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| {{About|yield curves as used in finance|the term's use in physics|Yield curve (physics)}}
| | A lagging computer is actually annoying and is very a headache. Almost each person whom utilizes a computer faces this problem several time or the additional. If the computer additionally suffers from the same issue, we will find it hard to continue functioning as usual. In such a situation, the thought, "what could I do to make my PC run quicker?" is recurring and infuriating. There's a answer, still!<br><br>StreamCI.dll errors are caused by a number of different problems, including that the file itself has been moved on a program, the file is outdated or we have installed several third-party audio drivers that are conflicting with the file. The wise news is the fact that if you would like to solve the error you're seeing, you need to look to first ensure the file & drivers are working okay on the PC as well as then resolving any StreamCI.dll errors which may be inside the registry of the computer.<br><br>The PC would have a fragmented difficult drive or the windows registry would have been corrupted. It might additionally be as a result of the dust plus dirt that needs to be cleaned. Whatever the problem, you can constantly find a answer. Here are several strategies on how to make the PC run faster.<br><br>If that refuses to work you should try plus repair the problem with a 'registry cleaner'. What arises on several computers is that their registry database becomes damaged plus unable to show your computer where the DLL files that it needs are. Every Windows PC has a central 'registry' database that shops information regarding all DLL files on the computer.<br><br>Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with improper values could lead to runtime mistakes and thereby the issue happens. You are recommended to scan the whole system registry plus review the result. Attempt the registry repair task using third-party [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities] software.<br><br>Why this issue arises frequently? What are the causes of it? In truth, there are 3 major causes that could cause the PC freezing problem. To solve the issue, you should take 3 steps inside the following paragraphs.<br><br>Perfect Optimizer is a advantageous Registry Product, updates consistently and has lots of qualities. Despite its cost, there are which the update are truly useful. They offer plenty of help through telephone, send plus forums. We could like to pay a visit to the free trial to check it out for oneself.<br><br>What I would recommend is to search on a own for registry products. You are able to do this with a Google search. Whenever you find products, look for reviews plus reviews regarding the product. Next you are able to see how others like the product, and how perfectly it functions. |
| {{distinguish2|Yield-curve spread – see [[Z-spread]]}}
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| {{Refimprove|date=June 2011}}
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| [[File:USD yield curve 09 02 2005.JPG|right|thumb|250px|The US dollar yield curve as of February 9, 2005. The curve has a typical upward sloping shape.]]
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| In [[finance]], the '''yield curve''' is a curve showing several yields or interest rates across different contract lengths (2 month, 2 year, 20 year, etc...) for a similar debt contract. The curve shows the relation between the (level of) [[interest rate]] (or cost of borrowing) and the time to [[Maturity (finance)|maturity]], known as the "'''term'''", of the debt for a given borrower in a given [[currency]]. For example, the [[United States dollar|U.S. dollar]] interest rates paid on [[United States Treasury security|U.S. Treasury securities]] for various maturities are closely watched by many traders, and are commonly plotted on a graph such as the one on the right which is informally called "the yield curve". More formal mathematical descriptions of this relation are often called the '''term structure of interest rates'''.
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| The shape of the yield curve indicates the cumulative priorities of all lenders relative to a particular borrower (such as the US Treasury or the Treasury of Japan). Usually, lenders are concerned about a potential default (or rising rates of inflation), so they offer long-term loans for higher interest rates than they offer for shorter-term loans. Occasionally, when lenders are seeking long-term debt contracts more aggressively than short-term debt contracts, the yield curve "inverts", with interest rates (yields) being lower for the longer periods of repayment so that lenders can attract long-term borrowing.
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| The [[yield (finance)|yield]] of a [[debt]] instrument is the overall rate of return available on the investment. In general the percentage per year that can be earned is dependent on the length of time that the money is invested. For example, a bank may offer a "savings rate" higher than the normal checking account rate if the customer is prepared to leave money untouched for five years. Investing for a period of time ''t'' gives a yield ''Y''(''t'').
