Macroeconomics for FinanceJoanna Mackiewicz-Łyziak

Lecture 8

Literature

• Mishkin F., ch. 18

• Sarno L., Taylor M., (2002), The Economics of Exchange Rates, ch.2 „Foreign exchange market efficiency”, ch.3 „Purchasing power parity and the real exchange rate”

Foreign exchange market

• Foreign exchange market is organized as an over-the-counter market in which several hundred dealers (mostly banks) stand ready to buy and sell deposits denominated in foreign currencies.

• BIS Triennial Central Bank Survey, 2016: trading in foreign exchange markets averaged $5.1 trillion per day in April 2016. FX swaps were the most actively traded instruments, at $2.4 trillion per day (47% of market turnover), followed by spot trading at $1.7 trillion (33% of market turnover).

• The US dollar was most traded currency; it was on one side of 88% of all trades. The euro was the second most traded currency (33%). The most actively traded emerging market currency was renminbi (4% market share, 8th most actively traded currency).

Foreign exchange market turnover by currency and currency pairs

Source: BIS Triennial Central Bank Survey. Foreign exchange turnover in April 2016: September 2016.

Geographical distribution of turnover – largest financial centres

Net-gross basis, daily averages in April, in billions of US dollars and percentages

Country2010 2013 2016

Amount % Amount % Amount %Australia 192 3.8 182 2.7 135 2.1Canada 62 1.2 65 1 86 1.3China 20 0.4 44 0.7 73 1.1Denmark 120 2.4 117 1.8 101 1.5France 152 3 190 2.8 181 2.8Germany 109 2.2 111 1.7 116 1.8Hong Kong SAR 238 4.7 275 4.1 437 6.7Japan 312 6.2 374 5.6 399 6.1Netherlands 18 0.4 112 1.7 85 1.3Singapore 266 5.3 383 5.7 517 7.9Switzerland 249 4.9 216 3.2 156 2.4UK 1854 36.8 2726 40.8 2426 37.1USA 904 17.9 1263 18.9 1272 19.4

Source: BIS Triennial Central Bank Survey. Foreign exchange turnover in April 2016, September 2016.

Exchange rates in the long run

• Law of one price (LOOP): If two countries produce an identical good, and transportation costs and trade barriers are very low, the price of the good should be the same throughout the world no matter which country produces it.

𝑃𝑖,𝑡 = 𝑆𝑡𝑃𝑖,𝑡∗ i=1,2,…, N

where Pi,t denotes the price of good i in terms of the domestic currency at time t, 𝑃𝑖,𝑡∗ is the price of good i in terms of the foreign currency at time t, and St is the

nominal exchange rate expressed as the domestic price of the foreign currency at time t.

Exchange rates in the long run

• The purchasing power parity (PPP) exchange rate is the exchange rate between two currencies which would equate the two relevant national price levels if expressed in a common currency at that rate, so that the purchasing power of a unit of one currency would be the same in both economies (absolute PPP).

• The theory of PPP is an application of the law of one price to national price levels rather than to individual prices:

𝑃𝑡 = 𝑆𝑡𝑃𝑡∗

where Pt and 𝑃𝑡∗ denote the national price levels.

• Relative PPP holds when the rate of depreciation of one currency relative to another matches the difference in aggregate price inflation between the two countries concerned.

∆𝑃

𝑃−∆𝑃∗

𝑃∗=∆𝑆

𝑆

Purchasing Power Parity, UK/US

Source: Mishkin, p.475

Why PPP cannot fully explain exchange rates?

• PPP rests on the following assumptions: • all goods are identical in both countries,

• transportation costs are very low,

• there are no trade barriers,

• the composition of consumer basket in every country is identical

• Are the assumptions realistic?

• PPP theory does not take into account existence of non-traded goods (whose prices are included in a measure of a country’s price level).

Real exchange rate

• Real exchange rate is defined as the ratio of the foreign price level and the domestic price level, where the foreign price level is converted into domestic currency units via the current nominal exchange rate.

𝑄𝑡 =𝑆𝑡𝑃𝑡

∗

𝑃𝑡• Changes in real exchange rate affect the competitiveness of traded goods.

• An increase in Q indicates that the foreign price (in domestic currency) of a bundle of goods has risen relative to the domestic price. It means that the real value of domestic currency has depreciated.

• When PPP holds, the real exchange rate is a constant so that movements in the real exchange rate represent deviations from PPP (hence, a discussion of the real exchange rate is tantamount to a discussion of PPP).

