 # Currency Forward Valuation

Assuming there is a forward contract to deliver 1000 GBP@1.5 USD/GBP and the current spot is 1.55 USD/GBP. Contract expires in 1 year. Interest rates for GBP is 5% and USD is 6% What is the value of this contract. I have seen a solution in Schweser notes for exactly this kind of question but I am not getting the hang of their logic, as I’m thinking in a different way. Can you guys comment on how to do this? Thanks

*bump* anyone?

Forward / Spot =(1+rD) / (1+rF) F/(1+rD) - S/(1+rF) As per schweser = PV of inflows - PV of outflows 1.5/1.06 - 1.55-1.05 0.0611*1000=-£61.1 Counterparty is having credit risk. Also, as manager is short on GBP…he would gain if GBP falls … in this case GBP increases in value… manager is loosing on forward contract.

Hi Rakesh, Agree with your calculation. However, should it be -USD61.1 as the answer? Would you please confirm? Tks!

As per my understanding : The Forward Rate, f0 if Interest Rate Parity holds is equal to 1.53538 USD/GBP spot0 * (1+rd)/ (1+rf) Since the contract is sold at 1.5 USD/GBP, the PV of the difference should be the value of the contract to the long position. (1.5358 - 1.5)/1.05 * 1000 = 33.6\$ Since this is a short position, he owes 33.6\$ or 21.7 GBP. Correct me if I’m wrong.

James@Houston Wrote: ------------------------------------------------------- > Hi Rakesh, > > Agree with your calculation. However, should it > be -USD61.1 as the answer? Would you please > confirm? > Tks! Hi James, You are right. Made a mistake while typing. Thanks apnesapne^2. If I remeber correctly, for ccy forwards we always discount forward rate denominated as (D/F) at domestic rfr and Sopt rate (D/F) at foreign rfr.

Hi apnesapne^2, Agree with Rakesh’s explanation about the (D/F), which is indirect method for the FX rates.

ibrookie Wrote: ------------------------------------------------------- > Assuming there is a forward contract to deliver > 1000 GBP@1.5 USD/GBP and the current spot is 1.55 > USD/GBP. Contract expires in 1 year. Interest > rates for GBP is 5% and USD is 6% > > What is the value of this contract. > > I have seen a solution in Schweser notes for > exactly this kind of question but I am not getting > the hang of their logic, as I’m thinking in a > different way. > > Can you guys comment on how to do this? > > Thanks ibrookie, Would you please post the Schweser answer? Thanks!!

Rakesh Wrote: ------------------------------------------------------- > Forward / Spot =(1+rD) / (1+rF) > > F/(1+rD) - S/(1+rF) > > As per schweser = PV of inflows - PV of outflows > > 1.5/1.06 - 1.55-1.05 > > 0.0611*1000=-£61.1 > > Counterparty is having credit risk. > > Also, as manager is short on GBP…he would gain > if GBP falls … in this case GBP increases in > value… manager is loosing on forward contract. how can you do it that way. 1.5/0.06 - 1.55/1.05 I did it the long way and got -64.76 calculated our the implied F rate using Forward / Spot =(1+rD) / (1+rF) the Forward rate comes out too F = 1.55* (1.06/1.05) which is 1.56476 usd/gbp (us interest rate over GBP interest rate) since the contract is 1.5 usd/gbp and F rate is worth 1.56476 usd/gbp, meaning GBP is worth more in the Foward rate for today, whoever long GBP is at a gain. contract shorts GBP, thus a lost. it’s (1.5 - 1.56476 ) * 1000 = -64.76

