G/L on a FRA

CFA Level II Derivatives
#1

Entering long 6x12 FRA; What is the gain/loss after 45 days ? ($10,000,000 Notional)

Today’s rates are:

30 day rate = 5.10%

90 day rate = 5.25%

180 day rate = 5.70%

360 day rate = 5.95%

After 45 days the new rates are:

135 day rate = 5.90%

315 day rate = 6.15%

#2

180-day contract on the 180-day LIBOR:

h = 180; m = 180; g = 45; h - g = 135; h + m = 360; h + m - g = 315

FRA = { [1 + 0.0595 * (360/360)] / [1 + 0.057 * (180/360)] - 1 } * (360/180) = 0.06028

Interest(h - g) = Interest(135) = 5.9%

Interest (h - g + m) = Interest (315) = 6.15%

Value = { 1 / [1 + 0.059 * (135/360)] } - { [1 + 0.06028 * (180/360)] / [1 + 0.0615 * (315/360)] } = 0.000817593

10M * 0.000817593 = 8175.93

#3

hey official answer is $8100,

but thx for that Value formula, it was the missing link to me

#4

Can you please post the solution? Thanks.

#5

You forgot to calculate the FRA rate at initiation to plug in that value formula. You used 0.057 and the right value was 0.0603

This question was on the 2010 cfai book. THe book is actually missing 3 pages on this reading, i didnt even realise until this

#6

Thanks for sharing. Updated the original post to show the right calculation.

#7

Hi Aether, i am working on the latest curriculum of CFAI…was going through the practice problems for Reading 48…

Question : A security is worth $225. An investor plans to purchase this asset in one year and is concerned that the price may have risen by then. to hedge this risk, the investor enters into a forward contract to buy the asset in one year. Assume that the risk free rate is 4.75%

Suppose that at expiration, the price of the asset is $190. Calculate the value of the forward contract at expiration. Also indicate the overall gain or loss to the investor on the whole transaction…

Ans : S(t) = $190, F(0,T) = 235.69, V (0,T) = 190-235.69 = -45.69

Loss to Long position = 45.69

Gain on asset = 35 (based on 225-190)

Net Loss = -10.69

My question is that as investor is not sure of the future movement of the asset he went long on the forward contract. On expiry he will take delivery of the asset at the fixed forward price and sells the asset in the market at the price prevailing in the market which is 190. When calculating Net loss why did we include both loss on long position and gain on asset.

What am i missing here??? I thought value of the forward contract should be taken as net loss or gain. Kindly explain if possible…

#8

This was raised in another post: http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91317353

It is easier to think of this concept in terms of closing out all your open positions. You’re not only selling the asset, but also closing out your forward position.

#9

Yes i also accessed that and asked the question once again…What all open positions are we talking about.

When i have gone long on forward i have only one open position and this position gets expired on expiry…

#10

In baby steps:

  1. You think you’ll buy the asset in a year for $225.
  2. Based on this price, you enter a forward contract which is worth $235.69.
  3. At expiration, the asset’s worth only $190. The forward contract gets executed.
  4. So instead of spending $225, you’re now going to pay only $190. Here’s the implicit gain of $35… more money in your bank account than what would have been had the asset been worth $225. Think of this as your opportunity cost (or in this case, gain).
  5. Simultaneously, the forward contract actually gets executed and books a loss of -$45.69.

Hope this helps.

#11

yup…that was useful…thanks a ton…

#12

aether could you identify who the long and short are in your example – im looking at question 10 pg 121 of derivative curriculm book . thx

#13

Axia needs USD for its operations. So it wants to own the asset (USD) in this case. Hence, it goes long the contract and Stream Partners goes short. If rates increase, Axia makes money. Otherwise, Stream Parters does.

#14

HI

I am not sure of the overall gain or loss calculation.

  1. Assuming that the price of the asset is going to rise. The investor enters into the forward contract as a long to buy the asset at $235.69. (Calculated from solution to A)

  2. At expiration, asset is worth $190 and forward contract gets executed at $235.69. SO the investor makes a loss on of - $45.69 on the contract itself.

  3. NOw the investor has to buy an asset at 235.69 due to his forward contract, but the actual market price is only $190. …STOPPPPP!!! I got it why the overall loss is only $10.69 enlightened

Just shows how much helpful this forum is to clear concepts. smiley

Just realized that at expiration the long party will only pay 45.69 to the short and get out of contract without actual taking the delivery of the asset. Hence he had a gain via opportunity to postpone his decision of buying the asset.(Aether thanks for mention of opportunity cost. That gave the insight)

Thanks for raising the topic here.

cheers,

dealdone