Term Structure Estimation for U.S. Corporate Bond Yields


 Mildred Randall
 2 years ago
 Views:
Transcription
1 Term Structure Estimation for U.S. Corporate Bond Yields Jerry Yi Xiao RiskMetrics Group RiskMetrics has developed a methodology for estimating the term structures of U.S. corporate bond yields. This paper describes the domestic U.S. corporate bond market and presents the RiskMetrics approach to yield curve estimation for this market. We also review some salient features and applications of our yield curve estimates for risk managers. 1 Introduction The term structure of corporate bond yields is essential to the calibration and testing of credit models and the pricing of credit sensitive instruments. For risk management, the yield spread over the defaultriskfree or government curve is a crucial measure for credit risk analysis, while the historical information of the term structure is essential for the calculation of the volatilities and correlations of defaultable future cash flows. The evolution of the credit term structure and of credit spreads is important when bonds of different credit ratings are actively traded and hedged. For regulators, the credit term structure provides information on the characteristics of credit risk and the correlation of credit risk with interest rate risk, which must be considered in setting regulatory standards for banking. The term structure of corporate credit yields is defined here as the relationship between the yields on corporate discount bonds, which generate only one cash flow at maturity, and the maturity dates of these instruments. For the US corporate bond market, as in any other bond market, the prices of discount bonds for a continuum of maturity dates are not available. Therefore, the term structure has to be estimated from the observed prices of a set of coupon bonds issued by corporations. Considerable effort has been made in the estimation of term structure of riskfree interest rates from the coupon bonds issued by governments. 1 These techniques have been widely adopted to empirically describe and forecast the term structure of interest rates. However, when it comes to the estimation of the term structure of corporate credit yields, accurate and robust techniques are still lacking. Indexes for corporate bond yields are typically averages of yields on a bucket of bonds that are chosen based on the characteristics of the bond such as remaining maturities and face values. These indexes, including Moody s Aaa and Baa yield indexes for nonfinancial seasoned corporate bonds, are defined for maturity buckets rather than specific times to maturity. They are generally 1 For example, see the survey by Zangari (1)
2 RiskMetrics Journal, Volume 2(1) 20 employed as benchmarks for performance and investment, i.e., to determine risk/return characteristics. In this document, we present RiskMetrics methodology for estimating term structures of U.S. corporate bond yields using exponential polynomials curve fitting. The characteristics and applications of these term structures will also be discussed. 2 Overview of U.S. Corporate Bond Market We begin by discussing some unique features of the U.S. corporate bond market. Generally, a corporate bond issue is characterized by its coupon rate, coupon frequency, maturity date, outstanding par value, seniority and security type, agency credit ratings (if rated), and possibly, provisions for paying off. The coupon rate of the corporate bond can be either fixed or floating according to some index rate. Although there are some exceptions, most of the U.S. corporate bonds pay coupons semiannually. In contrast to a Treasury bond which is backed by the full faith of the U.S. government, a corporate bond has a nonzero default probability. This default risk is gauged by credit ratings assigned by generally recognized rating agencies. Moody s and Standard & Poor s rating systems are the two most often used systems for corporate bonds. A onetoone mapping of the bond ratings between the two rating systems is also widely accepted. Bonds with a top four credit rating ( Moody s Aaa to Baa, Standard & Poor s AAA to BBB) are referred to as investmentgrade bonds while those with lower ratings are referred to as highyield or junk bonds. Seniority determines the priority order in which investors are compensated if default occurs. Junior bond holders will be compensated only after all the senior bond holders s claims are fulfilled. The security of a bond indicates how a bond issue is guaranteed by the issuer s property. A bond may be classified into mortgage bond, collateral trust bonds, equipment trust certificates, debenture bond, etc. These features will affect the risks associated with the investment in a bond. Embedded options are a feature of some corporate bonds. For example, a call provision allows the issuer to redeem the outstanding bond issue prior to maturity, while a put provision allows the investor to demand an early return of principal. Other bonds with embedded options include convertible bonds and bonds with sinking fund provision. The yields of these bonds are adjusted by the market to reflect the value of the embedded options. The prices reported by traders are clean prices as a percentage of par, that is, excluding the accrued interest since last coupon payment. The value of a bond investment is typically measured by yield to maturity, which is the internal rate of return paid on a bond if the investor buys and holds it to its maturity date with all coupons reinvested in the same bond. The yield to maturity of a bond can be calculated from its market price and cash flows. The spread between corporate bond yield and Treasury rate for