whystudy Wrote: ------------------------------------------------------- > Rakesh Wrote: > -------------------------------------------------- > ----- > > Forward / Spot =(1+rD) / (1+rF) > > > > F/(1+rD) - S/(1+rF) > > > > As per schweser = PV of inflows - PV of > outflows > > > > 1.5/1.06 - 1.55-1.05 > > > > 0.0611*1000=-£61.1 > > > > Counterparty is having credit risk. > > > > Also, as manager is short on GBP…he would > gain > > if GBP falls … in this case GBP increases in > > value… manager is loosing on forward > contract. > > > how can you do it that way. 1.5/0.06 - 1.55/1.05 > > I did it the long way and got -64.76 > > calculated our the implied F rate using Forward / > Spot =(1+rD) / (1+rF) > the Forward rate comes out too F = 1.55* > (1.06/1.05) which is 1.56476 usd/gbp (us interest > rate over GBP interest rate) > > since the contract is 1.5 usd/gbp and F rate is > worth 1.56476 usd/gbp, meaning GBP is worth more > in the Foward rate for today, whoever long GBP is > at a gain. contract shorts GBP, thus a lost. > it’s (1.5 - 1.56476 ) * 1000 = -64.76 whystudy, there is a tiny part missing in your last step. -64.76 is the FV in 1 yr. It needs to be divided by 1.06 in order to discount back to PV using domestic interest rate. We will get the same answer of -\$61.1 again.

James@Houston Wrote: ------------------------------------------------------- > whystudy Wrote: > -------------------------------------------------- > ----- > > Rakesh Wrote: > > > -------------------------------------------------- > > > ----- > > > Forward / Spot =(1+rD) / (1+rF) > > > > > > F/(1+rD) - S/(1+rF) > > > > > > As per schweser = PV of inflows - PV of > > outflows > > > > > > 1.5/1.06 - 1.55-1.05 > > > > > > 0.0611*1000=-£61.1 > > > > > > Counterparty is having credit risk. > > > > > > Also, as manager is short on GBP…he would > > gain > > > if GBP falls … in this case GBP increases > in > > > value… manager is loosing on forward > > contract. > > > > > > how can you do it that way. 1.5/0.06 - > 1.55/1.05 > > > > I did it the long way and got -64.76 > > > > calculated our the implied F rate using Forward > / > > Spot =(1+rD) / (1+rF) > > the Forward rate comes out too F = 1.55* > > (1.06/1.05) which is 1.56476 usd/gbp (us > interest > > rate over GBP interest rate) > > > > since the contract is 1.5 usd/gbp and F rate is > > worth 1.56476 usd/gbp, meaning GBP is worth > more > > in the Foward rate for today, whoever long GBP > is > > at a gain. contract shorts GBP, thus a lost. > > it’s (1.5 - 1.56476 ) * 1000 = -64.76 > > > > whystudy, > there is a tiny part missing in your last step. > -64.76 is the FV in 1 yr. It needs to be divided > by 1.06 in order to discount back to PV using > domestic interest rate. We will get the same > answer of -\$61.1 again. yes, you are right. always the NPV… i miss that everytime.

whystudy – I missed exactly the same thing doing a similar question in the 09 AM exam just last weekend. Hopefully this discussion would enable us to remember all the tiny steps and apply them accurately in the coming June exam while under tremendous time-pressure. Wish both of us best luck to knock this down!!

apnesapne^2, whystudy - I was doing the exact same thing and hence the schweser formula made no sense to me. I think I have understood it now - See, Schweser had also given the formula as F/(1+rD) - S/(1+rF), but to me it seemed a bit hard to understand purely by intuition as you would need to calculate expected forward exch rate by IRP and then see whats the loss/gain. Logically, to calculate the value of the contract, you need to compare the expectation of spot with forwards price. Anyways, this is how i arrived at the schweser formula, using IRP This is from the perspective of long position on USD Spot Price = SP0 Forward = Fd Expected Spot = SP0*(1+rd)/ (1+rf) Hence compare forward price with expected spot Forward contract value (At contract Expiry)= SP0*(1+rd)/ (1+rf) - Fd Forward contract value (At contract Expiry)= {SP0*/ (1+rf) - Fd/ (1+rd)} (1+rd) Now this needs to be discounted to today, i.e. by 1/(1+rd) Forward contract value (Today)= {SP0*/ (1+rf) - Fd/ (1+rd)} (1+rd)*1/(1+rd) Forward contract value (Today)= SP0*/ (1+rf) - Fd/ (1+rd) So now the formula and IRP become in line with each other.

CAFI 2009 AM exam guideline answer Q9 Part B1 shows both short and long methods in this discussion step by step. It can be a good reference for such currency forward contract. The short method (same as schweser formula mentioned above) seems hard to understand in the 1st place, but it starts to make sense after reading through the long method.