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| This [[Function (mathematics)|function]] ''Y'' is called the ''yield curve'', and it is often, but not always, an increasing function of ''t''. Yield curves are used by [[fixed income]] analysts, who analyze [[Bond (finance)|bonds]] and related securities, to understand conditions in financial markets and to seek trading opportunities. [[Economist]]s use the curves to understand economic conditions.
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| The yield curve function ''Y'' is actually only known with certainty for a few specific maturity dates, while the other maturities are calculated by [[interpolation]] (''see [[#Construction of the full yield curve from market data|Construction of the full yield curve from market data]] below'').
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| ==The typical shape of the yield curve==
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| [[File:GBP yield curve 09 02 2005.JPG|right|thumb|250px|The British pound yield curve on February 9, 2005. This curve is unusual (inverted) in that long-term rates are lower than short-term ones.]]
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| Yield curves are usually upward sloping [[asymptotically]]: the longer the maturity, the higher the yield, with diminishing marginal increases (that is, as one moves to the right, the curve flattens out). 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.
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| 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 catastrophic 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.
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| The opposite position (short-term interest rates higher than long-term) can also occur. For instance, in November 2004, the yield curve for [[Gilt-edged securities|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 premium]]s 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 depressions. | |
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| 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.
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| 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.
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| 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).
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| ===Types of yield curve===
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| 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 with high [[Bond credit rating|credit ratings]] (Aa/AA or above) borrow money from each other at the [[LIBOR]] rates. These yield curves are typically a little higher than government curves. They are the most important and widely used in the financial markets, and are known variously as the [[LIBOR]] curve or the [[swap (finance)|swap]] curve. The construction of the swap curve is described below.
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| Besides the government curve and the LIBOR curve, there are [[corporation|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 point]]s or 25{{Not a typo|bps}}) is the credit spread.
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| ==== Normal yield curve ====
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| <!-- Deleted image removed: [[File:normal-yield-curve.gif|thumb|100px|Normal Yield Curve]] -->
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| 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). This positive slope reflects investor expectations for the economy to grow in the future and, importantly, for this growth to be associated with a greater expectation that inflation will rise in the future rather than fall. This expectation of higher inflation leads to expectations that the [[central bank]] will tighten monetary policy by raising short term interest rates in the future to slow economic growth and dampen inflationary pressure. It also creates a need for a risk premium associated with the uncertainty about the future rate of inflation and the risk this poses to the future value of cash flows. Investors price these risks into the yield curve by demanding higher yields for maturities further into the future. In a positively sloped yield curve, lenders profit from the passage of time since yields decrease as bonds get closer to maturity (as yield decreases, price ''increases''); this is known as '''rolldown''' and is a significant component of profit in fixed-income investing (i.e., buying and selling, not necessarily holding to maturity), particularly if the investing is [[Leverage (finance)|leveraged]].<ref>[http://www.ft.com/intl/cms/s/0/04868cd6-d7b2-11e0-a06b-00144feabdc0.html ‘Helicopter Ben’ risks destroying credit creation], September 6, 2011, [[Financial Times]], by [[Bill Gross]]</ref>
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| 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. During this period of persistent deflation, a 'normal' yield curve was negatively sloped.
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| ==== Steep yield curve ====
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| 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 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.
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| 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.
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| ==== Flat or humped yield curve ====
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| <!-- Deleted image removed: [[File:flat-yield-curve.gif|thumb|100px|Flat Yield Curve]] -->
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| 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.
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| ==== Inverted yield curve ====
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| <!-- Deleted image removed: [[File:inverted-yield-curve.gif|thumb|100px|Inverted Yield Curve]] -->
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| An inverted yield curve occurs when long-term yields fall below short-term yields. See.<ref>[http://gregmankiw.blogspot.jp/2006/06/what-does-inverted-yield-curve-mean.html/ What does an inverted yield curve mean?]</ref>
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| Under unusual circumstances, long-term investors will settle for lower yields now if they think the economy will slow or even decline in the future. Campbell R. Harvey's 1986 dissertation<ref>[http://faculty.fuqua.duke.edu/~charvey/Research/Thesis/Thesis.htm [[Campbell Harvey]], 1986. University of Chicago Dissertation.]</ref> showed that an inverted yield curve accurately forecasts U.S. recessions. An inverted curve has indicated a worsening economic situation in the future 6 out of 7 times since 1970.<ref>[http://faculty.fuqua.duke.edu/~charvey/Term_structure/ Campbell R. Harvey, 2010. The Yield Curve: An update.]</ref> The New York Federal Reserve regards it as a valuable forecasting tool in predicting recessions two to six quarters ahead. 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.