Factors that affect exchange rates in the longrun

Factor Change in factor Response of the exchange rate

Domestic price level*

Trade barriers*

Import demand

Export demand

Productivity*

Note: Exchange rate is quoted as the domestic price of the foreign currency, so indicates domestic currency depreciation, and indicates the domestic currency appreciation.* Relative to other countries

• Anything that increases the demand for domestic goods relative to foreign goods tends to appreciate the domestic currency; anything that increases the demand for foreign goods relative to domestic goods tends to depreciate the domestic currency.

Exchange rates in the short run• Exchange rates are very volatile and exhibit large changes (sometimes several

percent) from day to day.

• Exchange rate is the price of domestic price deposits (denominated in the domestic currency) in terms of foreign bank deposits (denominated in the foreign currency).

• The asset market approach suggests that the most important factor affecting the demand for domestic and foreign deposits is the expected return on these assets relative to each other.

• When capital is mobile and when bank deposits are perfect substitutes (domestic and foreign bank deposits have similar risk and liquidity), if the expected return on domestic deposits is above that on foreign deposits, nobody will want to hold foreign deposits. If the expected return on foreign deposits is higher than on domestic deposits, nobody will want to hold domestic deposits.

Exchange rates in the short run

• The uncovered interest rate parity (UIP) condition

• For existing supplies of both domestic deposits and foreign deposits to be held, it must be true that there is no difference in their expected returns.

• The rate of return on foreign deposits depends on two factors: the foreign interest rate (iF) and the expected change in exchange rate.

• The condition for the equality of the expected returns on domestic and foreign deposits may be therefore written as:

𝑆𝑡+1𝑒

𝑆𝑡=1 + 𝑖𝐷

1 + 𝑖𝐹

• or, in approximation:

𝑖𝐷 = 𝑖𝐹 +𝑆𝑡+1𝑒 − 𝑆𝑡𝑆𝑡

where iD is the domestic interest rate, St is the spot exchange rate and 𝑆𝑡+1𝑒 is expected

exchange rate at time t+1.

Exchange rates in the short run

• Interest rate parity states that the domestic interest rate equals the foreign interest rate plus the expected appreciation of the foreign currency.

• If the domestic interest rate is above the foreign interest rate, this means that there is a positive expected appreciation of the foreign currency, which compensates for the lower foreign interest rate.

• For example, if iD=9% and iF=6%, the expected appreciation of the foreign currency must be 3%.

• The interest rate parity is an equilibrium condition for the foreign exchange market. The spot exchange rate will adjust for the interest rate parity to be fulfilled.

Covered interest rate parity (CIP)

• Based on Sarno, Taylor, ch. 2.

• If there are no barriers to arbitrage across international financial markets, then arbitrage should ensure that the interest rate differential on two assets, identical in every relevant respect except currency denomination, adjusted to cover the movement of currencies at the maturity of the underlying assets in the forward market, be continuously equal to zero, so that covered interest rate parity (CIP) should hold.

• Algebraically, the CIP condition may be expressed (ignoring transactions costs) as:𝐹𝑡(𝑘)

𝑆𝑡=1 + 𝑖𝑡

𝐷

1 + 𝑖𝑡𝐹

where 𝑆𝑡 is the spot exchange rate (domestic price of foreign currency) and 𝐹𝑡(𝑘)

is the k-period forward rate (i.e. the rate agreed now for an exchange of currencies k periods ahead.

• An approximation of CIP is often used:

𝑖𝑡𝐷 = 𝑖𝑡

𝐹 +𝐹𝑡(𝑘)

− 𝑆𝑡𝑆𝑡

Covered interest rate parity (CIP)

• Why CIP should hold?

• Any market deviations from CIP will result in arbitrage activity which will force the equality to hold.

• Suppose, for example that:

𝑖𝑡𝐷 <

𝐹𝑡𝑘

𝑆𝑡1 + 𝑖𝑖

𝐹 − 1

• If the above is true, arbitrageurs could make a riskless profit by borrowing the domestic currency for k periods at the interest rate iD, selling it spot for the foreign currency (yielding 1/S units of foreign currency for every unit of domestic currency), lending the foreign currency for k periods at the interest rate iF, and selling the foreign currency proceeds (principal plus interest) in the k-period forward market against the domestic currency.

Covered interest rate parity (CIP)

• At the end of k periods, the arbitrageur will have to repay (1+𝑖𝑡𝐷) for every unit of

domestic currency borrowed, but will receive (𝐹𝑡(𝑘)

/𝑆𝑡)(1+𝑖𝑡𝐹) units of domestic

currency for every unit of domestic currency borrowed and used in the arbitrage.

