I don’t understand why the approach that works in econ doesn’t work in derivatives. However, if I modify it in a way that doesn’t make sense I get the right answer. For example: Spot rate of euro = 1.0231 risk free = 4% risk free euro = 5% 6 month forward price of euros = 1.0225 What % profit can you earn through arbitrage? CFAI does it one way and gets 2.37% semiannual or 4.74% annual If you do it the way they say in econ: Arbitrage price \< forward market price, so sell forward and borrow to buy spot Semi annual risk free = 1.04^ (180/365) = 1.0195 Semi annual risk free euro = 1.05 ^(180/365) = 1.0244 Borrow $1,000 @ 1.0195 = $1,019.53 Convert $1,000 into euro at the spot rate of 1.0231 = 977.42 euros Lend 977.42 euros at euro risk free of 1.0244 = 1,001.27 euros Convert euros back to at the forward rate = 1,001.27 euros * 1.0225 = $1,023.8 Rate of return = [($1,023.8 / $1,019.53) - 1] = .4188% semi annual = .8376% annual, which is wrong HOWEVER, if you take the full amount that you borrow ($1,019.53) and use that instead of the $1,000, you get the right answer. Why does this work? Borrow $1,000 @ 1.0195 = $1,019.53 Convert $1,019.53 into euro at the spot rate of 1.0231 = 996.5 euros Lend 996.5 euros euros at euro risk free of 1.0244 = 1020.83 euros Convert euros back to at the forward rate = 1020.83 euros * 1.0225 = $1,043.79 Rate of return = [(1,043.79 / $1,019.53) - 1] = .2.38 semi annual = 4.76% annual, which is right This doesn’t make sense b/c you wouldn’t be able to lend more than you borrowed. Yet this approach worked in both derivative CFAI questions. This is easier for me than doing it the way they do in derivatives by trying to get the one unit of FC, but its a little disturbing that its different than econ and that it doesn’t make any sense.
This is happening with me as well. Can someone help? Thanks!
You guys are not comparing apples to apples.
In the first scenario you take [($1,023.8 / $1,019.53) - 1]
In the second scenario you take [(1,043.79 / $1,019.53) - 1]
Why are u guys diving by $1,019.53 in both cases?
Watch. Divide by $1,000 in the first case and keep the second case the same. You’ll get the same answer.
Agree with Capt.
You borrow $1000 bucks so your semi annual return is 23.8/1000 = 2.38% X 2 = 4.76% annualized…