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| Since the [[financial crisis of 2007–2008]], the U. S. [[Federal Reserve]] has maintained a [[zero interest-rate policy]] (ZIRP) for an "extended period of time", where the short term interest rate is practically set to zero.
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| ==Theory==
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| 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.
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| ===Market expectations (pure expectations) hypothesis===
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| {{main|expectation hypothesis}}
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| : <math>(1 + i_{lt})^n=(1 + i_{st}^{\text{year }1})(1 + i_{st}^{\text{year }2}) \cdots (1 + i_{st}^{\text{year }n})</math>
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| This [[hypothesis]] assumes that the various maturities are [[Substitute good|perfect substitutes]] and suggests that the shape of the yield curve depends on market participants' expectations of future interest rates. Using this, future rates, along with the assumption that [[arbitrage]] opportunities will be minimal in future markets, and that future rates are unbiased estimates of forthcoming spot rates, is 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 2-year interest rate can be calculated as the compounding of this year's interest rate by next year's interest rate. More generally, rates on a long-term instrument are equal to the [[geometric mean]] of the yield on a series of short-term instruments. This theory perfectly explains the observation that yields usually move together. However, it fails to explain the persistence in the shape of the yield curve.
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| Shortcomings of expectations theory:
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| Neglects the risks inherent in investing in bonds (because forward rates are not perfect predictors of future rates).
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| 1) [[Interest rate risk]]
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| 2) Reinvestment rate risk
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| ===Liquidity premium theory===
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| 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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| : <math>(1 + i_{lt})^n=rp_{n}+((1 + i_{st}^{\mathrm{year }1})(1 + i_{st}^{\mathrm{year }2}) \cdots (1 + i_{st}^{\mathrm{year }n}))</math>
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| Where <math>rp_n</math> is the risk premium associated with an <math>{n}</math> year bond.
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| ===Market segmentation theory===
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| This theory is also called the '''segmented market hypothesis'''. In this theory, financial instruments of different terms are not [[substitute good|substitutable]]. As a result, the [[supply and demand]] in the markets for short-term and long-term instruments is determined largely independently. Prospective investors decide in advance whether they need short-term or long-term instruments. If investors prefer their portfolio to be liquid, they will prefer short-term instruments to long-term instruments. Therefore, the market for short-term instruments will receive a higher demand. Higher demand for the instrument implies higher prices and lower yield. This explains the [[stylized fact]] that short-term yields are usually lower than long-term yields. This theory explains the predominance of the normal yield curve shape. However, because the supply and demand of the two markets are independent, this theory fails to explain the observed fact that yields tend to move together (i.e., upward and downward shifts in the curve).
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| ===Preferred habitat theory===
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| The preferred habitat theory is another guide 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.
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| ===Historical development of yield curve theory===
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| On 15 August 1971, U.S. President [[Richard Nixon]] announced that the U.S. dollar would no longer be based on the [[gold standard]], thereby ending the [[Bretton Woods system]] and initiating the era of [[floating exchange rate]]s.
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| Floating exchange rates made life more complicated for bond traders, including those at [[Salomon Brothers]] in [[New York]]. By the middle of the 1970s, encouraged by the head of bond research at Salomon, Marty Liebowitz, traders began thinking about bond yields in new ways. Rather than think of each maturity (a ten year bond, a five year, etc.) as a separate marketplace, they began drawing a curve through all their yields. The bit nearest the present time became known as the ''short end''—yields of bonds further out became, naturally, the ''long end''.
