Implied cost of borrowing USD via an FX swap

Question

EURUSD is quoted at 1.0879/84. Lets say O/N forward points are quoted at +0.032/+0.332. Lets say based on these quotes I want to derive my implied funding cost (USD interest rate) if I wanted to borrow USD via an FX swap (sell EURUSD spot, buy it forward). I want to sell EUR spot so I would lift the quoted bid (1.0879) I want to buy EUR forward so I would lift the quoted forward point offer (+0.332). Assume that the ON interest rate for EUR is -0.44%.

My equation that I'm trying to solve is this:

(1.0879)*[(1+x/365)/(1-0.0044/365)] = (1.0884+0.332/10000)

Solving for x gives me 17.5% which isn't even close to the answer (Bloomberg shows -0.3342% and 0.6587% bid and ask implied yield)... I cant figure out what I'm doing wrong. Can someone please help me?

Answer 1

You're not really using the same spot, are you?

$$ FX_{fwd} = FX_{spot} \frac{1+r}{1+r_f} = FX_{spot} + ForwardPoints$$

But you are using 1.0879 on one side of the equation and then 1.0884 on the other.

If you correct for that and for the fact that ibors are quoted in Act/360, you get 0.6586% which is very close to what you wanted.

from scipy.optimize import fsolve
spot = 1.0879
def f(x): return spot*(1+x/360)/(1-0.0044/360) - (spot+0.332/10000)
fsolve(f,0.1)

0.006586169611214752