3 21 Term Structure Estimation for U.S. Corporate Bond Yields the same expiry is the extra yield required to offset potential credit loss, liquidity risk, and securityspecific risk and to provide extra reward for risktaking. U.S. corporate markets use a 30/30 day count basis, which means interests on corporate bonds are based on a year of 30 days made up of day months. 3 Term structure estimation for corporate bonds 3.1 Parsimonious approach for government term structure estimation A number of central banks in developed countries have adopted the parsimonious approach to estimation of government bond term structure first proposed by Nelson and Siegel (1). This approach uses a specific type of exponential polynomial function for the instantaneous forward rate f (m) at time m. f (m) = β 0 + β 1 e m/τ 1 + β 2 ( m τ 1 )e m/τ 1, (1) where β 0, β 1, β 2 and τ 1 are four parameters to be determined from the data. The function is characterized by convergence towards a constant interest rate level in the long term. By varying these four parameters, this function is capable of describing the shapes of a wide range of forward rate curves. The spot or zerocoupon rate as a function of maturity is derived by integrating the forward rate (1) from 0 to m and dividing by m: z(m) = β 0 + (β 1 + β 2 ) (1 e m/τ 1 ) m/τ 1 β 2 e m/τ 1 (2) Svensson (14) proposed enhancing the function s flexibility by adding a fourth term to Nelson and Siegel s original forward rate function in (1), f (m) = β 0 + β 1 e m/τ 1 + β 2 ( m τ 1 )e m/τ 1 + β 3 ( m τ 2 )e m/τ 2. (3) The parameters in (3) are estimated via a nonlinear optimization procedure. For a given set of parameters, Svensson first uses the spot rates given by (3) to derive the zerocoupon rate for any future time m. For a given bond, he then uses these zero rates to determine its theoretical price, from which its yield to maturity can be calculated. These yields are calculated for all bonds using these parameters and compared to their actual market values. The final parameters are chosen so the sum of squared yield differences are minimized. The NelsonSiegel or Svensson approach to termstructure estimation is not a theory of the term structure. It does not attempt to explain typical features of the term structure. Nor is it a model for the evolution of the term structure through time. It is a phenomenological approach providing a close representation of the term structure at a given point in time.
4 RiskMetrics Journal, Volume 2(1) An empirical curvefitting approach for corporate bond term structure estimation Corporate and government bond curves The methodology described in Section 3.1 has been applied primarily to government bond yield curves. 2 In applying it to corporate bonds, it is important for us to understand the differences between corporate bonds and Treasury bonds and the difficulties they give rise to. Figure 1 U.S. Treasury yields.5 Off the run On the run.5 Yield (%) Year to Maturity Yields to maturity for U.S. Treasury securities with more than 30 days to maturity and more than three months of term at issue, excluding callable bonds and inflationindexed securities. The most important difference between Treasury and corporate bonds is the credit spread. There are no credit spreads among the Treasury instruments as they are all defaultfree. As shown in Figure 1, the yields to maturity of seasoned Treasury securities (except for callable or indexed) are very close to a single curve. The largest yield differences are between ontherun and offtherun bonds, and like the smaller differences among seasoned bonds, are regarded as mainly due to differences in liquidity. 3 However, for corporate bonds, credit spreads exist not only between two different credit rating categories, as indicated by the overall yield differences for bonds with Aa and A ratings in Figure 2, but also between bond issues in different industry categories within the same credit rating, as will be shown later. Furthermore, as seen in Figure 2, bond issues from different firms within the same industry and credit rating are traded at a wide range of yields. This dispersion generally results from the following causes: 2 Malz (1) further applied it to term structure estimation based on interbank interest rates. 3 For a discussion of the impact of recent liquidity changes in the Treasury market, see Fleming (2000).
5 23 Term Structure Estimation for U.S. Corporate Bond Yields Figure 2 Samples of market data Industrial Aa Industrial A Yield(%) Yield (%) Time to maturity (year) Time to maturity (year) Market data from Bridge Information System: observed yields to maturity for plain vanilla U.S. industrial corporate bonds with Moody s Aa and A ratings on August 24, One reason for the existence of credit spreads within the same credit rating and industry category is that rating agencies allow for some heterogeneity in each credit rating class. However, as indicated by the outliers in Figure 2, sometimes the market may perceive certain issues so differently from their credit ratings that they are traded at a much higher yield, or in other words, traded as if they have a lower credit rating even though the rating agencies have not downgraded them yet. 2. Liquidity is another source of difference. While the Treasury securities, especially ontherun Treasury instruments, are among the most liquid, corporate bonds are generally less liquid. Liquidity varies tremendously across different issues and contributes to the dispersion of the corporate bond yield. 3. Coupon effects introduced by both the slope of Treasury term structure and tax consideration also have impacts on yield. Since the yield variations due to coupon differences are generally small (usually a few basis points) compared to the first two effects, we ignore the coupon effect in our current term structure estimation. 4. More subtle factors for yields variation include seniority and security types of bonds. Although they are already taken into consideration when rating agencies assign credit ratings, they may still have some residual effects on the yields. 4 Again, we ignore this effect, as the resulting difference is usually small. 4 See, for example, Fridson and Garman (1).
