Charta is on Google Play: practise on the go. Get the app
Charta

Contrast a forward contract's value with its forward price.

FRM® Part I · Financial Markets and Products · Pricing Financial Forwards and Futures · FRM1.FM.10.e

The idea

The forward price and the value of a forward contract are different things. The forward price is the delivery price that would make a new contract with the same maturity worth zero today, and it changes as spot prices and rates change. The delivery price K is the fixed price written into an existing contract. At initiation K equals the forward price and the value is zero. Later, T is the time left to delivery, r the risk-free rate and F the current forward price for the remaining life. The long forward is then worth f = (F − K) × e^(−rT). This is the discounted difference between F and K. For an asset with no income, the long's value in terms of the spot price S is f = S − K × e^(−rT). The short position is worth the negative of this. Typical mistakes are to report F minus K without discounting, or to treat the forward price as the value of the contract. A contract's value can be positive or negative, whereas the forward price of a share, like any share price, is positive.

Formulas

Value of a long forward from the current forward price

f = (F − K) × e^(−r × T)

F
the current forward price for the remaining life
K
the delivery price written into the existing contract
r
the continuously compounded risk-free rate, per year
T
the time left to delivery, in years

Zero at inception, when K equals the forward price. Forgetting to discount F − K is the usual error; the short is worth the negative.

Value of a long forward on a non-income asset

f = S0 − K × e^(−r × T)

S0
the spot price now
K
the delivery price written into the existing contract
r
the continuously compounded risk-free rate, per year
T
the time left to delivery, in years

Spot less the present value of the delivery price. It can be negative, unlike a forward price.

A practice question

From the question bank, with the reason each wrong option is wrong.

Immediately after a forward contract is entered into at the prevailing forward price, its value to the long party is:

  1. zero - correct
  2. positive, because the long benefits if the price risesWhy not: Ignores that the short benefits equally if the price falls; the contract is set to have zero value.
  3. equal to the forward priceWhy not: Confuses price and value; the delivery price is not paid at inception.
  4. equal to the present value of the forward priceWhy not: Same confusion of price with value, with discounting added.

At initiation the delivery price equals the forward price, so the contract has zero value to both parties.

A harder one

A long forward on a non-income stock has delivery price USD 45.00 and one year to maturity. The spot price is USD 50.00 and the risk-free rate is 8% continuously compounded. The value of the long position is closest to:

  1. USD 1.26Why not: Compounds the delivery price (K x e^(rT)) instead of discounting it.
  2. USD 5.00Why not: Takes spot minus delivery price with no discounting of the delivery price.
  3. USD 8.47 - correct
  4. USD 9.16Why not: Takes the current forward price minus K without discounting.

f = S - K x e^(-rT) = 50 - 45 x e^(-0.08) = 50 - 41.53 = USD 8.47.

The hardest tier

A one-year forward on a non-income stock was entered into at its then forward price of USD 100 (spot then USD 95.12, with a risk-free rate of 5% continuously compounded). Six months later the spot price is USD 103 and the rate is unchanged. The value of the long position is closest to:

  1. USD 3.00Why not: Takes the spot price minus the delivery price, ignoring the time value of the delivery price.
  2. USD 5.47 - correct
  3. USD 5.63Why not: Uses the new forward price (103 x e^0.025 = 105.63) minus 100 without discounting.
  4. USD 7.88Why not: Takes the gain in the spot price since inception, as if the contract's value moved one-for-one with spot.

f = S - K x e^(-rT) = 103 - 100 x e^(-0.05 x 0.5) = 103 - 97.53 = USD 5.47.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Pricing Financial Forwards and Futures