I will give a ton of points to anyone who knows how to answer this question. I r
ID: 2789456 • Letter: I
Question
I will give a ton of points to anyone who knows how to answer this question. I really don't know how to solve this question.
Suppose that the CFO of the Vatican on Jan 1. 2017 had 10 million Euros to invest with a time horizon of 1 year until major renovations to St. Peter's Basilica and the papal residence were planned to begin. Suppose further that the interest rate at the time on 1 yea $ Libor deposits in the London interbank was 1.7% while the rate on 1 year Euro Libor deposits in the London market was (-.09). FInally, assume at that time 1 Euro was worth $1.04 in the FX market.
Question A) Based on the interest rate parity condition, what must the FX market have expected about the ($/euro) exchange rate by Jan 1, 2018? (an exact answer is required for full credit. Partial credit can be earned by identifying the direction of change in the $ cost of a Euro.)
Question b) Currently despite three 25 basis point increases in the US Fed Funds target rate range during 2017 and no increases in the ECB's overnight interbank rate the $ is now trading at 1.16 dollars per Euro. Assuming that this exchange rate does not change over the next 6 weeks what rate of return would the CFO of a US based company earn if she invested 10 million $ in 12 month Euro Libor deposits at the rate in part A?
C) how can you explain the difference between the breakeven rate in the $ to Euro FX rate based on the IRP condition and the actual change in that exchange rate over this year?
Explanation / Answer
Answer - A
Using interest rate parity theory,
Et(St+k) = St * (1+i$)/(1+ie)
Where,
Et(St+k) is the expected future spot exchange rate at time t + k
k is the number of periods into the future from time t
St is the current spot exchange rate at time t
i$ is the interest rate in US Libor
ie is the interest rate in EU Libor
One year from now k = 1 and t=0 so
Eo(S1) = 1.04 * (1+0.017)/(1-0.0009)
= 1.04 * 1.017/0.9991
= 1.058
Eo(S1) = 1.06 (approx.)
Exchange Rate would 1 Euro = $ 1.06
Answer B
Using above formula from A,
Et(St+k) = St * (1+i$)/(1+ie)
(1+ie) = St * (1+i$)/ Et(St+k)
= 1.04*1.095/1.16
1 Euro = $1.16, US Fed rate hike 25 basis points add to 1.7% 0.017+0.0025 = 0.0195 = 1.95%
ie = -0.018 = -0.02
ie = - 2%
If $10 million invested in Euro Libor rate at -2% then the amount would be in 6 weeks as given below
FV = 10*(1-0.02/8.6)^8.6
52 weeks in a year, 6 weeks means 52/6 = 8.6 periods
= 10*0.98 = $9.8 millions