0:11

In this video, we're going to be looking at the relationship between the current

spot rate.

And the future spot rate, for foreign exchange.

In the previous video, we looked at spot rate versus forward rate.

Here, the focus is on the future spot rate.

Which means that you don't sign any contract.

You don't know what the exchange rate is.

You transact later.

So you compare what you can do now, agree now and transact now.

With waiting now and transacting later, taking your chances.

So the risk some risk is involved here, which I'm going to address later on.

But for now, let's assume that risk is not an issue for the traders.

0:57

So, let's go back to the example that we had in the previous video.

Of a CD importer who needs to import CDs from the UK.

And she needs to deliver 10,000 pounds one year from now, in order to get the CDs.

1:16

As we've seen before,

one option is to buy the 10,000 pounds in the spot market right now.

Keep it for a year, and then pay for the CDs.

Other option we're going to be looking at, is waiting for one year.

And buying the 10,000 pounds, then fulfilling the contract.

And meanwhile, the importer will be holding dollars.

1:39

Suppose that I give you these numbers for

the spot rate, e, 0.50 pound per dollar.

ee, the expected exchange rate a year from now.

Because we don't know what the exact exchange rate is.

This is the expected value that we're putting in.

0.52 pound per dollar.

And let's say, interest rates are the same as we had in the previous video.

5% interest on US assets, 10% return on British pound assets.

Let's look at the numbers,

and do the calculations to see which option is better.

2:17

The exchange rate in the spot market is 0.5, remember.

The expected exchange rate is 0.52.

Domestic interest rate is 5%, foreign interest rate is 10%.

So if you go to the spot market,

we've seen this calculation in the previous video.

2:35

You take your 10,000 pounds that you need to deliver.

Figure out how many pounds you need now,

in order to have 10,000 pounds in the future.

That's this ratio here.

2:48

And then, you need to know the number of dollars that you need right now.

In order to be able to buy the 10,000 pounds.

This ratio is the number of pounds you need right now.

So, you divided it by 1 over e, to get the dollar value.

And we've seen that becomes $18,181.82.

Let's see what happens if the importer goes to forward market,

what should she expect?

She needs 10,000 pounds.

And in the future, she should expect to pay 10,000 divided by ee dollars.

And in order to have that much money,

she needs to set aside 1 over 1 plus interest rate in the US.

Times the amount of dollars that she needs, a year from now.

So that adds up to $18,315.05.

Again, if you compare these two.

It's clear that going to the spot market, in this case, is beneficial.

The reason that the spot market is still is the better option.

Is that ,despite the fact that the importer

believes that the dollar's going to gain 4% value.

Notice that it's 0.52 expected exchange rate, versus 0.5.

That's 4% gain, or expected gain, if the importer waits,

and tries to keep her dollars.

But she loses 5% interest,

because she's going to get 5% interest rather than 10% interest.

So overall, going to the foreign currency market right now.

And getting British pound right now, is a better deal for her.

4:29

So let's do some journalization of this analysis.

Suppose you have one unit of home currency.

And you want to know how many foreign currency

units you can expect to have a year from now.

Keeping it in dollars, for every dollar you get 1+ i.

And then you multiply it by the expected exchange rate.

And then you get the total number of foreign currency units you expect to

have a year from now.

Let's compare this with the option of buying the foreign currency right now,

on the spot market and keeping foreign currency.

So, 1 home currency becomes e units of foreign currency.

And you multiply it by 1 plus i star.

The number of foreign currency units you get for

1 unit of foreign currency a year from now.

If you deposit it in an account in the foreign country.

So overall you can 1 + i star times e foreign currency units,

if you buy the foreign currency right now.

So the comparison, in this case, when you want to see whether to buy right now, or

to wait for a future spot market.

Is between (1 + i) e e, and (1 + i star) e.

So let's suppose that you do the calculation.

And you see that keeping home currency, and exchanging it in the future.

Pays you more than the interest rate that you can earn on your foreign currency,

if you buy the foreign currency right now.

And in this case, as we've seen in the previous video,

is a better choice to keep the domestic currency and exchange it later.

The expected payoff is going to be bigger.

6:09

Examine this for the example that I had given you before.

Interest rate is 5% in domestic currency.

Expected exchange rate is 0.52.

Foreign exchange rate in this spot market is 0.5, and foreign interest rate is 10%.

Check to see if this is correct or not.

6:28

And I'm sure, very quickly, you are going discover that, in fact,

inequality should be the other way around.

That's because, as I mentioned before,

you get 4% better pay for keeping your currency.

But the problem is that foreign currency pays you 5% additional excess returns.

And it's still better to keep the foreign currency, and

take advantage of the interest rates in the foreign country.

7:00

Very similar to what we've done in the case of spot rates versus forward rates.

Here, we can also reorganize the inequality that tells

us what to do about foreign versus domestic currency.

Going to spot rate market or future spot market.

And therefore, we're to offer our,

if you want to engage in foreign currency exchange.

Whether to offer our foreign currency, or domestic currency.

The inequality was what we've seen before, as we've also done this before.

