Yield curve

Overview

A yield curve shows the relationship between yields and time to maturity for a set of comparable debt securities. In practice the term usually refers to curves built from a single issuer or market segment so that credit quality and other features are as similar as possible, for example the U.S. Treasury curve for government bonds. Different markets publish related curves for different purposes. Common examples include government bond curves, overnight indexed swap curves and interest rate swap curves. These families are produced by central banks and data providers from prices of instruments in each market and are kept comparable within a family by construction. Analysts often summarize the curve's shape with a "term spread" such as the difference between the 10-year Treasury yield and the 3-month Treasury bill rate. Central banks track these measures because a sustained inversion has historically preceded U.S. recessions and is used in simple recession-probability models. The yield curve is closely related to the term structure of interest rates. Official sources distinguish several ways to summarize it, including zero-coupon or "spot" curves, implied forward curves and par yield curves, each derived from the same underlying prices.

Significance of slope and shape

The slope is often summarised by a term spread. A common choice is the 10-year minus 3-month Treasury rates (the New York Fed's convention). Other pairs, such as 10-year minus 2-year, are also used in practice. A wider spread indicates a steeper slope. There are two common explanations for upward sloping yield curves. First, it may be that the market is anticipating a rise in the risk-free rate. If investors hold off investing now, they may receive a better rate in the future. Therefore, under the arbitrage pricing theory, investors who are willing to lock their money in now need to be compensated for the anticipated rise in rates—thus the higher interest rate on long-term investments. Another explanation is that longer maturities entail greater risks for the investor (i.e. the lender). A risk premium is needed by the market, since at longer durations there is more uncertainty and a greater chance of events that impact the investment. This explanation depends on the notion that the economy faces more uncertainties in the distant future than in the near term. This effect is referred to as the liquidity spread. If the market expects more volatility in the future, even if interest rates are anticipated to decline, the increase in the risk premium can influence the spread and cause an increasing yield. The opposite situation can also occur, in which the yield curve is "inverted", with short-term interest rates higher than long-term. For instance, in November 2004, the yield curve for UK Government bonds was partially inverted. The yield for the 10-year bond stood at 4.68%, but was only 4.45% for the 30-year bond. The market's anticipation of falling interest rates causes such incidents. Negative liquidity premiums can also exist if long-term investors dominate the market, but the prevailing view is that a positive liquidity premium dominates, so only the anticipation of falling interest rates will cause an inverted yield curve. Strongly inverted yield curves have historically preceded economic recessions. The shape of the yield curve is influenced by supply and demand: for instance, if there is a large demand for long bonds, for instance from pension funds to match their fixed liabilities to pensioners, and not enough bonds in existence to meet this demand, then the yields on long bonds can be expected to be low, irrespective of market participants' views about future events. The yield curve may also be flat or hump-shaped, due to anticipated interest rates being steady, or short-term volatility outweighing long-term volatility. Yield curves continually move all the time that the markets are open, reflecting the market's reaction to news. A further "stylized fact" is that yield curves tend to move in parallel; i.e.: the yield curve shifts up and down as interest rate levels rise and fall, which is then referred to as a "parallel shift".

Types of yield curve

There is no single yield curve describing the cost of money for everybody. The most important factor in determining a yield curve is the currency in which the securities are denominated. The economic position of the countries and companies using each currency is a primary factor in determining the yield curve. Different institutions borrow money at different rates, depending on their creditworthiness. The yield curves corresponding to the bonds issued by governments in their own currency are called the government bond yield curve (government curve). Banks and other issuers are quoted on swap curves, which reflect interbank funding and derivatives pricing and are typically above government curves of the same currency. Market participants refer to these as the swap curve. The construction of the swap curve is described below. Besides the government curve and the LIBOR curve, there are corporate (company) curves. These are constructed from the yields of bonds issued by corporations. Since corporations have less creditworthiness than most governments and most large banks, these yields are typically higher. Corporate yield curves are often quoted in terms of a "credit spread" over the relevant swap curve. For instance the five-year yield curve point for Vodafone might be quoted as LIBOR +0.25%, where 0.25% (often written as 25 basis points or 25bps) is the credit spread.

Normal yield curve

From the post-Great Depression era to the present, the yield curve has usually been "normal" meaning that yields rise as maturity lengthens (i.e., the slope of the yield curve is positive). A positive slope is consistent with expectations of higher future short-term rates and with term premia that compensate for uncertainty about inflation and rates at longer maturities. In a positively sloped curve, as a bond “rolls down” toward shorter maturities its yield typically falls and its price rises, contributing to return if yields are unchanged. However, a positively sloped yield curve has not always been the norm. Through much of the 19th century and early 20th century the US economy experienced trend growth with persistent deflation, not inflation. During this period the yield curve was typically inverted, reflecting the fact that deflation made current cash flows less valuable than future cash flows (i.e. the purchasing power of $1 would increase over time). During this period of persistent deflation, a 'normal' yield curve was negatively sloped.

Steep yield curve

Historically, the 20-year Treasury bond yield has averaged approximately two percentage points above that of three-month Treasury bills. In situations when this gap increases (e.g. 20-year Treasury yield rises much higher than the three-month Treasury yield), the economy is expected to improve quickly in the future. This type of curve can be seen at the beginning of an economic expansion (or after the end of a recession). Here, economic stagnation will have depressed short-term interest rates; however, rates begin to rise once the demand for capital is re-established by growing economic activity. In January 2010, the gap between yields on two-year Treasury notes and 10-year notes widened to 2.92 percentage points, its highest ever.

