covered interest arbitrage question current, forward, question, interest, equivalent

chunty

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?

stalkey

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?

yodacaia

1. 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)

profil

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

DSquaredSlim

Give 'em hell this year cpk.

yospaghetti

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



Edited 2 time(s). Last edit at Wednesday, April 28, 2010 at 04:58PM by pfcfaataf.

RMontgomery

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)]

CP

wizofoz

$31.5 is the right answer.

if the question doesn't have the "borrowing $1000" part, what would the arbitrage profit be?

xilinx_altera

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?

onelife1

Everyone has a different method. I have a way of doing these where it's just automatic for me.