Currency Forward Contract

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Char-Lee

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The spot rate for British pounds is $1.76. The US risk-free rate is 5.1 percent and the UK risk-free rate is 6.2 percent; both are compounded annually. One-year forward contracts are currently quoted at a rate of $1.75.
Identify a strategy with which a trader can earn a profit at not risk by engaging in a forward contract, regardless of their view of the pound’s likely movements. Describe the transaction the trader would make. Show rate of return that would be earned from this transaction. Assume the trader’s domestic currency is US dollar.
 
@ first glance we see UK rate is about 110 bips higher yet fwd only off 1 big figure…. must be opportunity for arb! Right away you should notice this disparity.
I’m gonna borrow 1,000 USD @ 5.1% and owe 1051 in one year.
Convert my 1051 to GBP @ 1.76 to get 597 pounds. Enter into FWD at same time.
Invest my 597 @ 6.2% to get 634 GBP in 1 year.
Convert back at fwd rate of 1.75 to get 1110 USD…
Pay back my loan of 1051 to get 59 USD risk Free…. Boo Yah!
Return should be around 5.9%
 
fxguy1234, i’m happy you were kicking around the board because I’ve been struggling with this one… more so because i can’t really follow CFAI’s answer. She if you can shed some light, because your answer makes sense to me.
CFAI answer verbatum
With the forward contract selling at $1.75, it is slightly overpriced. Thus, the trader should be able to buy the currency and sell a forward contract to earn a return in excess of the risk-free rate atno risk. The specific transactions are as follows
1) Take $1.76/(1.062) = $1.6573. Use it to buy 1/1.062 = 0.9416 GBP
2) Sell a forward contract to deliver 1.00 GBP in one year at the price of $1.75.
3) Hold position for one year, collecting interest at the U.K. risk-free rate of 6.2 percent. The 0.9416 GBP will grow to (0.9416)(1.062) = 1.00GBP
4) At expiration, deliver the pound and receive $1.75. This is a return of
1.75/1.6573 - 1 = 0.0559
A risk-free return of 5.59 percent is better than the US risk-free rate of 5.1 percent, a result of the fact that the forward contract is overpriced.
——————————————————————————–
also, why in step one do you discount the $1.76 by the GBP rf rate?
when i tried to solve this i said; ok, the forward quote is high so i want to short the forward and buy the asset… so that means buy GBP now and hold to deliver for the forward short position…. at this point my mind begins to melt
 
so when i put pen to paper to solve this is what i did
NOW
short forward 1.75 $/GBP
buy 1000 GBP / 1.062 = 941.6 GBP
borrow $ to pay for 1000 GBP: 941.6 GBP * 1.76 $/GBP = $1,657.2
At expiration
941.6 GBP * 1.062 = 1,000 GBP
Sell 1,000 GBP at 1.75 $/GBP for $1,750 to close contract
pay off dollar loan: 1,657.2 * 1.051 = 1,741.73
profit = 1750 - 1742 = $8
return should be 8/1742 = 0.47%
what did i mess up?
 
Char-Lee Wrote:
——————————————————-
> > CFAI answer verbatum
>
> With the forward contract selling at $1.75, it is
> slightly overpriced. Thus, the trader should be
> able to buy the currency and sell a forward
> contract to earn a return in excess of the
> risk-free rate atno risk. The specific
> transactions are as follows
>
> 1) Take $1.76/(1.062) = $1.6573. Use it to buy
> 1/1.062 = 0.9416 GBP
>
> 2) Sell a forward contract to deliver 1.00 GBP in
> one year at the price of $1.75.
>
> 3) Hold position for one year, collecting interest
> at the U.K. risk-free rate of 6.2 percent. The
> 0.9416 GBP will grow to (0.9416)(1.062) = 1.00GBP
>
> 4) At expiration, deliver the pound and receive
> $1.75. This is a return of
>
> 1.75/1.6573 - 1 = 0.0559
>
> A risk-free return of 5.59 percent is better than
> the US risk-free rate of 5.1 percent, a result of
> the fact that the forward contract is overpriced.
>
> ————————————————–
at step1) borrowed $1.6573.
at the end , should pay back $1.6573*1.051=1.7418.
which is not in CFA i calucation.
their explanation is strange.
is this from CFA i curriculum?
which page?
 
@fxguy, your calculations are not correct. especially this part: ‘I’m gonna borrow 1,000 USD @ 5.1% and owe 1051 in one year. Convert my 1051 to GBP @ 1.76 to get 597 pounds.’
the first part is correct, you borrow 1000USD but you do not convert 1051 at the spot!
@char-lee,
the post:
so when i put pen to paper to solve this is what i did
NOW
short forward 1.75 $/GBP
buy 1000 GBP / 1.062 = 941.6 GBP
borrow $ to pay for 1000 GBP: 941.6 GBP * 1.76 $/GBP = $1,657.2
……….
return should be 8/1742 = 0.47%
what did i mess up? IS CORRECT! YOU HAVE IT!
——————————————————————————-
here’s how i did it:
borrow domestic: USD
NOW:
borrow 1000USD.
convert 1000USD into GBP at spot=568.2GBP
put the 568.2GBP to work at 6.2% = 603.43GBP
FUTURE:
pay back USD: 1000*1.051=1051USD
return from GBP investment: 603.43GBP * 1.75=1056USD
so we have a RFR(GBP) of 5.6% vs. 5.1% RFR(USD)
depending on rounding you might get a slightly different result.
cheers
 
borrow $1000 -> payback $1051
Convert $1000 to Pound at Spot –> 568.18181 Pounds
Lend Pound and get back -> 603.40909090 Punds
Convert Pound to $ at Fwd Contract rate -> 1055.965909$
Payback 1051 from 1055.965909 –> Riskless profit 4.9659090909090
Does this look correct?
 
Barthezz, thank you! i thought i was loosing my mind.
to answer a question above, yes this is a CFAI questions. You can find it on page 42 of Volume 6 in Reading 60 (Forward Markets and Contracts).
 
ahhh yes end of calc for me…. 1000 to GBP, not 1051 (its what you owe)
I had the correct logic, although
 
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