Flat or humped yield curve

A flat yield curve is observed when all maturities have similar yields, whereas a humped curve results when short-term and long-term yields are equal and medium-term yields are higher than those of the short-term and long-term. A flat curve sends signals of uncertainty in the economy. This mixed signal can revert to a normal curve or could later result into an inverted curve. It cannot be explained by the Segmented Market theory discussed below.

Inverted yield curve

Under unusual circumstances, investors will settle for lower yields associated with low-risk long-term debt if they think the economy will enter a recession in the near future. For example, the S&P 500 experienced a dramatic fall in mid 2007, from which it recovered completely by early 2013. Investors who had purchased 10-year Treasuries in 2006 would have received a safe and steady yield until 2015, possibly achieving better returns than those investing in equities during that volatile period. Economist Campbell Harvey's 1986 dissertation showed that an inverted yield curve accurately forecasts U.S. recessions. An inverted curve has indicated a worsening economic situation in the future eight times since 1970. In addition to potentially signaling an economic decline, inverted yield curves also imply that the market believes inflation will remain low. This is because, even if there is a recession, a low bond yield will still be offset by low inflation. However, technical factors, such as a flight to quality or global economic or currency situations, may cause an increase in demand for bonds on the long end of the yield curve, causing long-term rates to fall. Falling long-term rates in the presence of rising short-term rates is known as "Greenspan's Conundrum".

Relationship to the business cycle

The slope of the yield curve is one of the most powerful predictors of future economic growth, inflation, and recessions. One measure of the yield curve slope (i.e. the difference between 10-year Treasury bond rate and the 3-month Treasury bond rate) is included in the Financial Stress Index published by the St. Louis Fed. A different measure of the slope (i.e. the difference between 10-year Treasury bond rates and the federal funds rate) is incorporated into the Index of Leading Economic Indicators published by The Conference Board. An inverted yield curve is often a harbinger of recession. A positively sloped yield curve is often a harbinger of inflationary growth. Work by Arturo Estrella and Tobias Adrian has established the predictive power of an inverted yield curve to signal a recession. Their models show that when the difference between short-term interest rates (they use 3-month T-bills) and long-term interest rates (10-year Treasury bonds) at the end of a federal reserve tightening cycle is negative or less than 93 basis points positive, a rise in unemployment usually occurs. The New York Fed publishes a monthly recession probability prediction derived from the yield curve and based on Estrella's work. All the recessions in the US since 1970 have been preceded by an inverted yield curve (10-year vs 3-month). Over the same time frame, every occurrence of an inverted yield curve has been followed by recession as declared by the NBER business cycle dating committee. The yield curve became inverted in the first half of 2019, for the first time since 2007.

Estrella and others have postulated that the yield curve affects the business cycle via the balance sheet of banks (or bank-like financial institutions). When the yield curve is inverted, banks are often caught paying more on short-term deposits (or other forms of short-term wholesale funding) than they are making on new long-term loans leading to a loss of profitability and reluctance to lend resulting in a credit crunch. When the yield curve is upward sloping, banks can profitably take-in short-term deposits and make new long-term loans so they are eager to supply credit to borrowers. This eventually leads to a credit bubble.

Theory

There are three main economic theories attempting to explain how yields vary with maturity. Two of the theories are extreme positions, while the third attempts to find a middle ground between the former two.

Market expectations (pure expectations) hypothesis

This hypothesis assumes that the various maturities are perfect substitutes and suggests that the shape of the yield curve depends on market participants' expectations of future interest rates. It assumes that market forces will cause the interest rates on various terms of bonds to be such that the expected final value of a sequence of short-term investments will equal the known final value of a single long-term investment. If this did not hold, the theory assumes that investors would quickly demand more of the current short-term or long-term bonds (whichever gives the higher expected long-term yield), and this would drive down the return on current bonds of that term and drive up the yield on current bonds of the other term, so as to quickly make the assumed equality of expected returns of the two investment approaches hold. Using this, futures rates, along with the assumption that arbitrage opportunities will be minimal in future markets, and that futures rates are unbiased estimates of forthcoming spot rates, provide enough information to construct a complete expected yield curve. For example, if investors have an expectation of what 1-year interest rates will be next year, the current 2-year interest rate can be calculated as the compounding of this year's 1-year interest rate by next year's expected 1-year interest rate. More generally, returns (1+ yield) on a long-term instrument are assumed to equal the geometric mean of the expected returns on a series of short-term instruments:

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Liquidity premium theory

The liquidity premium theory is an offshoot of the pure expectations theory. The liquidity premium theory asserts that long-term interest rates not only reflect investors' assumptions about future interest rates but also include a premium for holding long-term bonds (investors prefer short-term bonds to long-term bonds), called the term premium or the liquidity premium. This premium compensates investors for the added risk of having their money tied up for a longer period, including the greater price uncertainty. Because of the term premium, long-term bond yields tend to be higher than short-term yields and the yield curve slopes upward. Long-term yields are also higher not just because of the liquidity premium, but also because of the risk premium added by the risk of default from holding a security over the long term. The market expectations hypothesis is combined with the liquidity premium theory:

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Preferred habitat theory

The preferred habitat theory is a variant of the liquidity premium theory, and states that in addition to interest rate expectations, investors have distinct investment horizons and require a meaningful premium to buy bonds with maturities outside their "preferred" maturity, or habitat. Proponents of this theory believe that short-term investors are more prevalent in the fixed-income market, and therefore longer-term rates tend to be higher than short-term rates, for the most part, but short-term rates can be higher than long-term rates occasionally. This theory is consistent with both the persistence of the normal yield curve shape and the tendency of the yield curve to shift up and down while retaining its shape.