0:11

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

Â spot rate.

Â And the future spot rate, for foreign exchange.

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

Â Here, the focus is on the future spot rate.

Â Which means that you don't sign any contract.

Â You don't know what the exchange rate is.

Â You transact later.

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

Â With waiting now and transacting later, taking your chances.

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

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

Â 0:57

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

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

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

Â 1:16

As we've seen before,

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

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

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

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

Â And meanwhile, the importer will be holding dollars.

Â 1:39

Suppose that I give you these numbers for

Â the spot rate, e, 0.50 pound per dollar.

Â ee, the expected exchange rate a year from now.

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

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

Â 0.52 pound per dollar.

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

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

Â Let's look at the numbers,

Â and do the calculations to see which option is better.

Â 2:17

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

Â The expected exchange rate is 0.52.

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

Â So if you go to the spot market,

Â we've seen this calculation in the previous video.

Â 2:35

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

Â Figure out how many pounds you need now,

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

Â That's this ratio here.

Â 2:48

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

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

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

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

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

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

Â what should she expect?

Â She needs 10,000 pounds.

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

Â And in order to have that much money,

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

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

Â So that adds up to $18,315.05.

Â Again, if you compare these two.

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

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

Â Is that ,despite the fact that the importer

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

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

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

Â and tries to keep her dollars.

Â But she loses 5% interest,

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

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

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

Â 4:29

So let's do some journalization of this analysis.

Â Suppose you have one unit of home currency.

Â And you want to know how many foreign currency

Â units you can expect to have a year from now.

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

Â And then you multiply it by the expected exchange rate.

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

Â have a year from now.

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

Â on the spot market and keeping foreign currency.

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

Â And you multiply it by 1 plus i star.

Â The number of foreign currency units you get for

Â 1 unit of foreign currency a year from now.

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

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

Â if you buy the foreign currency right now.

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

Â to wait for a future spot market.

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

Â So let's suppose that you do the calculation.

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

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

Â if you buy the foreign currency right now.

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

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

Â The expected payoff is going to be bigger.

Â 6:09

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

Â Interest rate is 5% in domestic currency.

Â Expected exchange rate is 0.52.

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

Â Check to see if this is correct or not.

Â 6:28

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

Â inequality should be the other way around.

Â That's because, as I mentioned before,

Â you get 4% better pay for keeping your currency.

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

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

Â take advantage of the interest rates in the foreign country.

Â 7:00

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

Â Here, we can also reorganize the inequality that tells

Â us what to do about foreign versus domestic currency.

Â Going to spot rate market or future spot market.

Â And therefore, we're to offer our,

Â if you want to engage in foreign currency exchange.

Â Whether to offer our foreign currency, or domestic currency.

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

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

Â And come up with a comparison, between the expected

Â appreciation of the domestic currency In the coming year.

Â So, we compare the expected appreciation of home currency,

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

Â That's the percentage by which the domestic exchange rate

Â is going to appreciate.

Â As opposed to the excess interest that foreign currency offers.

Â If the expected appreciation is bigger than

Â excess return on foreign currency assets.

Â Then you keep the domestic currency.

Â Otherwise, you keep foreign currency.

Â 8:28

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

Â Let's assume that expected exchange rate and

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

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

Â 8:46

The participants in these markets, spot market now and

Â the ones who potentially can participate in the future.

Â Are going to be looking at two values.

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

Â Versus buying foreign currency and keeping it that way.

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

Â Those who have domestic currency will keep it.

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

Â domestic currency.

Â And therefore,

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

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

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

Â 9:30

If the inequality's reversed.

Â The payoff from holding domestic currency's lower than

Â payoff from holding foreign currency.

Â Then the opposite happens.

Â People who have foreign currency are going to keep it.

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

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

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

Â 9:54

So, in equilibrium of the market,

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

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

Â becomes equal to (1 plus i star) e.

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

Â Except that the left-hand side,

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

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

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

Â There are risks involved in this case.

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

Â Later on, we're going to come back and

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

Â 10:46

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

Â And, in Europe, it's 2%.

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

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

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

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

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

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

Â Rather than being 1%, becomes 3%.

Â And in Europe, the interest rate remains the same.

Â 11:29

And let's suppose that your expectations about the future

Â what the exchange rate is going to be.

Â Of one Euro for $1, remains the same.

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

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

Â 11:47

So, you plug in the numbers.

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

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

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

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

Â exactly 2%, from 0.99 to 1.01.

Â Exactly reflecting the change in the interest rate,

Â given the foreign interest rate.

Â The other thing to notice here,

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

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

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

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

Â In order to compensate those who are holding Euro.

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

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

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

Â It would be expected to depreciate.

Â Exactly where the difference between the interest rates, and

Â dollar assets versus Euro assets.

Â Let me comment on the relationship between covered interest parity and

Â interest parity.

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

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

Â which is a certain rate, it's contracted.

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

Â The two therefore, should be the same, theoretically.

Â 13:30

So this is how the market works, in fact.

Â People looking to the future, and

Â form ideas where the exchange rate might be going.

Â That's the expected exchange rate.

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

Â And that also reflects itself in the spot rate

Â of domestic currency versus foreign currency, right now.

Â So the two conditions basically mean,

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

Â Or reflects that expectation, which makes sense.

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

Â you expect it to be valued at e e.

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

Â them to also trade it at that rate.

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

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

Â the spot rate right now.

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

Â The long-term trends in the exchange rate,

Â how expectations about those trends are formed.

Â But that's for another module.

Â