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MISHKIN ECONOMICS OF MONEY 10TH EDITION PDF

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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. From the post- Great Depression era to the present, the yield curve has usually been "normal" meaning that yields rise as maturity lengthens i.

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.

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. Historically, the year Treasury bond yield has averaged approximately two percentage points above that of three-month Treasury bills.

In situations when this gap increases e. 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 , the gap between yields on two-year Treasury notes and year notes widened to 2.

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. 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.

Investors who had downloadd year Treasuries in would have received a safe and steady yield until , possibly achieving better returns than those investing in equities during that volatile period. Campbell R. Harvey's dissertation [4] showed that an inverted yield curve accurately forecasts U. An inverted curve has indicated a worsening economic situation in the future 7 times since 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". The slope of the yield curve is one of the most powerful predictors of future economic growth, inflation, and recessions. Louis Fed. 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 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.

All the recessions in the US since up through have been preceded by an inverted yield curve 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.

Table Note: In December portions of the yield curve inverted for the first time since the — Recession. The month average of the 10 year vs 3 month difference has not yet inverted as of April 15 ; even though the daily difference was inverted for 8 days in late March Therefore, the August inversion preceding the — Recession is the last set of events recorded in the table.

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 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.

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. 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. This theory is consistent with the observation that yields usually move together. However, it fails to explain the persistence in the shape of the yield curve. Shortcomings of expectations theory include that it neglects the interest rate risk inherent in investing in bonds.

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.

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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:. 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 download 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. This theory is also called the segmented market hypothesis. In this theory, financial instruments of different terms are not 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.

On 15 August , U. President Richard Nixon announced that the U. Floating exchange rates made life more complicated for bond traders, including those at Salomon Brothers in New York City. By the middle of the s, 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.

The bit nearest the present time became known as the short end —yields of bonds further out became, naturally, the long end. 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 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.

In 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.

The data is for lending in US dollar , taken from October 6, 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. The significant difficulty in defining a yield curve therefore is to determine the function P t. P is called the discount factor function or the zero coupon bond.

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. 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. 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. 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.

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. The large number of zeroes in the matrix A mean that function P turns out to be "bumpy". 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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