We can put all the e's on one side and all the i's on the other side.

And come up with a comparison, between the expected

appreciation of the domestic currency In the coming year.

So, we compare the expected appreciation of home currency,

which is (e e minus e) divided by e.

That's the percentage by which the domestic exchange rate

is going to appreciate.

As opposed to the excess interest that foreign currency offers.

If the expected appreciation is bigger than

excess return on foreign currency assets.

Then you keep the domestic currency.

Otherwise, you keep foreign currency.

8:28

As we've discussed in the case of forward versus spot market.

Let's assume that expected exchange rate and

interest rates in the domestic and foreign current markets are given to us.

And what we want to know is, what happens in the spot market right now.

8:46

The participants in these markets, spot market now and

the ones who potentially can participate in the future.

Are going to be looking at two values.

Keeping the domestic currency and exchange into foreign currency in the future.

Versus buying foreign currency and keeping it that way.

And if the left-hand side is bigger than the right-hand side, as we've seen before.

Those who have domestic currency will keep it.

Those who have foreign currency would like to earn, or buy, foreign and

domestic currency.

And therefore,

the value of the domestic currency in the spot market is going to rise.

And that means that this whole right-hand side is going to rise.

And it means that the two sides are going to come closer to each other.

9:30

If the inequality's reversed.

The payoff from holding domestic currency's lower than

payoff from holding foreign currency.

Then the opposite happens.

People who have foreign currency are going to keep it.

People who have domestic currency would want to buy foreign currency.

And that means that the domestic currency is going to lose value in the spot market.

And eventually, the two sides are going to come closer to each other.

9:54

So, in equilibrium of the market,

the two sides are going to be exactly equal to each other.

And the spot rate is going to readjust until (1 plus i) e e

becomes equal to (1 plus i star) e.

This condition is very similar to the covered interest parity condition.

Except that the left-hand side,

we have the expected exchange rate, which is not a certain number.

That's what traders expect to prevail in the future in the market.

That's why it's called interest parity, and not covered interest parity.

There are risks involved in this case.

However, we assume that people don't care about risk initially.

Later on, we're going to come back and

see, how one can adjust this relationship when there is risk.

10:46

Suppose that the interest rate in the US is 1%.

And, in Europe, it's 2%.

And, you expect the dollar and the Euro be one-for-one a year from now.

So, what's this spot rate right now, if interest parity condition holds?

So, you write the interest parity condition, and plug in the numbers.

One plus 0.01 times 1, equal to 1 plus 0.02 times e.

And the exchange rate, in this case, turns out to be 0.99.

Now, suppose that the interest rate goes up in the US by 2%.

Rather than being 1%, becomes 3%.

And in Europe, the interest rate remains the same.

11:29

And let's suppose that your expectations about the future

what the exchange rate is going to be.

Of one Euro for $1, remains the same.

So in this case, what is going to be this spot rate?

Or what should this spot rate be, for the market to be in equilibrium?

11:47

So, you plug in the numbers.

1 plus 0.03 times 1, equal to 1 plus 0.02 times e.

And if you calculate the exchange rate, it's going to be 1.01.

In the previous example, the interest rate, domestically, was 1 percent.

It went up by 2%, and you can see that the value of the dollar has jumped up by

exactly 2%, from 0.99 to 1.01.

Exactly reflecting the change in the interest rate,

given the foreign interest rate.

The other thing to notice here,

is that the dollar here is giving you higher interest rate.

And value of the dollar, right now in the market, is higher than its expected rate.

Another way of putting this is that, the dollar is giving you higher interest rate.

And it should be expected to depreciate, from 1.01 to 1.41.

In order to compensate those who are holding Euro.

If this depreciation does not hold true, compensating those who hold Euro.

Then people would want to hold dollars, and the dollar will be appreciating.

And if you appreciate so much until, from now till next year.

It would be expected to depreciate.

Exactly where the difference between the interest rates, and

dollar assets versus Euro assets.

Let me comment on the relationship between covered interest parity and

interest parity.

Because they're exactly the same in almost all ways.

Except that in the covered interest parity, we have forward rate,

which is a certain rate, it's contracted.

And in the interest parity condition, it's expected rate.

The two therefore, should be the same, theoretically.

13:30

So this is how the market works, in fact.

People looking to the future, and

form ideas where the exchange rate might be going.

That's the expected exchange rate.

When they come to the forward market, they make trades based on those expectations.

And that also reflects itself in the spot rate

of domestic currency versus foreign currency, right now.

So the two conditions basically mean,

that the forward rate is exactly the same as the expected rate.

Or reflects that expectation, which makes sense.

If you're trading a currency in the future, and

you expect it to be valued at e e.

The two sides, knowing that that might be the case, then It makes sense for

them to also trade it at that rate.

So the interest parity condition and the current interest parity conditions.

Jointly ensure consistency between the forward rate, the expected rate, and

the spot rate right now.

Later on, we're going to see what drives that expected rate.

The long-term trends in the exchange rate,

how expectations about those trends are formed.

But that's for another module.