Arbitrage-free models are frequently used to value bonds with embedded options. According to this theory, if the yield curve is upward sloping, this indicates that investors expect short-term rates to be higher in the future. Learn more in our Privacy Policy. Manage your Professional Learning credits, Return Analysis & Performance Measurement, We’re using cookies, but you can turn them off in Privacy Settings.

Section 2 explains the relationship between these two types of interest rates and why forward rates matter to active bond portfolio managers. Except for rounding errors, this matches the bond’s market price of $935.00. As a result, the bond will provide a cash flow of $1,004 in six months.

Analytics help us understand how the site is used, and which pages are the most popular. In other words, this is the one year rate that applies one year in the future. The one year rate one year forward can be determined by equalizing the returns to investing at the two year spot rate for two years and investing at the one year spot rate for one year and then reinvesting the proceeds for another year at the one year rate one year forward: The forward rate of interest can be written as f(t,T), where t is the time at which the rate begins and T is the time at which the rate matures. One of the key assumptions of the Expectations Theory is that investors do not have any preferences for bond maturities; they are indifferent between bonds of all maturities. Yields cannot be determined algebraically; they must be computed with a specialized financial calculator or Microsoft Excel. A spot interest rate (in this reading, “spot rate”) is a rate of interest on a security that makes a single payment at a future point in time. uuid:0ad4a231-1dd2-11b2-0a00-f0acffffb0ad Discount factors can be computed directly from the prices of Treasuries.

The swap rate curve is the name given to the swap market’s equivalent of the yield curve. The yields of longer-maturity bonds tend to be higher than the yields of shorter-maturity bonds since the longer maturity bonds are riskier. Level II The terms “Term Structure of Interest Rates” and “Yield Curves” intimidates most MBA students. Active bond portfolio management is consistent with the expectation that today’s forward curve does not accurately reflect future spot rates. %PDF-1.6 uuid:0b315db0-1dd2-11b2-0a00-10afffffc047 If the economy is expected to slow in the future, the yield curve tends to become flatter, since future rates are expected to be lower than they are now. If forward rates are realized, then all bonds, regardless of maturity, will have the same one-period realized return, which is the first-period spot rate. THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity.

ISBN 978-3-540-41772-9. A summary of key points concludes the reading. A forward rate of interest is a rate that applies to a future time interval. Since the price of a bond equals the present value of its promised future cash flows, the following relationship holds for the six-month bond: d(t) = the discount factor with a maturity of t years. When long-term rates exceed short-term rates, this indicates that investors expect future short-term rates to be greater than they are today. Under this theory, forward rates are determined solely by expected future spot rates. If you use the site without changing settings, you are agreeing to our use of cookies. Under the Liquidity Premium Theory, the implied five-year rate is computed as: (1 + X)5 = (1 + 0.05)(1+ 0.0625)(1 + 0.0750)(1 + 0.0875)(1 + 0.10). As a result, there can be a risk premium for different maturities along the yield curve, but they do not necessarily increase with maturity as they do under the Liquidity Premium Theory. Modern finance seeks to provide models for the shape of the yield curve and the use of the yield curve to value bonds (including those with embedded options) and bond-related derivatives. Advanced Financial Risk Management, An Integrated Approach to Credit Risk and Interest Rate Risk Management. This value is increased by one for each day; for example, 2 = January 2, 1900. The rate of interest that equalizes the return under both scenarios is known as the one-year rate one year forward. argues that the term structure is not determined by either liquidity or expected spot rates.

There is is only one important difference. Risk-neutrality only holds for short holding periods.

Bond yields or interest rates are plotted against X-axis while time horizons are plotted on Y-Axis. According to this theory, investors have a strong preference for a specific maturity and would require a premium to invest in other bonds with different maturities. These numerical values may be used for settlement and maturity. The five theories are the unbiased expectations theory, the local expectations theory, the liquidity preference theory, the segmented markets theory, and the preferred habitat theory. Discount factors cannot exceed 1 and will fall continuously as their maturity increases.

Sorry, you have Javascript Disabled! As an example, suppose that the one-year rates over the next five years are expected to be 5%, 6%, 7%, 8% and 9%, respectively. Each bond has a face value of $1,000 and makes semi-annual coupon payments. If the yield curve is flat, this indicates that investors expect short-term rates to be unchanged in the future. The yields are y(0.5), y(1), y(1.5) and y(2). Empirical evidence rejects the local expectations theory. we discussed the 5 theories of the term structure of interest rates. A graph of the term structure of interest rates is known as a yield curve. See in particular the section Theories of the term structure (section 4.7 in the fourth edition).

The liquidity premium theory has been advanced to explain the 3 rd characteristic of the term structure of interest rates: that bonds with longer maturities tend to have higher yields. The annual coupon rate is 0.8%, so the annual coupon payment is (0.008)($1,000) = $8. Except for a small rounding error, this matches the bond’s market price of $935.00. Term Structure of Interest Rates Theories. 10 Explanations of the long-term rates were too high. For the twenty-four month, 2.80% coupon bond, the yield is computed as: = YIELD(“1/1/16”, “1/1/18”, 2.8%, 93.5, 100, 2, 0).

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During periods of rising inflation, the entire yield curve shifts up as lenders require higher rates of return to compensate for the loss of purchasing power. The one-year rate two years forward is written as f(2,3); the two-year rate one-year forward is written as f(1,3). Traditional theories present various largely qualitative perspectives on economic forces that may affect the shape of the term structure. Swap curves and Treasury curves can differ because of differences in their credit exposures, liquidity, and other supply/demand factors.