Question

Suppose that you are the FX trading desk of ExxonMobil with an extra U.S. $1,000,000 to invest for six months. You are considering the purchase of U.S. T-bills that yield 1.810 percent (that's a six month rate) and have a maturity of 26 weeks. The spot exchange rate is $1.00 = ¥100, and the six month forward rate is $1.00 = ¥110. The 6-month interest rate in Japan (on an investment of comparable risk) is 13 percent. What is your strategy?

A. Take $1M, invest in U.S. T-bills

B. Take $1m, translate into yen at the spot, invest in Japan, and repatriate your yen earnings back into dollars at the spot rate prevailing in six months.

C. Take $1m, translate into yen at the spot, invest in Japan, hedge with a short position in the forward contract.

D. Take $1m, translate into yen at the forward rate, invest in Japan, hedge with a short position in the spot contract.

Answer 1

Solution:

My strategy Will be Option (C) i.e Take 1M$, translate into yen at the spot, invest in japan, hedge with a short position in the forward contract as Arbitrage Compared to other Options is High.

Calcution of Arbitrage Gain by Option C

   As per Interest rate parity theorem(IRPT) if Theoritical interest rate is different from actual intrest rate     there  exist  arbitrage Gain

Calculation of theoritical interest

let interest rate in japan be y% , interest rate in US ( T bill Rate) = 1.810%

  As per IRPT (Forward rate / Spot Rate = 1+ R.H.S currency rate / L.H.S currency Rate)

     110Yen/100Yen   = 1 + y%/1 + 1.810% ( given S.R 1$ = 100Yen , F.R 1$ = 110Yen )

   By solving above Equqtion Theritical Intrest Rate = 11.99% which is lower than Actual Intrest rate i.e 13%

In Japan interest is Over valued So Invest in Japan Barrowing from U.s

Arbitrage Process

  (1) Conver 1M$ at S.R 1$ = 100Yen i.e 100M Yen

  (2) Invest for 6 Months @ 13%

(3) Enter into Forword contract short position at F.R 1$ =110Yen

(4) Realise Investment along With Interest after 6 months

(5) Realised Amount = 100M Yen + 13 % =113M Yen

(6) Convert Realised Amount Into $ at F.R 1$ = 110 Yen

(7) Dollers Realised = 113M Yen / 110 Yen = 1.0273M $ ( Approx)  

(8) Arbitrage Gain = (1.0273M $ - 1M $) = 0.0273 $

Option (A) Invest in T bills in U.S @ 1.810% We get Total intrest of 0.0181( 1M $ x 1.810%) which is lower than Option C

Option (B) Take $1m, translate into yen at the spot, invest in Japan, and repatriate your yen earnings back into dollars at the spot rate prevailing in six months.

Option (D) Take $1m, translate into yen at the forward rate, invest in Japan, hedge with a short position in the    spot contract

There is no Clear informatio Regarding Spot Price after 6m so we Cannot calculate arbitrage gain for Option B, D .

   Hence option C is better Choice i.e  Take $1m, translate into yen at the spot, invest in Japan, hedge with short position in the forward contract.