6 RiskMetrics Journal, Volume 2(1) 24 The dispersion of the yields within a given rating category increases as the credit rating declines, suggesting an increasing disparity of credit quality and liquidity among bonds of lower credit ratings. In view of these features of corporate bond prices and yields, we need to properly group the bonds according to their credit ratings and industrial categories in estimating the corporate bond term structure. Criteria must also be introduced to exclude outliers in each group from the estimation process. Curve fitting for the corporate yield curves Although one would like to adopt the Svensson formula for the instantaneous forward rate and get the spot rates directly from the estimated parameters, the process is too computationally expensive to be practical given the number of curves to fit and the number of bonds involved. Instead, we fit a yield curve directly from the yields to maturity and then use a bootstrapping technique to arrive at the zerocoupon rates. Following the parsimonious approach, an exponential polynomial function is used as an empirical description of the yield of corporate bonds: y(m) = β 0 + β 1 e m/τ 1 + β 2 e m/τ 2, (4) where y(m) is the yield of bonds which mature in m years, τ 1, τ 2, β 0, β 1, and β 2 are the five unknown parameters which will be estimated in the least squares curve fitting process. Like the NelsonSiegel formula, (4) is flexible enough to incorporate different shapes of term structures. Since coupon effects are ignored in our estimation procedure, we may treat the yield in (4) as a par yield. Par yields are the yields of bonds trading at par and are thus equal to the assumed coupon rates. To account for the variation in liquidity of different bond issues, we use outstanding par values of each bond as one of the weighting factors for our curve fitting so that, in general, more liquid bonds carry higher weights. The curve fitting procedure minimizes the yield errors rather than price errors. However, it is also critical for the model to consistently fit the prices of the bonds used in the estimation. Therefore, a weighting of the yield errors in the minimization is introduced to correct for the variation in sensitivity of the price errors to yield errors. This can be best understood with the concept of duration, which relates the yield to maturity change of a bond to its price change, B B = D y, (5) where B is the bond price, and D is the modified duration. For a given yield change, the price change for a long term, hence a long duration, bond is much larger than that of a short term note with a small duration. Therefore, without proper weighting, a curve
7 25 Term Structure Estimation for U.S. Corporate Bond Yields fitting process that uniformly minimizes yield errors across the terms will tend to overfit the short term bond prices and underfit the long term bond prices. To correct for this effect, another weighting factor equal to the duration of a bond could be introduced for each yield error. To simplify the calculation, we use time to maturity as a weighting factor, as the differences are minimal. For a given set of bonds, the curve fitting process is accomplished into two steps: nonlinear estimation of (τ 1,τ 2 ) and linear regression to estimate β 0,β 1,β 2 for a given pair (τ 1,τ 2 ). We optimize (τ 1,τ 2 ) by minimizing the following weighted sum of squared yield errors F(τ 1,τ 2 ) = i [y i y(m i,τ 1,τ 2 )] 2 W i, () where W i is the weighting factor for ith bond, and y(m i,τ 1,τ 2 ) = β 0 (τ 1,τ 2 ) + β 1 (τ 1,τ 2 )e m i/τ 1 + β 2 (τ 1,τ 2 )e m i/τ 2, () in which β 0 (τ 1,τ 2 ), β 1 (τ 1,τ 2 ) and β 2 (τ 1,τ 2 ) represent parameters obtained from linear regression for given (τ 1,τ 2 ). Notice that the linear regression is also weighted with factor W i. For the estimation of τ 1 and τ 2, we first limit their ranges to an empirically plausible range [0.2, 50.0]. Then we construct a twodimensional grid for the whole range of τ 1 and τ 2, and evaluate F(τ 1,τ 2 ) on each of the nodes to get a rough estimate of (τ 1,τ 2 ). A finer grid is constructed around the first estimate for the final estimate of (τ 1,τ 2 ). This procedure increases the likelihood that we obtain a global optimum for (τ 1,τ 2 ). In the estimation procedure, there are outliers whose yields are far from those of the bulk of the group, indicating that the market does not perceive them to be in the same rating category or to have poor liquidity. To eliminate those bonds from the pool, we use the following iteration process: we first use all the bonds to fit a curve and measure the yield spread of each bond to the curve. We then select the bonds whose spreads to the fitted curve are within a certain region to do the next iteration of curve fitting. We repeat the process until the change of the curves for two consecutive steps is small. Note that for each step, we always select from the whole pool of bonds in the rating/industry category. To define the proper inclusion region for the yield differences, we specify the lower and upper cutoff levels and determine the two corresponding cutoff thresholds based on the distribution of these differences. Experience suggests a lower cutoff of 2% and upper cutoff of 5%. We illustrate in Figure 3 with the outliers excluded from the final fitting process marked by open squares.
