Lecture 3: Interest Rate Parity, Speculation, and Risk PDF

Lecture 3: Interest Rate Parity, Speculation, and Risk Steven J. Riddiough Associate Professor of Finance University of Toronto International Financial Management Arbitrage Frictions Hedging Speculation...

Lecture 3: Interest Rate Parity, Speculation, and Risk Steven J. Riddiough Associate Professor of Finance University of Toronto International Financial Management Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Learning Objectives By the end of this lecture (and practice problems) you will be able to: 1 explain covered and uncovered interest rate parity 2 exploit arbitrage opportunities in forward exchange rate markets 3 hedge foreign exchange rate risk and speculate on foreign exchange rates using forward exchange rates 4 describe tests of uncovered interest rate parity and the reasons that researchers have concluded that the condition fails to hold International Financial Management Interest Rate Parity, Speculation, and Risk 2 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Forward Exchange Rates In Lecture 1, we defined the notation for forward exchange rates: the k-period forward exchange rate at time t is given by Ft →t +k This is the exchange rate that you can transact at in k-periods time that you agree upon (i.e., a contract is arranged) today Question: How does an FX dealer know what price to quote for a forward exchange rate? Does she have to predict the future spot price? International Financial Management Interest Rate Parity, Speculation, and Risk 3 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Arbitrage in FX Markets Arbitrage will be a familiar concept to you Simultaneously buying and selling the same or equivalent assets or commodities for the purpose of making certain (risk-free) profits Sounds “too good to be true” Since it is such a good deal, economists typically assume these opportunities do not exist (for long) It allows us to obtain the price at which arbitrage does not occur, i.e. the no-arbitrage price Practically, two portfolios with the same payoff and equal risk should have the same price Otherwise, buy the low price portfolio and sell the high price portfolio This assumes a perfect market (e.g., no taxes, no transaction costs) International Financial Management Interest Rate Parity, Speculation, and Risk 4 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Two Strategies and No Arbitrage Assuming no-arbitrage will help us find the value for Ft →t +k Strategies Price Payoff 1. Lend $1 for k-periods at it ,k $1 $1(1+it ,k ) 2. Convert $1 to foreign currency at St $1 then lend $1 S1t for k-periods at it∗,k F t → t +k then convert back to dollars at Ft →t +k $1 St (1 + it∗,k ) it ,k is the k-period risk-free rate in the domestic economy (here I assume it is the US but it does not need to be) it∗,k is the k-period risk-free rate in the foreign economy St is the number of US dollars for 1 unit of the foreign currency, hence $1 converts to 1/St units of foreign currency International Financial Management Interest Rate Parity, Speculation, and Risk 5 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Covered Interest Rate Parity Compare the two strategies: In both cases we start with $1 (prices are the same) and lend at the risk-free rate (no risk of default—the return is guaranteed) All prices (interest rates, spot rates, and forward rates) are agreed upon (contracted) today Key insight: Zero risk for both strategies and the same price =⇒ must have the same payoff! Ft →t +k 1 + it ,k (1 + it∗,k ) = 1 + it ,k =⇒ Ft →t +k = St St 1 + it∗,k This is covered interest rate parity (CIRP) International Financial Management Interest Rate Parity, Speculation, and Risk 6 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Eurocurrency In practical terms there is no “risk-free” rate, so what are it ,k and it∗,k ? We are typically referring to the interest rates that international banks charge one another to borrow and lend unsecured (e.g., USD LIBOR) This leads us to some confusing terminology: Eurocurrency refers to any currency (not just euros) being lent/borrowed outside of the country it was originally issued E.g., Eurodollars are dollars traded outside of the US, Euroeuros (yes, seriously!) are euros traded outside of the Eurozone Banks involved in the eurocurrency market are called Eurobanks they can hold deposits and make loans in foreign currency they are NOT necessarily based in Europe (but they might be) International Financial Management Interest Rate Parity, Speculation, and Risk 7 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up CIRP with Continuous Compounding Brief aside: The theoretical value for a forward exchange rate is: 1 + it ,k F t → t + k = St 1 + it∗,k However, for convenience academics often assume the interest rates are continuously compounded and take the (natural) log of both sides: ft →t +k − st = it ,k − it∗,k where ft →t +k = ln(Ft →t +k ), st = ln(St ), which makes life easier in a few ways (e.g., linearises the relationship) International Financial Management Interest Rate Parity, Speculation, and Risk 8 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up