Term-Structure-and-the-Volatility-of-Interest-Rate.ppt

Term Structure and the Volatility of Interest RatesChapter 8 Term Structure and the Volatility of Interest RatesMajor learning outcomes:Yield curve(shapes and shifts)LIBOR and swap curvesBasic understanding of term structure theories(pure expectations,liquidity preference,preferred habitat(market segmentation)Measuring yield curve riskKey Learning OutcomesIllustrate and explain parallel and nonparallel shifts in the yield curve,a yield curve twist,and a change in the curvature of the yield curve(i.e.,butterfly shift).Describe and explain the factors that have been observed to drive zero-coupon U.S.Treasury returns and discuss the relative importance of each factor.Explain the various universes of Treasury securities that are used to construct the theoretical spot rate curve,and discuss their advantages and disadvantages.Explain the swap rate curve(LIBOR curve)and discuss the reasons that market participants have increasingly used the swap rate curve as a benchmark rather than a government bond yield curve.Key Learning OutcomesExplain the various theories of the term structure of interest rates(i.e.,pure expectations theory,liquidity preference theory,preferred habitat theory,and market segmentation)and the implications of each theory for the shape of the yield curve.Compute the effects of how to measure the yield curve risk of a security or a portfolio using key rate duration.Compute and interpret the yield volatility given historical yields.Differentiate between historical yield volatility and implied yield volatility.Explain how yield volatility is forecasted.Yield Curve ShapesHistorically,four shapes have been observed for the yield curve:(1)normal or positively sloped(i.e.,the longer the maturity,the higher the yield),(2)flat(i.e.,the yield for all maturities is approximately equal),(3)inverted or negatively sloped(i.e.,the longer the maturity,the lower the yield),and(4)a humped yield curve.Yield Curve ShapesYield Curve SpreadThe spread between long-term Treasury yields and short-term Treasury yields is referred to as the steepness or slope of the yield curve.Some investors define the slope of the yield curve as the spread between the 30-year yield and the 3-month yield and others as the spread between the 30-year yield and the 2-year yield.Yield Curve ShiftA shift in the yield curve refers to the relative change in the yield for each Treasury maturity.A parallel shift in the yield curve refers to a shift in which the change in the yield for all maturities is the same;a nonparallel shift in the yield curve means that the yield for all maturities does not change by the same number of basis points.Parallel Yield Curve ShiftYield Curve ShiftHistorically,the two types of nonparallel yield curve shifts that have been observed are a twist in the slope of the yield curve and a change in the curvature of the yield curve.A flattening of the yield curve means that the slope of the yield curve has decreased;a steepening of the yield curve means that the slope has increased.Non-Parallel Yield Curve ShiftYield Curve ShiftA butterfly shift is the other type of nonparallel shiftA change in the curvature or humpedness of the yield curve.Non-Parallel Yield Curve Shift:ButterflyTreasury Returns Resulting from Yield Curve MovementsHistorically,the factors that have been observed to drive Treasury returns are a(1)shift in the level of interest rates,(2)a change in the slope of the yield curve,and(3)a change in the curvature of the yield curve.The most important factor driving Treasury returns is a shift in the level of interest rates.Two other factors,in decreasing importance,include changes in the yield curve slope and changes in the curvature of the yield curve.Constructing the Theoretical Spot Rate Curve for TreasuriesThe universe of Treasury issues that can be used to construct the theoretical spot rate curve is:(1)on-the-run Treasury issues,(2)on-the-run Treasury issues and selected off-the-run Treasury issues,(3)all Treasury coupon securities and bills,and(4)Treasury strips.The problem with using Treasury coupon strips is that the observed yields may be biased due to a liquidity premium or an unfavorable tax treatment.Constructing the Theoretical Spot Rate Curve for TreasuriesThere are three methodologies that have been used to derive the theoretical spot rate curve:(1)bootstrapping when the universe is on-the-run Treasury issues(with and without selected off-the-run issues),(2)econometric modeling for all Treasury coupon securities and bills,and(3)simply the observed yields on Treasury coupon strips.The Swap Curve(LIBOR Curve)The swap rate is the rate at which fixed cash flows can be exchanged for floating cash flows.In a LIBOR-based swap,the swap curve provides a yield curve for LIBOR.A swap curve can be constructed that is unique to a country where there is a swap market.The swap spread is primarily a gauge of the credit risk associated with a countrys banking sector.The Swap CurveThe advantages of using a swap curve as the benchmark interest rate rather than a government bond yield curve are(1)there is almost no government regulation of the swap market making swap