8 RiskMetrics Journal, Volume 2(1) 2 Figure 3 Curve fitting and outlier elimination: investment grade bonds Industrial Aa Industrial A Yield(%) Yield (%) Time to maturity (year) Time to maturity (year) U.S. industrial corporate bonds with Moody s Aa and A ratings on August 24, Although the above procedure works well in most cases, the leastsquare procedure curve becomes unstable when τ 1 and τ 2 are very close to each other, that is, when (4) is an overfit for the yield. When this occurs, we reduce the number of exponential terms and use the following formula instead: Y (m) = β 0 + β 1 e m/τ 1. () For highyield categories, because of their extremely wide range of yields, as shown in Figue 4, we assume a flat term structure and carry out the same outlier elimination process. Once estimates of the parameters in (4) are obtained, we can compute the par yield for bonds with any time left to maturity, for example, 0.5 year, 1 year, 1.5 years, 2 years, etc. We then work from the short end of the yield curve to compute the zero rates via bootstrapping. 3.3 Bond data and results The raw data of some,000 actively traded fixedcoupon U.S. corporate bonds are provided daily to RiskMetrics by Bridge Information Systems. For our term structure estimates, we first filter out bonds with embedded options and bonds with coupon payment frequencies other than semiannual. We also exclude illiquid bonds with less than USD 0 million of outstanding par values. The total number of qualified bonds is about 5,000 each day.
9 2 Term Structure Estimation for U.S. Corporate Bond Yields Figure 4 Curve fitting and outlier elimination: highyield bonds Yield (%) Time to maturity (year) Industrial Ba bond yields on August 24, 2000 The qualified bonds are categorized into three industry groups, financial, industrial and utility, according to the sectors of issuers. The bonds are then further grouped by their credit ratings. A typical data example is shown in Table 1 with industry and credit rating breakdown. We use Moody s symbols for credit ratings for convenience. For each rating category, we pick only bonds whose unmodified ratings from Moody s and S&P agree. Table 1 Number of qualified Vanilla Bonds on 0/14/2000 Financial Industrial Utility Total Aaa Aa A Baa Ba B Caa Total Based on available data, we group bonds into 1 categories (see Table 2) and estimate the term structure for each pool. One may notice that there is no term structure estimation for industrial Aaa bonds. This is due to the small number of bonds in this group which makes a yield curve estimate unreliable. For utilities, since the Aaa, Aa, and A bonds
10 RiskMetrics Journal, Volume 2(1) 2 Table 2 The categories for which term structures are estimated Financial: Aaa Aa A Baa Ba Industrial: Aa A Baa Ba Utilities: Aaa+Aa+A Baa Ba All Industries: Aaa Aa A Baa Ba B+Caa+Ca+C Constant par yield, flat term structure. appear to trade on the same curve, a single yield curve is estimated for these three credit ratings. In reporting term structures, we choose a set of terms to maturity or vertexes and report daily yields and zero rates corresponding to those vertexes. If, for a certain group on a certain day, there are not enough bonds in the long or short end, the term structure vertexes in those ranges will not be reported. For example, if there are no financial Aaa bonds with time to maturity more than years, financial Aaa yields on that day for terms longer than years will not be reported. A snapshot of all the corporate yield curves on August 24, 2000 is displayed in Figure 5. For each credit rating, yields are generally different for different industry groups; bonds of financial firms, for example, have higher yields. The differences among industries increase as the credit rating drops. We also note a large rise in yield from Baa to Ba across all industries as the bonds cross from investment grade to high yield. An important result of the term structure estimation for credit sensitive derivatives is credit spread over the Treasury curve. For each vertex of an industryrating group, we may get a rate estimate for each business day using our methodology, resulting in a time series of the corresponding rates. We will call each of these rate estimates for a given vertex and industryrating group an index. Figure displays the time series of the year yield indexes and their spreads over Treasury yields for all industries. Yield spreads for these indexes were negatively correlated with Treasury rates in the year This result is in agreement with the study using monthly changes of Moody s seasoned bond index by Duffie (1). 4 Volatilities of the indexes 4.1 Effects of pool size Each corporate yield curve is estimated from a different bond pool, which is refreshed every business day. As seen in Table 1, the number of bonds in each pool varies widely. A natural question to ask is whether the difference in the number of bonds affects the volatility of the indexes.
