(11 of 18) Ch.21 - Interest rate parity: example - YouTube

Okay.

Let's look at an example; the exchange rate for the Japanese Yen, S0, is currently 120

yen per dollar, the risk-free interest rate in the U.S.A. is 10% and the risk-free rate

in Japan is 5% what should the one year forward rate be in order to prevent the covered interest

arbitrage?

So, this complicated question is essentially asking you to use the interest rate parity

formula, that's the only one you can use that links today's exchange rate and the two risk

free rates in two different countries.

We have the approximate version of it and we are later going to use the exact interest

rate parity formula.

The approximate interest rates parity formula says, to find the one year forward rate, we

take today's exchange rate, which is 120 Yen per dollar, and we multiply it by, open parenthesis,

1 plus, and then the difference between the Japan and the U.S. risk free rates so .05

in decimals minus .10 in decimals, the math gives us 114 Yen per dollar.

The exact formula looked a little bit different, the exact interest rate parity formula says

F1 equals S0, times and then we have the fraction of 1 plus, the interest rate in Japan, divided

by 1 plus the interest rate in the United States.

When we plug in our numbers into this formula, we have 120 times, open parenthesis, 1 plus

.05, closed parenthesis, divided by, open parenthesis 1 plus .1, closed parenthesis.

Which gives a slightly different answer 114.55 Yen per $1, so the two answers are very, very,

close, I would say, you know, it's always safer to use the exact interest rate parity

because it gives you the true answer, the correct answer, whereas, any approximate formulas

give you a little bit of an error.

By the way, the approximate interest rate parity can be used in the financial calculator,

let me bring it up.

Let's turn it off and back on, let's clear everything and start all over.

So, we want to find the one year forward, it's like finding the future value after one

year, so what's one year?

That's our N, N equal to 1.

So, let me start with that, 1N, what does the present value, if you need to find the

future value?

The present value equivalent in this problem is the current spot exchange rate, 120 Yen

per dollar, so I put 120, I make the sign negative, and then I press the PV button.

So, we have PV minus 120, we have N equal to 1, there's one more thing we need to enter

before we press compute FV, and that's the interest rate, the IY, what's the equivalence

of the interest rate in this exchange rate problem?

It's the difference between the foreign and the domestic interest rates 5% minus 10% what

is that?

That's negative 5% so I put 5, plus minus IY, and then I press compute future value,

114.

So, 114 yen per dollar is the one year forward rate between the Japanese Yen and the dollar

that would, you know, that would allow investments to be different between which country they

invest their money to, whether it's Japan or the United States.