Interest rate parity relates to the spot and forward exchange rates and the nominal interest rates expressed in the two currencies. It is often casually stated that interest rate parity requires equality between the interest rate differential and the forward premium or discount in the foreign exchange market. Analogously, if the domestic interest rate is less than the foreign interest rate, the foreign currency must be sold at a discount in the futures market.
This is typically done in the external foreign exchange market, the interbank market that is most closely linked to the foreign exchange market.
Covered Interest Arbitrage with Transaction Costs (Advanced)
How the external currency market affects other capital markets External exchange rates on the interbank market form the basis for the interest rates at which investors and companies can borrow and lend. For example, in Exhibit 6.2, banks accept 3-month CAD deposits at 1.05% in the interbank market, but the deposit rate available to a corporate customer may be 10 basis points less, or 0.95%. 1 LIBOR in other currencies is calculated using the middle half of the rates from eight, 12 or 16 banks.
Loan agreements involving corporations and sovereign countries often specify that the interest rate on a loan is a fixed spread over LIBOR. The determination of the spread depends on the possibility of the borrower defaulting on the loan. The failure of an attempt to implement covered interest rate arbitrage from the dollar to the pound is summarized by moving counterclockwise around the box in Figure 6.3.
Note: The exchange rates and interest rates associated with each arrow indicate the funds received in the currency at the point of the arrow from the sale of a unit of the currency at the tail of the arrow. We use data from Appendix 6.2 along with current and forward exchange rates also appearing in the Financial Times to examine how much would have been lost in trying to arbitrage between, say, the U.S. To eliminate exchange risk, we can contract to sell this amount of yen for dollars at the future rate.
Does Covered Interest Parity Hold?
Default Risks
We now examine three reasons why apparent arbitrage opportunities may not result in riskless profitable transactions: default risk, currency control, and political risk. There may also be some default on the forward contracts (again, because some banks are risky), and this may also lead to deviations from interest rate parity that do not represent arbitrage opportunities. Banks must constantly assess the risk of their counterparties, and a bank's risk managers set limits on the amount of trading that can be done with any particular counterparty.
2 Assessment of credit risk became crucial during the crisis of 2007 to 2010, which the box discusses in detail.
Deviations from Interest Rate Parity During the Financial Crisis 3
The graph clearly shows that the problems at several financial institutions in the United States, Europe and elsewhere created obvious arbitrage opportunities in the foreign exchange market, which expanded significantly after the collapse of Lehman. However, the arbitrageur would borrow dollars at the ask rate (properly represented by LIBOR), but lend at the ask rates for various currencies, not the LIBORs used in the calculations. As stated in Chapter 3, the crisis caused an increase in the volatility of the forex exchange rate, which led to an increase in transaction costs in the spot and especially futures markets.
Because different banks had very different exposures to "toxic" assets, LIBOR exhibited wide dispersion across banks, and many financial institutions had difficulty raising funds in the money markets. Therefore, default risk is unlikely to explain the large differences we observe in the graph. Most financial institutions have long-term assets financed by short-term liabilities, which they roll over in typically well-functioning money markets.
Now, if everyone tries to use the forward markets to do this, there could be upward pressure on the forward rate. As a safe haven currency, the dollar rose in the spot markets (S fell), but the actions of many banks prevented the dollar from strengthening proportionately in the futures market (F did not fall as much as it should have). With many more financial institutions in trouble and money market funds that invested in commercial paper issued by Lehman Brothers losing money, liquidity in the money markets almost completely dried up.
Exchange Controls
Political Risk
H EDGING T RANSACTION R ISK IN THE M ONEY M ARKET
If you have an open position (either a claim or a liability) denominated in a foreign currency, you are exposed to transaction currency risk. First, in some currency markets (such as some developing countries), futures contracts may not be available. Second, individual firms cannot borrow and lend at the interest rates available in the interbank market, meaning that the two strategies may not be equivalent, depending on the forward offer the firm receives.
Third, when the time horizons are long, forward contracts can be expensive as the bid-ask spread increases significantly. Therefore, it can be beneficial to consider borrowing and lending to hedge one's currency risk. For now, we focus on short-term money market hedges to get the logic correct.
The general principle is that if the underlying transaction gives you a liability (a trade payable) denominated in a foreign currency, you must have a corresponding asset in the money market to secure a hedge. If, on the other hand, the underlying transaction gives you an asset (a receivable) denominated in a foreign currency, you must have a corresponding liability in the money market to ensure a hedge. Because the investment is fully hedged against currency risk, this additional reward must be due to default risk and is typically called the country risk premium.
Epilogue
Hedging a Foreign Currency Liability
Hedging a Foreign Currency Receivable
Before we explore interest rate parity over longer time frames, we need to explain the term structure of interest rates. While interest rates for shorter maturities are available in the market, interest rates for longer maturities must be derived from coupon bond prices. Long-term interest rates are useful in calculating the present value of cash flows of long-term projects.
After we look at the term structures of interest rates for two currencies, we can combine them with interest rate parity to examine the term structure of the forward premiums or discounts between two currencies. If you do nothing to hedge the transaction's currency risk, you are exposed to losses if the yen falls against the pound. In Chapter 3, we eliminated the transaction's currency risk by selling the forward yen for pounds.
You borrow the cash value of your yen holdings and use the yen you receive from selling your sweaters to pay off the principal and interest on your yen loan. To be hedged, you must convert the borrowed yen principal into pounds at the spot exchange rate. At these interest rates and exchange rates, the money market hedging strategy is therefore effectively equivalent to the forward hedging strategy.
The Term Structure of Interest Rates Spot Interest Rates
Yield to maturity is easy to calculate for a variety of maturities, and market participants often discuss the yield curve. Just as the term structure of interest rates refers to the relationship between the maturity and the spot interest rate for different maturities, the yield curve is the relationship between the maturity and the yield on bonds with those maturities. When the yield curve slopes upward, the term structure of interest rates also slopes upward.
Note that yen interest rates are lowest across all maturities, and interest rates for shorter yen maturities are. As a result, the yield curve for the yen is said to be ascending or upward sloping. Note that the yield curves for all other currencies are also upward sloping, which is commonly observed.
For pure discount bonds, the yield to maturity is the spot interest rate for that maturity because there are no cash flows between now and the maturity date. When there are intermediate coupon payments and not all spot rates for different maturities are the same, there must be a difference between the yield to maturity on the bond and the spot rate for the bond's maturity. Notes: The yield curve data is taken from exchange rates (see Chapter 21) for various currencies published in the Financial Times for 18 January 2011.
Long-Term Forward Rates and Premiums
S UMMARY
When the money markets are free of arbitrage, this relationship between these four variables is called interest rate parity. When domestic and foreign interest rates and spot and forward exchange rates are in such equilibrium that no covered interest arbitrage is possible, the interest rates and exchange rates are said to satisfy interest rate parity. In the presence of transaction costs, interest rate parity is characterized by two inequalities, indicating that covered interest arbitrage leads to losses in both directions.
Empirical evidence shows that interest rate parity holds in quiet periods and for short maturities. If interest rate parity is met, money market hedging is equivalent to futures market hedging. If interest rate parity is met, there is no possibility of covered interest arbitrage.
Interest rate parity is often said to be satisfied when the difference between the interest rates denominated in two currencies is equal to the forward premium or discount between the two currencies. How does a coupon bond's yield to maturity differ from the spot interest rate that applies to cash flows that occur at the bond's maturity date. If the 180-day dollar interest rate is 7% p.a. is, what is the annualized 180-day interest rate on Swiss francs that will prevent arbitrage.