11 2 Term Structure Estimation for U.S. Corporate Bond Yields Figure 5 Example of term structure output 11 Financial 0/24/ Industrial 0/24/2000 yield Baa A Aa yield Ba Baa A Aaa Aa maturity maturity 11 Utility 0/24/ General 0/24/2000 yield Ba Baa yield Ba Baa Aaa+Aa+A Aaa maturity Snapshot of term structures on August 24, maturity Figure Curve time series 11 Ba 5 Ba 4 Baa Yield (%) A Aaa Spread (%) 3 Baa 2 A 5 Treasury 1 Aaa 4 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year 2000 Time series of U.S. corporate year yields and spreads over Treasury yields. To answer this question, we first choose a group of bonds, e.g. financial Aa, and randomly select, for each day, a certain number of bonds to construct an index. Since each daily
12 RiskMetrics Journal, Volume 2(1) 30 set of bonds is selected randomly, the volatility of this pseudoindex is higher than the real index. As we increase the number of bonds in building these pseudoindexes, the volatility decreases due to diversification effects. Figure shows this relationship for year indexes of different groups. It is clear from Figure that for all the different groups, as long as we have about 50 bonds in the pool, the diversification effects are high enough to yield an index whose volatility level will be relatively stable for further increases of the pool size. On one hand, this lower bound for bond numbers restricts the range of indexes we can reliably construct. On the other hand, this result provides assurance that volatilities of the indexes are accurate measures of market volatilities. Figure Effects of pool size on index volatility Volatility (%) Number of Bonds Used for Calculation The horizontal axis shows the number of bonds randomly picked within the corresponding groups to calculate year pseudoindexes. 4.2 Index volatility and credit rating As we measure the volatility of each index, we find that high yield indexes usually have a lower volatility than investment grade indexes. Within the investmentgrade universe, the volatility between different rating categories is smaller, but can still be observed, with Baa curves having lower volatility than Aaa curves. Since an index can be roughly regarded as an average of a pool of bonds, this apparently counterintuitive result can be simply understood in terms of diversification. It is known that diversification effect is greater when there is lower correlation between individual instruments in the portfolio. As it turns out, the lower the credit ratings, the lower the correlation between individual bonds. Therefore, this reverse volatility order is caused by the difference in correlation as the credit rating drops.
13 31 Term Structure Estimation for U.S. Corporate Bond Yields 5 Volatility of individual bonds 5.1 Characterizing bond volatility relative to an index To characterize the volatility of individual bonds, we can perform an analysis for individual bonds and the indexes based on the theme that is analogous to the definition of beta for equity market based on the Capital Asset Pricing Model. To do this, we first transform the daily change of a par yield index to daily change of prices, which in turn give us the returns based on the index. In Figure, we plot the daily returns for the year Baa index against returns for three Baa rated individual bonds with time to maturity close to years. One important observation is that, except for some large jumps, the individual returns are close to the market return. In other words, the beta is close to one. 5 Figure Index and individual bond returns IIN /15/0 IGR LMT /01/0 IGR CTX.50 03/01/0 IGR r IIN 0 r LMT 0 r CTX r Baa r Baa r Baa Daily returns for index plotted against returns for individual bond in 2000 For a more precise analysis, we use a onefactor model to analyze a pool of bonds with maturity close to the term of an index, 5 If we carefully study the time series of individual bonds of a given group, we may notice that most of their yields usually follow a general trend (the index) and maintain constant spreads. Individual spreads may jump, from time to time, to other values and then keep constant again. This leads to the behavior shown by the returns in Figure. The phenomenon shows the pricing practices of a lot of bond traders.
14 RiskMetrics Journal, Volume 2(1) 32 r i,t µ i σ i = ρ i ( rm,t µ m σ m ) + 1 ρi 2 ɛ i,t, () where r i,t is the daily return from the ith bond, r m,t is the daily returns from the corresponding index, ρ i is the correlation between the bond and index returns, and ɛ i,t is the idiosyncratic term of the bond. Individual bonds have a mean return µ i and a variance of σi 2, while the index has a mean return µ m and a variance σm 2. The return for an individual bond can then be expressed as σ i σ i r i,t = (µ i ρ i µ m ) + ρ i r m,t + 1 ρi 2 σ i ɛ i,t, () σ m σ m from which we may estimate the parameters β i = ρ i σ i σ m, (11) α i = µ i ρ i σ i σ m µ m. (12) As suggested by Figure and confirmed again by the results in Table 3, α i is essentially zero and beta i is close to one for all the groups considered. Therefore, () can be simplified to r i,t = r m,t + ε i,t. (13) To capture the individual bond volatility relative to an index, instead of introducing beta as equity market models, we may introduce a new factor R i = σ i σ m, (14) which is simply the ratio of the bond volatility to the index. For simplicity we may compute the parameter for each industryrating category which is the average of R i over all the bonds within the category. Some results are shown in Table 3. With the relationship in (11) and β 1, R should be equal to 1/ρ, where ρ is the average correlation between individual bond and the index of a certain category. As reflected in the last column of Table 3, the average correlation of individual bonds to the index is higher for higherrated bonds. Therefore, lower correlation is associated with higher volatility of individual bonds relative to the volatility of the index. This is consistent with the finding of section 4 that the average correlation of individual bonds with one another is higher for higherrated pools.
