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2.3.1 Spot Interest Rates

Interest rate quotes have been directly available from the over-the-counter market for many years, for example, through the multicontributor "deposit" pages of Reuters. These interest rates are offered by banks to other banks who want to make either a deposit (at the bid interest rate) or take a credit (at the ask interest rate). The quotes come in bid-ask pairs and are called spot interest rates, cash interest rates, or interbank interest rates. Another traditional name, "Eurodeposits," suffers from possible confusion with the new currency named Euro. For quite some time, the spot interest rate (IR) market is no longer the most liquid IR market. This role is now taken by the IR futures market, see Section 2.4. The low liquidity of the spot IR market is reflected by the rather large spread between bid and ask quotes.

The actual rate at which a bank is ready to lend money to another one also depends on the credit rating of that bank. A bank with a low credit rating has to be ready to pay a higher IR in order to attract a lender; the IR level is increased by the credit spread. This fact makes the IR quotes less universally applicable than the FX quotes.

The credit spread can lead to serious data problems, which can lead to spurious statistical results. The story of the Japanese interest rates in the second half of the 1990s is the best illustration. There was a banking crisis in Japan that lowered the credit ratings of Japanese banks. In some data sources such as the Reuters deposit pages, these banks dominated some daytimes corresponding to the working hours of East Asian time zones. All of the IR quotes during these daytimes were systematically higher than the quotes at other daytimes. The market was split between low-rating banks and high-rating banks, causing two spurious statistical effects: (1) too high absolute values of returns (level changes) over time intervals of around 12 hr and (2) strong negative autocorrelation of returns at lags of around 12 hr. These spurious effects are solely due to periodically shifting credit ratings, which can be avoided by eliminating all the low-rating (or all high-rating) quotes from the sample. For a long time, Japanese Yen (JPY) interest rates were very low, below 1 % for Japanese banks. The credit spread led to a strange effect around 1998 by pushing the IR levels for non-Japanese banks (dominating the European and American time zones) slightly below zero. Since then, this has been a classical example rejecting zero as an absolute minimum of IRs. Slightly negative interest rates can be possible and valid under special circumstances.

Spot interest rates always refer to a deposit of fixed duration, the maturity period. The following maturity periods are quoted in the market: overnight (O/N), "tomorrow next" (T/N, the next business day after tomorrow), 1 week (S/W), 1 month (1M), 2 months (2M), 3 months (3M), 6 months (6M), 9 months (9M), and 1 year (1Y). Among these maturity periods, the 3-month maturity often has the largest market and the best data followed by the 1-month, 2-month, 6-month, and 1-year maturities. Spot interest rates are the only IR instruments that always inform us on interest rate levels for time intervals starting now and extending over

less than 3 months. Therefore, their use is inevitable when constructing yield curves; see Section 2.4.2.

Spot IRs are quoted in annualized form and in percentage terms. A 3-month IR of 6%, for example, means that the invested capital is multiplied by 1.015 after 3 months, because 3 months = 0.25 years and 0.25- 6% = 1.5% - 0.015.

2.3.2 Foreign Exchange Forward Rates

Foreign exchange (FX) forward rates share some characteristics with the spot IRs. They also refer to the interbank market and are quoted for the same maturities as the spot IRs (see Section 2.3.1). They are quoted on the same traditional Reuters deposit pages.

FX forward transactions are similar to FX spot transactions, except that the actual transaction takes effect in the future, at maturity.12 The timing of FX forward transactions leads to a difference in interest payments as compared to FX transactions. Due to the delayed transaction, the buyer of an FX forward contract earns some interest on the base currency of the FX rate (the currency in which the FX rate is expressed) instead of the exchanged currency. If the interest rates of the two currencies deviate, there is a net interest payment flow from or to the buyer during the maturity period. This fact determines the price of the FX forward contract, called the outright forward rate. In order to avoid riskfree arbitrage, the outright forward rate deviates from the simultaneously quoted FX spot price by an amount to offset the deviations in interest payments. The price deviation between FX spot prices and outright forward rates thus reflects the interest rate differential between the two exchanged currencies rather than the absolute level of those IRs.