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| Academics had to play catch up with practitioners in this matter. One important theoretic development came from a Czech mathematician, [[Oldrich Vasicek]], who argued in a 1977 paper that bond prices all along the curve are driven by the short end (under risk neutral equivalent martingale measure) and accordingly by short-term interest rates. The mathematical model for Vasicek's work was given by an [[Ornstein–Uhlenbeck process]], but has since been discredited because the model predicts a positive probability that the short rate becomes negative and is inflexible in creating yield curves of different shapes. Vasicek's model has been superseded by many different models including the [[Hull–White model]] (which allows for time varying parameters in the Ornstein–Uhlenbeck process), the [[Cox–Ingersoll–Ross model]], which is a modified [[Bessel process]], and the [[Heath–Jarrow–Morton framework]]. There are also many modifications to each of these models, but see the article on [[short rate model]].
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| Another modern approach is the [[LIBOR market model]], introduced by Brace, Gatarek and Musiela in 1997 and advanced by others later.
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| In 1996 a group of derivatives traders led by Olivier Doria (then head of swaps at Deutsche Bank) and Michele Faissola, contributed to an extension of the swap yield curves in all the major European currencies. Until then the market would give prices until 15 years maturities. The team extended the maturity of European yield curves up to 50 years (for the lira, French franc, Deutsche mark, Danish krone and many other currencies including the ecu). This innovation was a major contribution towards the issuance of long dated zero coupon bonds and the creation of long dated mortgages.
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| ==Construction of the full yield curve from market data==
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| {| class="toccolours" border="1" cellpadding="4" cellspacing="0" align="right" style="margin: 0em 1em 0em 1em;"
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| |+ '''Typical inputs to the money market curve'''
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| |-
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| |'''Type'''
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| |'''Settlement date'''
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| |'''Rate (%)'''
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| |-
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| |Cash
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| |Overnight rate
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| |5.58675
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| |-
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| |Cash
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| |Tomorrow next rate
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| |5.59375
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| |-
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| |Cash
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| |1m
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| |5.625
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| |-
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| |Cash
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| |3m
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| |5.71875
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| |-
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| |Future
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| |Dec-97
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| |5.76
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| |-
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| |Future
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| |Mar-98
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| |5.77
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| |-
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| |Future
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| |Jun-98
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| |5.82
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| |-
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| |Future
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| |Sep-98
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| |5.88
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| |-
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| |Future
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| |Dec-98
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| |6.00
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| |-
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| |Swap
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| |2y
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| |6.01253
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| |-
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| |Swap
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| |3y
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| |6.10823
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| |-
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| |Swap
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| |4y
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| |6.16
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| |-
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| |Swap
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| |5y
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| |6.22
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| |-
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| |Swap
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| |7y
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| |6.32
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| |-
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| |Swap
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| |10y
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| |6.42
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| |-
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| |Swap
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| |15y
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| |6.56
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| |-
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| |Swap
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| |20y
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| |6.56
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| |-
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| |Swap
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| |30y
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| |6.56
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| |-
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| |colspan="3"|
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| A list of standard instruments used to build a money market yield curve.
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| |-
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| |colspan="3"|
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| The data is for lending in [[US dollar]], taken from October 6, 1997
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| |}
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| The usual representation of the yield curve is a function P, defined on all future times ''t'', such that P(''t'') represents the value today of receiving one unit of currency ''t'' years in the future. If P is defined for all future ''t'' then we can easily recover the yield (i.e. the annualized interest rate) for borrowing money for that period of time via the formula
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| :<math>Y(t) = P(t)^{-1/t} -1. </math>
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| The significant difficulty in defining a yield curve therefore is to determine the function P(''t''). P is called the discount factor function.
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| Yield curves are built from either prices available in the ''bond market'' or the ''money market''. Whilst the yield curves built from the bond market use prices only from a specific class of bonds (for instance bonds issued by the UK government) yield curves built from the [[money market]] use prices of "cash" from today's LIBOR rates, which determine the "short end" of the curve i.e. for ''t'' ≤ 3m, [[financial futures|futures]] which determine the midsection of the curve (3m ≤ ''t'' ≤ 15m) and [[interest rate swap]]s which determine the "long end" (1y ≤ ''t'' ≤ 60y).
