Topic 15: what determines exchange rates in the short run?MATERIAL FROM CHAPTER 14

IntroductionThe basic question is here is why do exchange rates move up and down on a daily (hourly) basis? What might drive them over a few weeks or months?

The essential answer is that in the short run exchange rates are an important component of the prices of financial assets and people and firms trade these in huge volumes ($ trillions) every day. So exchange rates are also rather variable on a daily basis, just as are stock and bond prices.

If exchange rates are a component of asset prices (or returns) they must be related to asset markets in the countries where the currencies are traded. This basic insight gives us our theories of what drives exchange rates in the short run: they must move to ensure that the interest returns (measured in one currency) are the same in both markets.

This idea simply comes from thinking of exchange rates as prices that achieve short-run equilibrium in asset markets across borders.

Typically we think of this equilibration as coming from both hedged (risk-free) and speculative (risky) investments.

Risk-free: covered interest arbitrageWe have already studied this idea (Chapter 12) in part by analyzing covered interest parity(through forward arbitrage). Just as a reminder, there are 2 riskless ways for a US investor to invest a sum of money, say $1m, for a period such as 90 days:

1. Directly invest in the US for 90 days. Proceeds = $1m*(1 + i$) and the % return per $ = i$, where this is the 90-day interest rate.

2. Invest abroad using the spot and forward rates. To recall this process briefly:

A. Take $1m dollars and buy euros at today’s spot exchange rate. The investor receives $1m/E (that is, divide by the spot rate, because 1/E determines the amount of euros per $).

B. Invest these euros at i€ for 90 days. The proceeds from that are now [$1m/E]*(1 + i€).

C. Sign a contract today to sell those euros for $ in 90 days at today’s forward rate, F (which is in $/€). The investor gets back [$1m/E]*(1 + i€)*F, in dollars. The % return per $ is [(1 + i€)*F]/E.

Covered interest arbitrageAgain, just to do an example:

Let i$ = 0.03 (3% per 90 days). Then investment 1 generates $1m*(1.03) = $1,030,000 and the return is $30,000/$1m = 3%.

Let Let i€ = 0.035 (3.5% for 90 days). It seems at this basic level that euro assets pay a higher return. But we need to compute the returns in $.

So let E = 1.25 and F = 1.22. Then investment 2 generates, by step: (1) [$1m/1.25] = €800,000 (spot) (2) [€800,000*(1.035)] = €828,000 (interest rate) (3) [€828,000 *1.22 $/€] = $1,010,160 (forward). Return is $10,160/$1m = 1.016%.

The investor gets $30,000 in the first case and $10,160 in the second case. US assets pay more, so investors would buy more of those and fewer Euro assets until we get to an equal return for both investments.

Covered interest parity conditionAgain, what this says is that the covered interest parity condition in its pure form is:

(1 +i$) = [(1 + i€)*F]/E.

To simplify, here’s some basic math that you DO NOT need to worry about. Recall that the forward premium or discount is f = (F – E)/E = F/E – 1. Thus, F/E = f + 1. Then the condition above can be written as

(1 +i$) = [(1 + i€)*F]/E = f + 1 + i€*(f + 1) => 1 + i$ = f + 1 + i€ + i€*f

In this equation, the “1s” cancel and the term i€*f can be ignored because it’s so small. (Example: if i€ = 0.035 and f = 0.01 then i€*f = 0.00035.)

Thus, as a very good approximation we can write the covered interest parity condition (CIP) as:

CIP: i$ = i€ + f

In words for the foreign exchange market to be in equilibrium in the short run we must have that the interest rate in a home country (the US) is equal to the interest rate in a foreign country (Europe) plus the forward premium or discount on the foreign country’s currency.

We saw some actual examples from recent data in Notes 13.

Covered interest parity conditionWhy does this hold?

i$ is the direct interest return on home (US) assets.

i€ + f is the indirect interest return on foreign (EU) assets, taking account of the difference between spot and forward exchange rates.

Again, the euro % return has 2 components: the usual interest component plus f. The latter is the (instantly known) additional percent return in arbitraging forward.

◦ If f > 0 (premium) it means the current F is higher than the current spot so you know you’ll get back more dollars forward than you spend spot.

◦ If f < 0 then you’ll get back fewer dollars than you spend spot.

Recap: CIP condition is i$ = i€ + f, or i$ - i€ = f.

This is an arbitrage condition and should always hold. It means that if the US interest rate is higher (lower) than the euro rate the euro must be at a forward premium (discount).

Risky: speculation and uncovered interest parityNow let’s consider speculation, or taking risky positions when trading currencies. Speculation happens a great deal, judging by the huge volumes of trades in currency markets. So how can we bring that in?

