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# FRM 2008 PII q21 - Delta of long forward

#### fullofquestions

##### New Member
The dividend yield of an asset is 10% per annum. What is the delta of a long forward contract on the
asset with 6-month to maturity?
a. 0.95
b. 1.00
c. 1.05
d. Can not be determined without further information.

Calculation:
The value of a long forward contract
f = S0 e-qT – K e-rT,
where S0, q, T, K, and r are the asset price, dividend yield, time to maturity,
delivery price, and risk-free rate, respectively.
It follows that the delta of the forward = e-qT.
Given q = 10% and T = 1/2, we have delta = e-10% / 2 = 0.95

a. Correct. Shown from the calculations above.
b. Incorrect. Derived erroneously by not accounting for the dividend.
c. Incorrect. Derived erroneously by mixing up the sign of exponential.
d. Incorrect. It can be determined with the given information as shown above.

The explanation comes a bit short. Without r we really cannot tell if delta is positive or negative. This answer is incomplete in my opinion. Is this correct?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi FoQ,

Question is correct: delta of a futures contract would require rate (r), but delta of a *forward* is 1.0 w/o dividend, or exp(-qT) with dividend. Futures with dividend = exp[(r-q)*T]

David