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| The example given in the table at the right is known as a [[LIBOR]] curve because it is constructed using either LIBOR rates or [[swap rates]]. A LIBOR curve is the most widely used interest rate curve as it represents the credit worth of private entities at about A+ rating, roughly the equivalent of commercial banks. If one substitutes the LIBOR and swap rates with government bond yields, one arrives at what is known as a government curve, usually considered the risk free interest rate curve for the underlying currency. The spread between the LIBOR or swap rate and the government bond yield, usually positive, meaning private borrowing is at a premium above government borrowing, of similar maturity is a measure of risk tolerance of the lenders. For the U. S. market, a common benchmark for such a spread is given by the so-called [[TED spread]].
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| In either case the available market data provides a matrix ''A'' of cash flows, each row representing a particular financial instrument and each column representing a point in time. The (''i'',''j'')-th element of the matrix represents the amount that instrument ''i'' will pay out on day ''j''. Let the vector ''F'' represent today's prices of the instrument (so that the ''i''-th instrument has value ''F''(''i'')), then by definition of our discount factor function ''P'' we should have that ''F'' = ''AP'' (this is a matrix multiplication). Actually, noise in the financial markets means it is not possible to find a ''P'' that solves this equation exactly, and our goal becomes to find a vector ''P'' such that | |
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| : <math> AP = F + \varepsilon \, </math>
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| where <math>\varepsilon</math> is as small a vector as possible (where the size of a vector might be measured by taking its [[norm (mathematics)|norm]], for example).
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| Note that even if we can solve this equation, we will only have determined ''P''(''t'') for those ''t'' which have a cash flow from one or more of the original instruments we are creating the curve from. Values for other ''t'' are typically determined using some sort of [[interpolation]] scheme.
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| Practitioners and researchers have suggested many ways of solving the A*P = F equation. It transpires that the most natural method – that of minimizing <math>\epsilon</math> by [[least squares regression]] – leads to unsatisfactory results. The large number of zeroes in the matrix ''A'' mean that function ''P'' turns out to be "bumpy".
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| In their comprehensive book on interest rate modelling James and Webber note that the following techniques have been suggested to solve the problem of finding P:
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| #Approximation using [[Lagrange polynomials]]
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| #Fitting using parameterised curves (such as [[Spline (mathematics)|spline]]s, the [[Fixed income attribution#Modeling the yield curve|Nelson–Siegel]] family, the Svensson family or the Cairns restricted-exponential family of curves). Van Deventer, Imai and Mesler summarize three different techniques for [[curve fitting]] that satisfy the maximum smoothness of either forward interest rates, zero coupon bond prices, or zero coupon bond yields
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| #Local regression using [[Kernel (statistics)|kernels]]
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| #[[Linear programming]]
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| In the money market practitioners might use different techniques to solve for different areas of the curve. For example at the short end of the curve, where there are few cashflows, the first few elements of P may be found by [[bootstrapping (finance)|bootstrapping]] from one to the next. At the long end, a regression technique with a cost function that values smoothness might be used.
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| ==How the yield curve affects bond prices==
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| There is a time dimension to the analysis of bond values. A 10-year bond at purchase becomes a 9-year bond a year later, and the year after it becomes an 8-year bond, etc. Each year the bond moves incrementally closer to maturity, resulting in lower volatility and shorter duration and demanding a lower interest rate when the yield curve is rising. Since falling rates create increasing prices, the value of a bond initially will rise as the lower rates of the shorter maturity become its new market rate. Because a bond is always anchored by its final maturity, the price at some point must change direction and fall to par value at redemption.
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| A bond's market value at different times in its life can be calculated. When the yield curve is steep, the bond is predicted to have a large [[capital gain]] in the first years before falling in price later. When the yield curve is flat, the capital gain is predicted to be much less, and there is little variability in the bond's total returns over time.