The arbitrage relation between outright FX forward rates /, spot interest rates / and FX spot rates p can be formulated as follows:

1 "I" *cxpr,bid i year

/bid = Pbid - -.-~-wz (2.2)

1 cxch.ask ] vear

1 + expr.ask lvear

/ask - /?ask ~ : ~m~

1 \ vear

where m is the maturity period (e. g. 0.25 years for a 3-month period). This formula can be found in usual textbooks such as Walmsley (1992) but only for a middle price, not for bid and ask. It is valid for maturity periods up to one year. For longer periods, formulas based on compound interest are needed. The interest rates / should not be used in percentage (e.g., 0.05 should be used instead of 5%). The index "exch" denotes the exchanged currency of the FX rate; the index "expr" defines the (numeraire) currency in which one unit of the exchanged currency is expressed.

12 The transaction is actually booked at the value date, which is usually two days after the maturity date or, if that is a holiday, the first business day afterward. This fact hardly has an influence on prices, it just affects the timing of bookkeeping. Therefore, value dates can bc ignored in most studies.

Instead of outright FX forward prices /, the difference f - pis usually quoted, which is the outright forward price minus the simultaneously valid FX spot price. This difference is less volatile than the outright forward price and can be positive or negative according to the sign of the interest rate differential. A positive difference is called forward premium, a negative difference is forward discount. Both are also called "forward points." This formulation relates to the units of "basis points" in which they are usually quoted, which is the multiples of the last decimal digil of normal FX spot quotes. As an example, assume an FX spot rate of 1.5025/30 ( = 1.5025, pask = 1.5030) and quoted forward points of -23/-20. The outright forward price is therefore /bid = 1.5002 (- 1.5025 - 0.0023) and /ask = 1.5010 (= 1.5030-0.0020).

FX forward premiums and discounts are also called FX swap rates, following another common view where an FX forward transaction is seen as a spot transaction plus a "swap" transaction (swapping two currencies during the maturity period). In fact, there is a large market for such FX swap transactions independent from spot or outright forward transactions.

Equation 2.2 can be used to compute synthetic forward rates from an FX spot rate and the spot IRs of both underlying currencies. Such synthetic FX forward rates are less reliable than direct quotes. They have a distinctly higher bid-ask spread. This implies that an FX forward transaction is more efficient than a substitute set of transactions, consisting of an FX spot transaction plus a deposit in one currency plus a loan in the other one. Direct forward quotes exist for most FX rates against the USD, but may not be available for some FX cross rates (see Section 2.2.2). For these currency pairs, synthetic forward rates are needed.


2.4.1 General Description of Interest Rate Futures

Short-term interest rate (IR) futures are the most liquid financial instrument for the interest rate markets. In particular, the IR futures markets with expiry periods of up to one year (or slightly longer) are more liquid than the over-the-counter spot IR market, as presented in Section 2.3.1. The transaction costs are lower; atypical bid-ask spread is about 10% (or less) of the quoted spread of cash interest rates.13 The mechanism of price formation for futures is faster than for cash contracts (Fung and Leung, 1993; Garbade and Silber, 1985). As a consequence, IR futures markets yield high-quality intraday data.

IR futures markets are futures markets in the sense of Section 2.1.2. More specifically, an interest rate futures contract is a futures contract on an asset whose price is dependent solely on the level of interest rates, (Hull, 1993).

3 The bid-ask spread on the Chicago Mercantile Exchange (CJVIE) Eurodollar contract, for example, can be as small as half a basis point. A basis point corresponds to 1 /100 of 1 %, and its monetary value (in the case of three-month IR futures) is $25. The minimum price movement for the CME Eurodollar is half a basis point.

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