15 33 Term Structure Estimation for U.S. Corporate Bond Yields Table 3 Statistical characteristics for industrial bonds α β R ρ Aaa ± ± ± Aa 0.00 ± ± ± A ± ± ± Baa ± ± ± An important implication of these observations is that a bond index should not be treated as the market portfolio. As indicated by the high correlations shown in Table 3, systematic risk plays a dominant role in the risk of corporate bond portfolios, and diversifiable risk is insignificant. This is especially the case for bonds with high credit ratings due to their higher correlations with one other. Portfolio theory, which is focused mainly on the notion of diversification, is not very applicable in analyzing bond portfolios. It thus does not justify the use of bond indexes as an optimal market portfolio. Therefore, systematic risk analysis based on the shape and level of the term structure, instead of analysis based on classic portfolio theory, should be the focus of bond investment. 5.2 Decomposition of bond volatility Another interesting result arises from the decomposition of individual bond volatility into the contribution from Treasury volatility, index spread volatility, and residual spread volatility. The spread volatility itself can also be used in valuation of some credit derivatives. To a first approximation, the daily return of a bond can be related to the daily change of bond yield through the duration relationship in (5), in which y should be taken as the yield change between two consecutive business days. Since we have the times series of the indexes, we may decompose the times series of individual bond yield into three parts: Bond yield = Treasury par yield + Corporate index spread + Residual spread, (15) in which the term for the Treasury and corporate index equals to the time to maturity of the bond. Now (5) can be written as B B = D ( T + S + ɛ), (1) where T, S, and ɛ are the daily changes in Treasury par yield, index spread, and residual spread respectively. With the time series of T, S, and ɛ, we may calculate the volatility of each component and the correlation between one another, and relate them to the price volatility of the bond by assuming that the modified duration is reasonably stable within the time frame under consideration.
16 RiskMetrics Journal, Volume 2(1) 34 This simple volatility decomposition gives us a general idea of the relative contributions to the total risk of a bond. The term structure of Treasury yield and corporate index enters into the equation indirectly through the modified duration D. A more elaborate approach to volatility decomposition, which uses zero coupon rates and calibrated residual spread, incorporates term structure through the notion of partial duration. A detailed description of this approach and its application to risk budgeting for corporate bond portfolios is presented by J. Mina in this issue of the Journal. Conclusion In this article, we present our methodology for the estimation of U.S. corporate bond term structures based on market data. The technique is based on a parsimonious approach which properly balances accuracy and computational costs. The estimation procedure can successfully handle the wide dispersion of the yields within each credit rating/industry group, while capturing the liquidity and duration effects as well. These corporate curve time series data can provide important yield, spread, volatility and correlation information for U.S. corporate bonds, which can be useful for risk managers, traders, and regulators. References Duffie, G. R. (1). The relation between Treasury yields and corporate bond yield spreads, Journal of Finance 53(): Fleming, M. J. (2000). The benchmark U.S. Treasury market: recent performance and possible alternatives, FRBNY Economics Ploicy Review (April): Fridson, M. S. and Garman, M. C. (1). Valuing LikeRated Senior and Subordinated Debt, Journal of Fixed Income (3): 3 3. Malz, A. M. (1). Interbank Interest Rates as Term Structure Indicators, Federal Reserve Bank of New York, mimeo. Nelson, C. R. and Siegel, A. F. (1). Parsimonious modeling of yield curves, Journal of Business 0(4): Svensson, L. E. (14). Estimating and interpreting forward interest rates: Sweden 124, Discussion Paper 51, Center for Economic Policy Research. Zangari, P. (1). An investigation into term structure estimation methods for RiskMetrics, RiskMetrics Monitor pp
INSTITUTIONAL INVESTMENT & FIDUCIARY SERVICES: Building a Better Portfolio: The Case for High Yield Bonds
14\GBS\22\25062C.docx INSTITUTIONAL INVESTMENT & FIDUCIARY SERVICES: Building a Better Portfolio: The Case for High Yield Bonds By Adam Marks, Area Vice President and Jamia Canlas, Senior Analyst By looking
More informationUnderstanding Fixed Income
Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding
More informationBonds and Yield to Maturity
Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.
More informationChapter 10. Fixed Income Markets. FixedIncome Securities
Chapter 10 FixedIncome Securities Bond: Tradable security that promises to make a prespecified series of payments over time. Straight bond makes fixed coupon and principal payment. Bonds are traded mainly
More informationEquityindexlinked swaps
Equityindexlinked swaps Equivalent to portfolios of forward contracts calling for the exchange of cash flows based on two different investment rates: a variable debt rate (e.g. 3month LIBOR) and the
More informationSSgA CAPITAL INSIGHTS
SSgA CAPITAL INSIGHTS viewpoints Part of State Street s Vision thought leadership series A Stratified Sampling Approach to Generating Fixed Income Beta PHOTO by Mathias Marta Senior Investment Manager,
More informationInterest Rate Swaps and Fixed Income Portfolio Analysis
White Paper Interest Rate Swaps and Fixed Income Portfolio Analysis Copyright 2014 FactSet Research Systems Inc. All rights reserved. Interest Rate Swaps and Fixed Income Portfolio Analysis Contents Introduction...