rates across different markets more comparable,(2)the supply of swaps depends only on the number of counterparties that are seeking or are willing to enter into a swap transaction at any given time,(3)comparisons across countries of government yield curves is difficult because of the differences in sovereign credit risk,and(4)there are more maturity points available to construct a swap curve than a government bond yield curve.From the swap yield curve a LIBOR spot rate curve can be derived using the bootstrapping methodology and the LIBOR forward rate curve can be derived.Expectations TheoryExpectations TheoryThe three forms of the expectations theory(the pure expectations theory,the liquidity preference theory,and the preferred habitat theory)assume that the forward rates in current long-term bonds are closely related to the markets expectations about future short-term rates.The three forms of the expectations theory differ on whether or not other factors also affect forward rates,and how.Pure Expectations TheoryThe pure expectations theory postulates that no systematic factors other than expected future short-term rates affect forward rates.Because forward rates are not perfect predictors of future interest rates,the pure expectations theory neglects the risks(interest rate risk and reinvestment risk)associated with investing in Treasury securities.The broadest interpretation of the pure expectations theory suggests that investors expect the return for any investment horizon to be the same,regardless of the maturity strategy selected.The local expectations form of the pure expectations theory suggests that the return will be the same over a short-term investment horizon starting today and it is this narrow interpretation that economists have demonstrated is the only interpretation that can be sustained in equilibrium.Pure Expectations TheoryTwo interpretations of forward rates based on arbitrage arguments are that they are(1)breakeven rates and(2)rates that can be locked in.Advocates of the pure expectations theory argue that forward rates are the markets consensus of future interest rates.Forward rates have not been found to be good predictors of future interest rates;however,an understanding of forward rates is still extremely important because of their role as break-even rates and rates that can be locked in.Liquidity Preference TheoryThe liquidity preference theory and the preferred habitat theory assert that there are other factors that affect forward rates and these two theories are therefore referred to as biased expectations theories.The liquidity preference theory states that investors will hold longer-term maturities only if they are offered a risk premium and therefore forward rates should reflect both interest rate expectations and a liquidity risk premium.Preferred Habitat TheoryThe preferred habitat theory,in addition to adopting the view that forward rates reflect the expectation of the future path of interest rates as well as a risk premium,argues that the yield premium need not reflect a liquidity risk but instead reflects the demand and supply of funds in a given maturity range.Measuring Yield Curve RiskA common approach to measure yield curve risk is to change the yield for a particular maturity of the yield curve and determine the sensitivity of a security or portfolio to this change holding all other key rates constant.Key Rate DurationKey rate duration is the sensitivity of a portfolios value to the change in a particular key rate.The most popular version of key rate duration uses 11 key maturities of the spot rate curve(3 months,1,2,3,5,7,10,15,20,25,and 30 years).Ladder PortfolioBarbell PortfolioBullet PortfolioYield Volatility and MeasurementVariance is a measure of the dispersion of a random variable around its expected value.The standard deviation is the square root of the variance and is a commonly used measure of volatility.Yield volatility can be estimated from daily yield observations.The observation used in the calculation of the daily standard deviation is the natural logarithm of the ratio of one days and the previous days yield.The selection of the time period(the number of observations)can have a significant effect on the calculated daily standard deviation.A daily standard deviation is annualized by multiplying it by the square root of the number of days in a year.Typically,either 250 days,260 days,or 365 days are used to annualize the daily standard deviation.Yield Volatility and MeasurementImplied volatility can also be used to estimate yield volatility based on some option pricing model.In forecasting volatility,it is more appropriate to use an expectation of zero for the mean value.The simplest method for forecasting volatility is weighting all observations equally.A forecasted volatility can be obtained by assigning greater weight to more recent observations.Autoregressive conditional heteroskedasticity(ARCH)models can be used to capture the time series characteristic of yield volatility in which a period of high volatility is followed by a period of high volatility and a period of relative stability appears to be followed by a period that can be characterized in the same way.