current spot rate is $2 per $CS, CS’s interest-free rate is 3%, U.S. interest-free rate is 5%, one year forward rate is $2.1 per $CS. what’s the profit from borrowing $1000 or equivalent $CS?
F = 2 /CS \* (1.05/1.03) = 2.038835 /CS CS overvalued in F mkt, $ undervalued in F mkt. 1. Borrow $1000, at t=1, owe 1000*1.05 = $1050 $1000 is equivalent to $1000* (1 CS/$2) = 500 CS 2. Lend 500 CS, at t=1, receive 500*1.03 = 515 CS 3. Sell 515 CS forward, 515 CS * ($2.1 / 1 CS) = $1081.5 Profit = $31.5 Correct?
Short fwd, buy spot; profit = $58.25 2.1/1.05 - 2/1.03 = 58.25
F = 2* 1.05/1.03= 2.0388 dollar per C dollar US = undervalued in F mkt buy F borrow US 1000 convert to $C at sport $C500 earn interest 1.03 *500 =$C 515 covert at F one yr later 2.1 * 515= 1081.5 Pay back 1000*1.05= $1050 profit 1081.5-1050 =$31.5 * not so sure but this would be my attempt
Everyone has a different method. I have a way of doing these where it’s just automatic for me.
$31.5 is the right answer. if the question doesn’t have the “borrowing $1000” part, what would the arbitrage profit be?
agree with topher’s method
I tried this problem from a different perspective than usual in an attempt to 1. understand the material better, and 2. bring together two peices of the curriculum Obviously, I must be conecting dots that do not exist. The way I approached the problem was to find the value of a currency fwd contract and interpret that as the profit where: V = S/(1+rf) - F/(1+r) So if you short the fwd and buy the spot you end up with: 2.1/1.05 - 2/1.03 = .05825 * 1000 = 58.25 Anyone know what went wrong here? I would think these formulas would be interchangeable somehow. I was thinking it might have something to do with the fact that I shorted the fwd whereas this is the value to the long investor (that’s why I rearanged the equation above to show the higher fwd value less the lower spot)
finninja – the 2$ is Current Spot. Not the spot at the time that the Future was due (1 year later).
Give 'em hell this year cpk.
CPK, are you thinking that this should be the spot defined by IRP? 2.1/(1+.05) - 2.0388/(1+.03) = .02058
FinNinja Wrote: ------------------------------------------------------- > I tried this problem from a different perspective > than usual in an attempt to 1. understand the > material better, and 2. bring together two peices > of the curriculum > > Obviously, I must be conecting dots that do not > exist. > > The way I approached the problem was to find the > value of a currency fwd contract and interpret > that as the profit where: > > V = S/(1+rf) - F/(1+r) > > So if you short the fwd and buy the spot you end > up with: > > 2.1/1.05 - 2/1.03 = .05825 * 1000 = 58.25 > > Anyone know what went wrong here? I would think > these formulas would be interchangeable somehow. > > I was thinking it might have something to do with > the fact that I shorted the fwd whereas this is > the value to the long investor (that’s why I > rearanged the equation above to show the higher > fwd value less the lower spot) your calculation is almost correct, which ccy is 1000 notional? becuse the rates are usd/cad the notional should be in cad, 1000usd devided by current spot is 500cad. the profit is then in usd and the calculation gives upfont (PV) profit using forward 500 notional cad therefore your profit is different to the others solution because they use more cash in t0. so profit = 58.25 / 2= 29.125 realized in t0
For it to net out - instead of the 2.03xxx number you need the Actual Spot- not the expected spot based on IRP. [2.0388xx is the E(S)]
cannot edit my previous post continue here and if we used forward notional 515 (see tophers post) the t0 usd profit would be 30. and fv (x 1.05) equals 31.50
Profit is definitely $31.50 1. Borrow US $1000 @ USD rate = $1000 x 1.05 = $1050 2. Convert $1000 USD to $CS at current spot rate = CS$500 3. Invest CS$500 at foreiign interest rate of 3% = CS$500 4. Convert back to $US at end of year rate = $500 x 2.10 = US$1,081.50 5. Pay back lenders $1,050 and profit $31.50
pfcfaataf Wrote: ------------------------------------------------------- > cannot edit my previous post > > continue here > > and if we used forward notional 515 (see tophers > post) the t0 usd profit would be 30. and fv (x > 1.05) equals 31.50 pfcfaataf - could you post your work?
- sell forward 500 cs ag 1050 usd 2. discount (finance) this to t0 485.44 cs and 1000 usd 3. convert 485.44 cs at spot 970.78 us 4. net us t0 you get 29.126 usd profit this is mathematically equal to (2.1/1.05 - 2/1.03) x 500 the profit is upfront and I convert forward only 1050 usd and equivalent cs here I also borrow 1000 usd but need only roughly 970.78 usd to convert at spot to cs if I wanted to invest my own usd into this (meaning I dont need to borrow anything) I would invest only 970.78 and I would receive in 1y 1050 usd = return = (1050 - 970.78)/970.78 = 8.16 pct if say topher wanted to invest his own usd he would invest 1000 usd in t0 and receive 1081.5 in t1= return on his investment = 8.15 pct same pct return (difference due to rounding)
maybe I should add that tophers calculation is better because he sends more cash through this arbitrage opportunity.
so let me hear your two centavitos: gain on usd investment roughly = .02 loss on forward = .05 = arbitriage gain from investing and borrowing and all that good stuff = 1000*.03 =30 I realize this is pretty simple but could my logic be used on exam day?