By adding market expectations about what will happen to future spot rates (which are uncertain). (Recall that forward rates are known today, but future spot rates are not.)

Speculation is accepting risk (e.g., waiting in the spot market) to try to make a profit.

Here is an example.

Let F be the 60-day forward rate on euros. Example F = 1.25.

Let exp(E60) be the expected market spot rate in 60 days. (Note: textbook uses exp(Et+1) to indicate the future.) (Technically this is the average expectation among all speculative traders.)

◦ Example, suppose that exp(E60) = 1.27. This is unknown, but captures the market’s expectation.

◦ Note that exp(E60) = 1.27 > F = 1.25.

Uncovered interest parityThat is, the market expects the spot rate in 90 days on the euro to end up higher than the current forward rate on the euro. How could speculators take advantage?

Speculators would contract now to buy euros forward because the (current and known) price is lower than they expect to get in the spot market in 90 days (1.25 vs. 1.27). The expected profit is 2 cents per dollar invested at risk.

◦ Example: an investor sells $1m in the forward market, knowing she will get $1m/(1.25) = €800,000 in 90 days.

◦ Wait 90 days and sell these euros the in spot market. If your expectation is right you will get €800,000*1.27 = $1,016,000, or a risky profit of $16,000 per million invested.

◦ But she could be wrong. If in 90 days the spot rate is 1.22 she gets back €800,000*1.22 = $976,000, a loss of $24,000 per $1m.

Note that speculators would invest until the forward rate equals the expected future spot rate. For if the expected spot rate is higher than F, these investors will be buying euros in the forward market (driving up F). Similarly, if the expected spot rate is lower, investors will be selling euros in the forward market (driving down F).

Uncovered interest parityIMPLICATION: This speculative investment will continue until the forward exchange rate equals the market’s expected future spot rate. (In 30 days, 60 days, 90 days,…).

(Not quite, actually, because there may be some risk premium that investors must get to undertake this risk. But we’ll ignore that).

So we can state our open interest parity or uncovered interest rate parity (UIRP) condition:

UIRP: F = exp(Et+1).

One thing this means is that today’s forward rates are the best predictor we have of expectations about future rates.

Combined conditionsCombining equilibrium conditions

Let’s combine these conditions (both of which hold):◦ CIP: i$ - i€ = f

◦ UIRP: F = exp(Et+1 )

But recall that f = [F – E]/E

Together these imply that i$ - i€ = [exp(Et+1 ) – E]/E = exp(Et+1)/E - 1

That is, in equilibrium the interest-rate differential between 2 markets equals both the forward premium or discount and the expected percentage change in the spot rate.

If i$ > i€ the market anticipates exp(Et+1) > E so it is expecting the euro to rise in value.

Short-run exchange ratesAll of this gives us the short-run (asset market) view of exchange rates. Solving that last condition for the current spot rate gives us:

E = exp(Et+1 )/(1+ i$ - i₡)

With this condition we can say a lot about why exchange rates may be volatile from day to day.

Suppose the following things happen suddenly (that is, they are not expected).◦ If exp(Et+1 ) rises (that is, the euro is expected to appreciate and the $ to depreciate) then E (the spot rate)

rises now.

◦ If the US interest rate rises then E falls now (instant appreciation of the $). This is because investors buy US assets => the $ appreciates in the spot market (and there is a cheaper euro, which is a lower E).

◦ If the euro interest rate rises then E rises now (instant depreciation of the $) Investors buy euro assets => the $ depreciates (more expensive euro, a higher E).

All of this means that today’s monetary conditions and expectations are critical for understanding how exchange rates vary by day or by week.

Basic summary(Flexible) exchange rates are highly variable in the short run.

Announcements of news (unanticipated events, or “shocks”) affect expectations and change exchange rates right away.

Central banks can influence exchange rates via interest rate policy and vice-versa.

Practical example? ◦ There are many but consider the ongoing rise of the dollar relative to the euro. ◦ One likely factor explaining it is that the 2017 US tax reform and 2018 higher government expenditures imply more US

government borrowing, which is pushing up US interest rates faster than euro interest rates are rising. This makes US assets more valuable and draws investments into buying dollar-based assets.

◦ In turn, the spot $ has appreciated (the spot euro, or E, has fallen in value). ◦ Note also that there must be a forward premium on the euro to compensate investors for foregoing the higher US interest

rate. ◦ And that means there is an expectation in the market that the euro will rise over the next 60 or 90 or 180 days.

The material above is enough for our purposes; it makes the basic points about links between asset markets, exchange rates and volatility. The rest of chapter 14 is interesting but not worth class time.