More informationCREATING A CORPORATE BOND SPOT YIELD CURVE FOR PENSION DISCOUNTING DEPARTMENT OF THE TREASURY OFFICE OF ECONOMIC POLICY WHITE PAPER FEBRUARY 7, 2005
CREATING A CORPORATE BOND SPOT YIELD CURVE FOR PENSION DISCOUNTING I. Introduction DEPARTMENT OF THE TREASURY OFFICE OF ECONOMIC POLICY WHITE PAPER FEBRUARY 7, 2005 Plan sponsors, plan participants and
More informationCHAPTER 9 DEBT SECURITIES. by Lee M. Dunham, PhD, CFA, and Vijay Singal, PhD, CFA
CHAPTER 9 DEBT SECURITIES by Lee M. Dunham, PhD, CFA, and Vijay Singal, PhD, CFA LEARNING OUTCOMES After completing this chapter, you should be able to do the following: a Identify issuers of debt securities;
More informationThe Taxonomy of Fixed Income Securities: A CNO Approach
The Taxonomy of Fixed Income Securities: A CNO Approach Finance theory cannot identify the true boundary between debt and equity There is nothing more complex than trying to draw a line which does not
More informationHighyield bonds. Bonds that potentially reward investors for taking additional risk. Highyield bond basics
Highyield bonds Bonds that potentially reward investors for taking additional risk Types of highyield bonds Types of highyield bonds include: Cashpay bonds. Known as plain vanilla bonds, these bonds
More informationChapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixedincome securities. Stocks. Real assets (capital budgeting). Part C Determination
More informationFIN 472 FixedIncome Securities Corporate Debt Securities
FIN 472 FixedIncome Securities Corporate Debt Securities Professor Robert B.H. Hauswald Kogod School of Business, AU Corporate Debt Securities Financial obligations of a corporation that have priority
More informationBond valuation and bond yields
RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments
More informationFixed Income Securities
3st lecture IES, UK October 7, 2015 Outline Bond Characteristics 1 Bond Characteristics 2 Bond Characteristics Government bond listing Rate Maturity mo/yr Bid Asked Chg Ask yld 3.000 July 12 108:22 108:2320
More informationBond Valuation. Capital Budgeting and Corporate Objectives
Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What
More informationBond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview
Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation
More informationExpected default frequency
KM Model Expected default frequency Expected default frequency (EDF) is a forwardlooking measure of actual probability of default. EDF is firm specific. KM model is based on the structural approach to
More informationM.I.T. Spring 1999 Sloan School of Management 15.415. First Half Summary
M.I.T. Spring 1999 Sloan School of Management 15.415 First Half Summary Present Values Basic Idea: We should discount future cash flows. The appropriate discount rate is the opportunity cost of capital.
More informationMarket Implied Ratings FAQ Updated: June 2010
Market Implied Ratings FAQ Updated: June 2010 1. What are MIR (Market Implied Ratings)? Moody s Analytics Market Implied Ratings translate prices from the CDS, bond and equity markets into standard Moody
More informationWhy highyield municipal bonds may be attractive in today s market environment
Spread Why highyield municipal bonds may be attractive in today s market environment February 2014 Highyield municipal bonds may be attractive given their: Historically wide spreads Attractive prices
More informationUse of fixed income products within a company's portfolio
Theoretical and Applied Economics Volume XIX (2012), No. 10(575), pp. 514 Use of fixed income products within a company's portfolio Vasile DEDU The Bucharest University of Economic Studies vdedu03@yahoo.com
More informationBonds, in the most generic sense, are issued with three essential components.
Page 1 of 5 Bond Basics Often considered to be one of the most conservative of all investments, bonds actually provide benefits to both conservative and more aggressive investors alike. The variety of
More information Short term notes (bonds) Maturities of 14 years  Mediumterm notes/bonds Maturities of 510 years  Longterm bonds Maturities of 1030 years
Contents 1. What Is A Bond? 2. Who Issues Bonds? Government Bonds Corporate Bonds 3. Basic Terms of Bonds Maturity Types of Coupon (Fixed, Floating, Zero Coupon) Redemption Seniority Price Yield The Relation
More informationRisk and Return in the Canadian Bond Market
Risk and Return in the Canadian Bond Market Beyond yield and duration. Ronald N. Kahn and Deepak Gulrajani (Reprinted with permission from The Journal of Portfolio Management ) RONALD N. KAHN is Director
More informationExam 1 Morning Session
91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark
More informationOpportunities and risks in credit. Michael Korber Head of Credit
Opportunities and risks in credit Michael Korber Head of Credit August 2009 Overview Fixed income assets, characteristics and risks Where the current opportunity is in fixed income markets How to access
More informationCDO Research Data Feed Glossary of Terms
CDO Research Data Feed Glossary of s Moody s Investors Service Synthetic CDOs WARF The Weighted Average Rating Factor as calculated by Moody's is independent of the Trustee's and collateral manager's calculations
More informationRobeco High Yield Bonds
Important Information 1. Robeco High Yield Bonds (the Fund aims to provide long term capital growth. The Fund invests at least two thirds of its total assets in bonds, asset backed securities and similar
More informationVALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below
VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following riskfree debt instrument, which promises to make the respective
More informationTopics to be Discussed Description of Fixed Income Securities Characteristics Used to Evaluate Securities. Fixed Income Securities
Topics to be Discussed Description of Characteristics Used to Evaluate Securities Treasury Bonds Agency Bonds Municipal Bonds Corporate Bonds Institutional Bonds Evaluation of Bonds Preferred Stock Description
More informationChapter 5: Valuing Bonds
FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A longterm debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations
More informationChapter 11. Stocks and Bonds. How does this distribution work? An example. What form do the distributions to common shareholders take?