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| Rising (or falling) interest rates rarely rise by the same amount all along the yield curve—the curve rarely moves up in parallel. Because longer-term bonds have a larger duration, a rise in rates will cause a larger capital loss for them, than for short-term bonds. But almost always, the long maturity's rate will change much less, flattening the yield curve. The greater change in rates at the short end will offset to some extent the advantage provided by the shorter bond's lower duration.
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| The yearly 'total return' from the bond is a) the sum of the coupon's yield plus b) the capital gain from the changing valuation as it slides down the yield curve and c) any capital gain or loss from changing interest rates at that point in the yield curve.<ref>[http://www.retailinvestor.org/bondPrice.html Changes to a Bond's Value Over Time as Rates Change]</ref>
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| ==Relationship to the business cycle==
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| The slope of the yield curve is one of the most powerful predictors of future economic growth, inflation, and recessions.<ref>Arturo Estrella & Frederic S. Mishkin, ''[http://www.mitpressjournals.org/doi/abs/10.1162/003465398557320?journalCode=rest The Review of Economics & Statistics, Predicting U.S. Recessions: Financial Variables as Leading Indicators]'', 1998</ref> One measure of the yield curve slope (i.e. the difference between 10-year Treasury bond rates and the [[federal funds rate]]) is included in the [[Conference Board Leading Economic Index|Index of Leading Economic Indicators]].
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| An inverted yield curve is often a harbinger of [[recession]]. A positively sloped yield curve is often a harbinger of [[inflation]]ary growth. Work by Dr. Arturo Estrella & Dr. 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 (he uses 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 that a rise in unemployment usually occurs.<ref>Arturo Estrella & Tobias Adrian , ''[http://www.newyorkfed.org/research/staff_reports/sr397.pdf FRB of New York Staff Report No. 397]'', 2009</ref>
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| All of the recessions in the US since 1970 (up through 2011) 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 [[National Bureau of Economic Research|NBER]] business cycle dating committee.
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| {| class="wikitable sortable"
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| ! Event !! class="unsortable"|Date of Inversion Start !! class="unsortable"|Date of the Recession Start !! Time from Inversion to Recession Start !! Duration of Inversion !! Time from Disinversion to Recession End !! Duration of Recession !! Max Inversion
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| ! !! !! !! Months !! Months !! Months !! Months !! Basis Points
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| | 1970 Recession || Dec-68 || Jan-70 || 13 || 15 || 8 || 11 || −52
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| | 1974 Recession || Jun-73 || Dec-73 || 6 || 18 || 3 || 16 || −159
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| | 1980 Recession || Nov-78 || Feb-80 || 15 || 18 || 2 || 6 || −328
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| | 1981-1982 Recession || Oct-80 || Aug-81 || 10 || 12 || 13 || 16 || −351
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| | 1990 Recession || Jun-89 || Aug-90 || 14 || 7 || 14 || 8 || −16
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| | 2001 Recession || Jul-00 || Apr-01 || 9 || 7 || 9 || 8 || −70
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| | 2008-2009 Recession || Aug-06 || Jan-08 || 17 || 10 || 24 || 18 || −51
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| | Average since 1969 || || || 12 || 12 || 10 || 12 || −147
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| | Std Dev since 1969 || || || 3.83 || 4.72 || 7.50 || 4.78 || 138.96
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| |}
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| Dr. Estrella has postulated that the yield curve affects the [[business cycle]] via the balance sheet of banks.<ref>Arturo Estrella, ''[http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1532309 FRB of New York Staff Report No. 421]'', 2010</ref> When the yield curve is inverted banks are often caught paying more on short-term deposits than they are making on 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 long-term loans so they are eager to supply credit to borrowers resulting in a [[Economic bubble|credit bubble]].
