take the predicted/expected prepaid price, and compute future value, we are computing the future value of the contract, not the asset itself.

Question 16

elaborate on the equilibrium condition on something like copper

Answer 16

it relates to the cost of extraction, not storage. ASSUMING that it is easily extractable and can be done swiftly.

Question 17

why might it look like commodities can create arbitrage opportunities?

Answer 17

Shorting it requires someone willing to lend out the commodity. Since doing this is a risk free loan, they would require a rate. this rate will make arbitrage go away.

this creates the concept of lease

Question 18

what is cash and carry

Answer 18

buy asset in spot market, store (carry) the asset until maturity, sell a forward contract at the overpriced forward price

It is a way of exploiting mispricing between spot and forward based on the cost of holding

Question 19

what is reverse cash and carry

Answer 19

short asset, invest proceeds in risk free loan, buy the asset back at maturity via a cheapish forward

Question 20

how can we view storage costs?

Answer 20

As a negative dividend

Question 21

how does storage cost affect reverse cash and carry

Answer 21

It doesnt, since no party involved in the trade has the issue of storing it

Question 22

Recall the 3 steps to making a trade

Answer 22

1) Agree on price
2) Transfer cash
3) Transfer shares

Question 23

4 types of trades

Answer 23

1) Outright purchase (pay now, get now)
2) Fully leveraged purchase (pay later, get now)
3) Prepaid forward contract (pay now, get later)
4) Forward contract (pay later, get later)

These are defined by changing the timing of the cash transfer and the timing of the share transfer

Question 24

what is “allowed” by the seller when he sells something using a prepaid forward?

Answer 24

He retains ownership for some time, but has already sold the asset

Question 25

We can derive the pricing of a prepaid forward using 3 differnet methods...?

Answer 25

1) analogy 2) No arbitrage 3) present value

Question 26

derive prepaid forward price using analogy

Answer 26

If there are no dividends on the stock, then the prepaid forward have a value at t=T that is equal to the stock itself. The question is how much we are willing to pay NOW to get this later. The answer is that it is exactly the same as buying spot.

Question 27

derive prepaid forward price using present value

Answer 27

for this, we need to first compute the expected value of the stock at t=T, and then we discount it using the appropriate risk rate alpha. How do we compute expected value? By definition, we expect it to increase by alpha. so we compound and discount using alpha, which cancel out. This leaves us with: S_0 e^(alpha-alpha)t = S_0 spot price NB: in the absence of dividends

Question 28

derive prepaid forward price using no arbirtage

Answer 28

This is done by considering what would happen if the prepaid forward price is either higher or lower than spot. It essentially creates a scenario where we have risk free profit with zero net investment.

Question 29

elaborate on pricing prepaid forwards with dividends

Answer 29

The first thing to understand is that since the prepaid forward doesnt give you the dividends, it should be worth less than the stock itself. In the case of a discrete dividend, we simply take the spot price, and then subtract the sum of present value computed discrete dividends. If the dividend is continuous, we need to adjust so that we actually end up at t=T with a single share. This is done by multiplying the stock price at t=0 by e^(-∂t). This makes us invest a smaller amount initially, and because of the continuous dividend yield, which is auto-reinvested, we end up with a single share. This builds on a couple of assumptions that are not met in practice, but the idea is that by investing less than a share, we end up with a share. This allows us to compare the asset price to the prepaid forward price.

Question 30

if we know the prepaid forward price, how do we find the forward price?

Answer 30

We use future value computation using the risk free rate. We use risk free rate because the alternative is to invest the proceeds in a risk free asset in the meantime, rather than paying at t=0.

Question 31

formula for forward price when continuous dividend

Answer 31

Question 32

define forward premium

Answer 32

forward premium is the ratio between forward price and spot price

Question 33

does forward price predict the future price?

Answer 33

forward price equals the expected future spot price, but with a discount for the risk of the asset. This is a systematic error.

Question 34

elaborate on the risk of a forward contract, relate it to pricing

Answer 34

if we enter a forward contract, we are not compensated for hte time value of money. however, we are compensated for the risk premium of the asset. We end up with: ForwardPrice = prepaidForward x e^(rT) = ExpectedFutureStockPrice x e^(-aT) e^(rT) = ExpFutStockPrice x e^(-(a-r)T)

Question 35

how can a market maker offset the risk of a forward contract?

Answer 35

Synehtetic forward If the market maker takes the short side of a forward contract, he must hedge it by creating a synthetic forward long position. A long synehtetic forward position can be established using stock+borrwoing. What the market maker needs, is the same payoff as the forward position in which he is short. At maturity, the long position in the forward contract earns "S_T - F_{0,T}". this is the payoff we need as well. If we borrow S_0 e^(-∂T), we get a share at t=T. We need to repay S_0 e^((r-∂)T). With this position, at maturity, we (market maker) get S_T - S_0 e^((r-∂)T), which we recognize as the forward price in the case of cont div: S_T - F_{0,T}. the price of this position must be the same as the regular forward, because their payoffs are the same.

Question 36

compare forwards and futures

Answer 36

Futures are exchange traded. Futures settle daily, while forwards settle at expiration. This means that payment is done daily. Becauseo f this, futures are very liquid. It is easy to enter offsetting positions. Offsetting is done by simply taking the reverse trade. Since settlement is done daily, loss == profit, and nothing happens. Forwards are typically more tailored and customized and OTC, while futures are standardized.