Question

1. Suppose the spot rate is $0.115 per Mexican peso and the forward rate is $0.109 per peso. The 3 month Mexican interest rate (annualized) is 18% and the 3 month US interest rate (annualized) is 5%. Is there an arbitrage opportunity here? If not, explain how you know. If so, how much could a US investor earn in 3 months in the US versus 3 months in Mexico (starting with $100,000)? How about a Mexican investor with 750,000 pesos to invest (how much could they earn in the US versus in Mexico)?

Answer 1

	Forward rate= USD per Mexican Peso * (1+Interest rate in USA)/(1+Interest rate in Mexico)
	Forward rate=	=0.115*(1+0.05*3/12)/(1+0.18*3/12)
	Forward rate=	$                     0.111
	Since the given forward rate is 0.109, we can see that some arbitrage opportunity is available.
	As we can see, the US currency is getting stronger, it is better to invest in the US.
	So the funds available are invested in the US
	Equivalent Mexican peso	=100000/0.115
	If invested in Mexico	869,565.22
	Amount in Mexico after 3 months	=869565.22*(1+18%*3/12)
		908,695.65
	The amount converted back to USD	=908695.65*0.109
		99,047.83
	Amount after investment in the US after 3 months=	=100000*(1+5%*3/12)
		$                101,250
	So this way there will be gain	101250-99048.83
	So this way there will be gain	$               2,201.17
Mexican investor
	If invested in Mexico	750,000.00
	Amount in Mexico after 3 months	=750000*(1+18%*3/12)
		783,750.00
	If invested in the US, then equivalent USD=	750000*0.115
		$             86,250.00
	The amount after investment in the US after 3 months=	=86250*(1+5%*3/12)
		$             87,328.13
	The amount converted back to Mexican Peso=	87328.13/0.109
		$           801,175.50
	So this way there will be gain	801175.50-783750
	So this way there will be gain in the Mexican peso	17,425.50