CIRP when k Varies When we talk about risk-free rates, we are typically referring to eurocurrency deposit rates These are the rates banks charge one another to borrow and lend They are quoted on an annualized basis Question: Assume the current 90-day US dollar rate is 2.5% and the 90-day UK pound rate is 3.5%. What is the 90-day forward exchange rate if the current spot exchange rate is $1.45/£? Convert the interest rates using a days/360 convention (this is how the FX market actually works, with some (very) minor exceptions) 90 1 + 0.025 × 360 1.00625 F90 = $1.45/£ 90 = $1.45/£ = $1.4464/£ 1 + 0.035 × 360 1.00875 International Financial Management Interest Rate Parity, Speculation, and Risk 9 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Exploiting Arbitrage Opportunities If in the previous example, the actual quoted forward exchange rate was F90 = $1.50/£, then an arbitrage opportunity would exist =⇒ F90 is too high, so we want to sell British pounds in the forward market Strategy: 1 Borrow $1 at it ,90 2 Convert to $1/St = £0.6897 and lend at it∗,90 3 In 90-days, receive £0.6957 (£0.6897 × 1.00875) and convert to $1.0435 at the 90-day forward rate of F90 = $1.50/£ 4 Repay $1.00625 on the dollar borrowing and pocket the difference of $0.03728 Of course, you could have borrowed more than $1. On $1,000,000 you would have made a $37,284 risk-free profit International Financial Management Interest Rate Parity, Speculation, and Risk 10 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Bid-Ask Spreads So far we have assumed there are no bid-ask spreads on any prices Doing so ensures CIRP holds exactly But it is unrealistic and we should take these costs into account In the previous example we borrowed at it ,90 but in reality we would borrow at the high (ask price), denote it itask ,90 Moreover, we would buy £’s at the high price Stask , lend £’s at a lower rate bid ,∗ it ,90 , and receive less $’s on the forward rate F90 bid The question about arbitrage now becomes: bid F90 ? (1 + itbid ,∗ ask ,90 ) − (1 + it ,90 ) > 0 Stask If the left-hand side is > 0, then an arbitrage opportunity still exists International Financial Management Interest Rate Parity, Speculation, and Risk 11 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Homework In the previous example we consider one case when 1 + it ,k F t → t + k > St 1 + it∗,k But a second case could also arise if the forward exchange rate is relatively undervalued Question 1: How would you exploit the opportunity if F90 = $1.4000/£ in the previous example? Assume there are no transaction costs and that you could borrow up to $1,000,000 (or foreign currency equivalent) Question 2: Now assume there are bid-ask spreads, what inequality would need to be satisfied to ensure an arbitrage opportunity still exists? International Financial Management Interest Rate Parity, Speculation, and Risk 12 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Evidence on CIRP pre-GFC Since the 1980’s researchers have been testing CIRP Recall the current era of “freely” floating exchange rates begins following the collapse of the Bretton Woods System Mark Taylor (1987): “the covered interest parity condition is tested using high-frequency [data]... [t]he results overwhelmingly support the market efficiency hypothesis” Akram, Rime, and Sarno (2008): “We investigate deviations from covered interest rate parity...[t]he analysis unveils that: i) short-lived violations of CIRP arise; ii) the size of CIRP violations can be economically significant; iii) their duration is, on average, high enough to allow agents to exploit them, but low enough to explain why such opportunities have gone undetected in much previous research using data at lower frequency” International Financial Management Interest Rate Parity, Speculation, and Risk 13 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Evidence on CIRP post-GFC Since the GFC, covered interest rate parity has gone crazy! Source: Du, Tepper, and Verdelhan (2018) International Financial Management Interest Rate Parity, Speculation, and Risk 14 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Explanations for the post-GFC “Anomaly” Since the GFC there have been large deviations from CIRP (across maturities, i.e., across values of k from months to multiple-years) Academic research is ongoing; a variety of alternative explanations have been proposed without yet reaching a consensus The most frequent argument is that banks (intermediaries) are constrained from exploiting these opportunities, principally due to regulation introduced after the GFC (e.g., bank leverage constraints) =⇒ there is an opportunity but it cannot be exploited or the opportunity is too small given the capital required An alternative is that interbank lending/borrowing is not riskless =⇒ there is not an opportunity since the “true” costs are higher than the data suggests International Financial Management Interest Rate Parity, Speculation, and Risk 15 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Hedging Transaction Risk If you have an open position (account receivable or payable) denominated in foreign currency