• The net profit equals to [(𝐹𝑡(𝑘)

/𝑆𝑡)(1+𝑖𝑡𝐹)- (1+𝑖𝑡

𝐷)], and is positive.

• The simple laws of supply and demand imply that such arbitrage will induce movements in iD, iF, S and F until CIP holds.

However…Cross-currency basis against the US dollar

Source: BIS Quarterly Review, September 2016.

Foreign exchange market efficiency

• In an efficient speculative market prices should fully reflect information available to market participants and it should be impossible for a trader to earn excess returns to speculation.

• In its simplest form, the efficient markets hypothesis can be reduced to a joint hypothesis that foreign exchange market participants are, in an aggregate sense, endowed with rational expectations and are risk-neutral.

• The literature usually distinguishes between three different forms of market efficiency (Fama E.F., 1970, Efficient capital markets: a review of theory and empirical work, The Journal of Finance Vol. 25(2)):• weak form: the current price incorporates all the information contained in past prices;• semi-strong form: the current price incorporates all publicly available information, including

its own past prices;• strong form: prices reflect all information that can possibly be known.

Foreign exchange market efficiency

• The strong form of market efficiency is, in theory, expected not to hold, mainly because secret non-random intervention by central banks occurs in exchange markets.

• Semi-strong form efficiency is the version of efficiency closest to the rational expectations hypothesis since it is assumed that economic agents know the true model of the economy and use all publicly available information in forming expectations.

• The basic relationship which is used to test for foreign exchange market efficiency is the uncovered interest rate parity (UIP).

Testing for the foreign exchange market efficiency

• Covered and uncovered interest parity together imply that the forward rate should be equal to the market expectation of the future spot rate.

• Under rational expectations, the expected change in the exchange rate should differ from the actual change only by a rational expectations forecast error.

• Assuming covered interest rate parity, the uncovered interest parity condition can be tested by estimating a regression of the form:

∆𝑘𝑠𝑡+𝑘 = 𝛼 + 𝛽 𝑓𝑡𝑘− 𝑠𝑡 + 𝜇𝑡+𝑘

where 𝑓𝑡(𝑘)

≡ ln 𝐹𝑡(𝑘)

, 𝑠𝑡 ≡ ln 𝑆𝑡 and 𝜇𝑡+𝑘 is a disturbance term.

Testing for the foreign exchange market efficiency• If agents are risk-neutral and have rational expectations, we should expect the

slope parameter β to be equal to unity and the disturbance term 𝜇𝑡+𝑘 - the rational expectations forecast error under the null hypothesis – to be uncorrelated with information available at time t.

• Empirical studies based on the estimation of this equation, for a large variety of currencies and time periods, generally report results which are unfavorable to the efficient markets hypothesis under risk neutrality.

Carry trade

• A currency carry trade – a leveraged cross-currency position designed to take advantage of interest rate differentials and low volatility.

• The strategy involves borrowing funds at a low interest rate in one currency (the funding currency; such as Japanese yen or Swiss franc) and buying a higher yielding asset in another (the target currency; such as Australian dollar, New Zealand dollar, EME currencies).

• The strategy is only profitable as long as the gains from interest rate differentials are not expected to be overwhelmed by exchange rate movements in the short to medium term.

• UIP is not expected to hold. (Galati et al., 2007)

Recent data

Source: BIS Quarterly Review, September 2017

Recent data cont.

• Carry trade index (EM-8) – returns from carry trade rose sharply.

• According to the index for 8 EME currencies returns from carry trade have been positive in 11 of the past 17 years (Bloomberg).

• Speculative positions: US dollar and Japanese yen – net short; euro, Australian dollar, EME currencies – net long.

And some older…

Source: BIS Quarterly Review, December 2007

And some older… cont.

• Sharpe ratio – the average return earned in excess of the risk-free rate per unit of volatility or total risk.

• In the graph: Sharpe ratio calculated as the ratio of annualized excess returns to the annualized standard deviation of returns. As the risk-free rate is used the one-month US dollar Libor rate. Carry trade returns are calculated as the returns on a US dollarcollateral account from a strategy of borrowing in yen with a leverage ratio of 10, to buy an Australian or New Zealand dollar deposit for one month, allowing for profits and losses to be cumulated.

• Strategies such as the carry trade were profitable, but every once in a while the low-interest-rate currency undergoes a sudden appreciation…

=> for example, 1997-1998 Asian currency crisis (Thailand, Korea, Indonesia, Russia) and currency crisis in Brazil

• Sometimes the carry traders themselves are the ones who lead the turnaround.