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| ==See also==
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| *[[Short-rate model]]
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| *[[Zero-coupon bond]]
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| *[[Zero interest rate policy]]
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| ==Notes==
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| {{reflist}}
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| ==References==
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| ===Books===
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| *{{cite book | title = Interest Rate Modelling | author = Jessica James & Nick Webber | publisher = John Wiley & Sons | year = 2001 | isbn = 0-471-97523-0 }}
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| *{{cite book | title = Interest-Rate Option Models | author = [[Riccardo Rebonato]] | publisher = John Wiley & Sons | year = 1998 | isbn = 0-471-97958-9}}
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| *{{cite book | title = Inventing Money | author = Nicholas Dunbar | publisher = John Wiley & Sons | year = 2000 | isbn = 0-471-89999-2}}
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| *{{cite book | title = Estimating and Interpreting the Yield Curve | author = N. Anderson, F. Breedon, M. Deacon, A. Derry and M. Murphy | publisher = John Wiley & Sons | year = 1996 | isbn = 0-471-96207-4}}
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| *{{cite book | title = Interest Rate Models – An Introduction | author = Andrew J.G. Cairns | publisher = Princeton University Press | year = 2004 | isbn = 0-691-11894-9 }}
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| *{{cite book | title = Options, Futures and Other Derivatives | author = John C. Hull | publisher = Prentice Hall | year = 1989 | isbn = 0-13-015822-4}} See in particular the section ''Theories of the term structure'' (section 4.7 in the fourth edition).
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| *{{cite book | title = Interest Rate Models – Theory and Practice | author = Damiano Brigo, Fabio Mercurio | publisher = Springer | year = 2001 | isbn = 3-540-41772-9}}
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| *{{cite book | title = Advanced Financial Risk Management, An Integrated Approach to Credit Risk and Interest Rate Risk Management | author = Donald R. van Deventer, Kenji Imai, Mark Mesler | year = 2004 | publisher = John Wiley & Sons | isbn = 978-0-470-82126-8}}
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| ===Articles===
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| * Ruben D Cohen (2006) "A VaR-Based Model for the Yield Curve [http://rdcohen.50megs.com/YieldCurveabstract.htm [download]]" ''Wilmott Magazine'', May Issue.
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| *{{cite book | author = Lin Chen |year= 1996 | title= Stochastic Mean and Stochastic Volatility – A Three-Factor Model of the Term Structure of Interest Rates and Its Application to the Pricing of Interest Rate Derivatives | publisher= Blackwell Publishers}}
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| * Paul F. Cwik (2005) "The Inverted Yield Curve and the Economic Downturn [http://pcpe.libinst.cz/nppe/1_1/nppe1_1_1.pdf [download]]" ''[[New Perspectives on Political Economy]]'', Volume 1, Number 1, 2005, pp. 1–37.
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| * Roger J.-B. Wets, Stephen W. Bianchi, "Term and Volatility Structures" in {{cite book | title = Handbook of Asset and Liability Management, Volume 1 | author = Stavros A. Zenios & William T. Ziemba | publisher = North-Holland | year = 2006 | isbn = 0-444-50875-9 }}
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| *{{cite journal |last=Hagan|first= P.|authorlink= |coauthors= West, G.|date=June 2006|title= Interpolation Methods for Curve Construction
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| |journal= Applied Mathematical Finance|volume= 13|issue= 2|pages= 89–129|id= |url= http://www.finmod.co.za/Hagan_West_curves_AMF.pdf|accessdate= |quote= }}
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| *Rise in Rates Jolts Markets – Fed's Effort to Revive Economy Is Complicated by Fresh Jump in Borrowing Costs author = Liz Rappaport. Wall Street Journal. May 28, 2009. p. A.1
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| ==External links==
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| *[http://www.ecb.int/stats/money/yc/html/index.en.html/ Euro area yield curves] – European Central Bank website
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| *[http://stockcharts.com/charts/YieldCurve.html Dynamic Yield Curve] – This chart shows the relationship between interest rates and stocks over time.
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| *[http://www.newyorkfed.org/research/current_issues/ NYFed Current Issue] – Current Issue of New York Federal Reserve outlining their view of inverted yield curve
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| {{Bond market}}
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| [[Category:Economics curves]]
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| [[Category:Fixed income market]]
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