then you are exposed to transaction FX risk You can hedge the FX exposure in one of two ways: 1 Enter a currency forward contract 2 Enter a “synthetic” currency forward contract using interest rates (known as a “money market hedge”) Example: You are a US importer of French wine and have agreed to pay €4 million once you receive the next shipment, scheduled in 90 days Assume: St = $1.10/€, F90 = $1.08/€ and the annualized 90-day interest rates are 6.00% in US dollars and 13.519% in euros International Financial Management Interest Rate Parity, Speculation, and Risk 16 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Liability Hedging: An Example The forward is fairly priced (HW: verify this), so both hedging solutions are equally appropriate Solution 1: Enter a forward contract In 90 days you wish to buy euros (and sell dollars), you need to enter a long position in the forward to lock-in a rate of F90 = $1.08/€ =⇒ total cost of €4Mil × $1.08/€ = $4,320,000 Solution 2: Enter a money-market hedge Buy the PV of €4Mil today (€3,869,230) at St = $1.10/€ =⇒ cost of $4,256,153 today This is equivalent to $4,320,000 in 90-days time ($4,256,153 × 1.015) International Financial Management Interest Rate Parity, Speculation, and Risk 17 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Speculating in the Foreign Exchange Market An implication of CIRP is that an investor should be indifferent between: 1 Lending at the risk-free rate in the domestic economy 2 Lending at the risk-free rate in the foreign economy and hedging the exchange rate exposure Ft → t +k 1 + it ,k = (1 + it∗,k ) | {z } St Lending at home | {z } Lending overseas and hedging =⇒ even if the foreign interest rate is high, an investor can only “lock in” the domestic risk-free rate International Financial Management Interest Rate Parity, Speculation, and Risk 18 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Currency Excess Returns Question: what happens if the investor decides not to lock in the exchange rate (i.e., does not use forward contracts) when investing abroad? The payoffs to lending 1 unit of domestic currency could be different: ? St + k 1 + it ,k = (1 + it∗,k ) | {z } St Lending at home | {z } Lending overseas and not hedging The currency excess return (CER) from lending in foreign currency is: St +k CER = (1 + it∗,k ) − (1 + it ,k ) St International Financial Management Interest Rate Parity, Speculation, and Risk 19 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Uncovered Interest Rate Parity The currency excess return only equals zero if St +k = Ft →t +k This brings us to Uncovered Interest Rate Parity (UIRP) According to UIRP, investors should only expect to receive the domestic risk-free rate when investing in the risk-free rate overseas Et [ St + k ] = F t → t + k But what about exchange rate risk? Good question! Instead of no-arbitrage conditions, we require two assumptions about investors: 1 Risk neutral (do not require extra compensation for uncertainty) 2 Rational expectations (i.e., expectations are consistent with risk neutrality and all available information is incorporated into prices) International Financial Management Interest Rate Parity, Speculation, and Risk 20 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up The Unbiasedness Hypothesis and Market Efficiency UIRP is often viewed in terms of market efficiency Imagine that the forward exchange rate is not an unbiased predictor: Et [St +k ] 6= Ft →t +k =⇒ CER 6= 0 If all investors have the same information then why would some expect to earn a negative return on a forward contract and others a positive return? This line of thinking does not exclude risk, the parity condition can be adapted to incorporate a risk premium, i.e., Et [St +k ] = Ft →t +k + risk premium... but testing the condition is tricky since we need to know the true equilibrium risk model for determining expected exchange rates International Financial Management Interest Rate Parity, Speculation, and Risk 21 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up A Simple Test Is UIRP a good description of how exchange rates behave? How can we test it? To begin, recall the definition of UIRP: Et [ St + k ] = F t → t + k Subtract St from both sides and divide by St : Et [ St + k ] − St Ft →t +k − St = St St In words, this says that the expected exchange rate return (i.e., appreciation or depreciation) equals the forward premium (not annualized) Unfortunately we do not observe expectations but realized returns, so we can test whether the average exchange rate return equals the average forward premium using a simple t-test International Financial Management Interest Rate Parity, Speculation, and Risk 22 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Empirical Evidence Based on this simple test it is hard to reject UIRP but the power of the tests might be low (standard errors are large) Source: Bekaert and Hodrick (2018) Table 7.4 International Financial Management Interest Rate Parity, Speculation, and Risk 23 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Regression analysis A natural alternative is regression analysis that uses data conditionally: Et [ St + k ] − St Ft →t +k − St =α+β + εt +k St St If UIRP holds then: α = 0: the average exchange rate return is zero β = 1: when interest rates are above their historical average the exchange rate depreciates International Financial Management Interest Rate Parity, Speculation, and Risk 24 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Empirical Evidence Empirically, many studies have found that β 6= 1 Source: Bekaert and Hodrick (2018) Table 7.5 International Financial Management Interest Rate Parity, Speculation, and Risk 25 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Why Does UIP Fail? According to UIRP a high interest rate currency should depreciate against a currency with a low interest rate In the data that is exactly what we see! BUT the depreciation does not fully offset the interest rate differential And currencies with higher than average interest rates appreciate =⇒ UIRP does not appear to hold exactly and CER’s are not zero This is a hot topic in academic research; there are at least 4 explanations: 1 Investors are rational but risk averse (it holds with a risk adjustment) 2 Investors are irrational (behavioural explanation) but risk neutral 3 It does hold! But we have not seen enough data (peso problem) 4 It does hold! But we do not measure expectations correctly International Financial Management Interest Rate Parity, Speculation, and Risk 26 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up The Carry Trade Going back to the simple test, we see that the average forward premium is in absolute terms bigger than the average exchange rate return =⇒ exchange rates do not fully offset interest rate differentials A naive trading strategy that exploits this finding is the currency carry trade long position in currencies with high interest rates and a short position in currencies with low interest rates can be entered in the money market or using forward contracts Homework: write down the currency excess return on a forward strategy and compare it with the money market approach Historically the return has been high and the risk-adjusted return (Sharpe ratio) over twice as high as observed in developed stock markets International Financial Management Interest Rate Parity, Speculation, and Risk 27 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Currency Risk Currency excess returns may reflect compensation for risk and therefore carry traders are compensated for bearing this risk On a technical (advanced) point: the fact β1 in the regressions is < 0 indicates the volatility of the risk premium must be (very!) high Hard to rationalize this finding theoretically Standard equilibrium models of risk, e.g., the CAPM, cannot explain carry trade returns But carry returns are typically negative in times of stress (e.g., the global financial crisis), consistent with a risk-based story Alternate currency-specific risks have been proposed recently International Financial Management Interest Rate Parity, Speculation, and Risk 28 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up The Peso Problem A peso problem invalidates statistical inference There is a “rare event” that could occur Not a black swan because investors anticipate it (put some positive weight on its occurrence) Since we have not observed this event, statistical inference fails—essentially under-weights the likelihood of it occurring (small sample problem) Implication: there may be a very large negative return in the future that will wipe out past carry trade returns Evidence on the peso problem is weak (it is not easy to test!) Recent evidence finds that a peso problem can only account for around one-third of carry returns International Financial Management Interest Rate Parity, Speculation, and Risk 29 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Main Takeaways Covered interest parity provides a no-arbitrage relationship between forward exchange rates, spot exchange rates, and money market (eurocurrency) interest rates If the condition fails, a possible arbitrage opportunity emerges Need to consider frictions (e.g., transaction costs) and whether they eliminate the profits from an arbitrage strategy Uncovered interest rate parity provides a guide to the relationship between the forward rate and future spot exchange rates If it holds, currency excess returns are expected to equal zero In the data currency excess returns do not equal zero: high interest rate currencies depreciate by less than the interest rate differential The currency carry trade strategy exploits this non-zero excess return International Financial Management Interest Rate Parity, Speculation, and Risk 30 / 31 Arbitrage Frictions Hedging Speculation Currency Risk Wrap Up Homework Required: 1 Attempt the practice problems Optional: 1 Readings: Burnside et al. (2011) and Du et al. (2018). Extracts from these papers will be provided to you 2 Attempt the additional problem questions from the textbook Anything unclear? International Financial Management: Third Edition by Geert Bekaert and Robert Hodrick, Chapters 6 and 7. Ask me! International Financial Management Interest Rate Parity, Speculation, and Risk 31 / 31