Chapter 11. Stocks and Bonds Chapter Objectives To identify basic shareholder rights and the means by which corporations make distributions to shareholders To recognize the investment opportunities in
More informationTerminology of Convertable Bonds
Bellerive 241 P.o. Box CH8034 Zurich info@fam.ch www.fam.ch T +41 44 284 24 24 Terminology of Convertable Bonds Fisch Asset Management Terminology of Convertible Bonds Seite 2 28 ACCRUED INTEREST 7 ADJUSTABLERATE
More informationChapter 9 Bonds and Their Valuation ANSWERS TO SELECTED ENDOFCHAPTER QUESTIONS
Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED ENDOFCHAPTER QUESTIONS 91 a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as
More informationAlliance Consulting BOND YIELDS & DURATION ANALYSIS. Bond Yields & Duration Analysis Page 1
BOND YIELDS & DURATION ANALYSIS Bond Yields & Duration Analysis Page 1 COMPUTING BOND YIELDS Sources of returns on bond investments The returns from investment in bonds come from the following: 1. Periodic
More informationSpectrum Insights. Bond and stock market around the same size Australian bonds vs Australian stock market
Market capitalization $b Spectrum Insights Damien Wood, Principal JUNE 9, 2015 Corporate bonds often provides investors with an income stream that is above deposit rates, but less risky than dividends
More informationCHAPTER 16: MANAGING BOND PORTFOLIOS
CHAPTER 16: MANAGING BOND PORTFOLIOS PROBLEM SETS 1. While it is true that shortterm rates are more volatile than longterm rates, the longer duration of the longerterm bonds makes their prices and their
More informationBond Snapshot with Kathy Jones The Year of the Taper
Bond Snapshot with Kathy Jones The Year of the Taper Kathy Jones, Vice President Fixed Income Strategist Schwab Center for Financial Research February 2014 Overview of Topics Tapering Implications Where
More informationBond Market Perspectives
LPL FINANCIAL RESEARCH Bond Market Perspectives March 26, 2013 HighYield Bonds and the Credit Cycle Anthony Valeri, CFA Market Strategist LPL Financial Highlights More speculative issuance has increased
More informationChapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 41
Chapter 6 Interest rates and Bond Valuation 2012 Pearson Prentice Hall. All rights reserved. 41 Interest Rates and Required Returns: Interest Rate Fundamentals The interest rate is usually applied to
More informationManaging Currency Mismatch. May 2010
Managing Currency Mismatch May 2010 FX Volatility 2 Very High Volatility in Asian Currencies Currency Performance % 140 130 120 110 100 90 80 70 60 50 40 Jan06 Jun06 Dec06 Jun07 Dec07 May08 Nov08
More informationFixedincome opportunity: Short duration high yield
March 2014 Insights from: An income solution for a low or rising interestrate environment Generating income is a key objective for many investors, and one that is increasingly difficult to achieve in
More informationBackground. Discount rates for valuation, including taking account of liquidity. Seamus Creedon (Working Party Chairman)
Discount rates for valuation, including taking account of liquidity Seamus Creedon (Working Party Chairman) 1517 JUNE 2008 HILTON DEANSGATE, MANCHESTER Background Extensive feedback to IASB on discount
More informationHOSPIRA (HSP US) HISTORICAL COMMON STOCK PRICE INFORMATION
30Apr2004 28.35 29.00 28.20 28.46 28.55 03May2004 28.50 28.70 26.80 27.04 27.21 04May2004 26.90 26.99 26.00 26.00 26.38 05May2004 26.05 26.69 26.00 26.35 26.34 06May2004 26.31 26.35 26.05 26.26
More informationLecture 12/13 Bond Pricing and the Term Structure of Interest Rates
1 Lecture 1/13 Bond Pricing and the Term Structure of Interest Rates Alexander K. Koch Department of Economics, Royal Holloway, University of London January 14 and 1, 008 In addition to learning the material
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationDistressed Debt Prices and Recovery Rate Estimation
Distressed Debt Prices and Recovery Rate Estimation Robert Jarrow Joint Work with Xin Guo and Haizhi Lin May 2008 Introduction Recent market events highlight the importance of understanding credit risk.
More informationLecture 2 Bond pricing. Hedging the interest rate risk
Lecture 2 Bond pricing. Hedging the interest rate risk IMQF, Spring Semester 2011/2012 Module: Derivatives and Fixed Income Securities Course: Fixed Income Securities Lecturer: Miloš Bo ović Lecture outline
More informationNavigating Rising Rates with Active, MultiSector Fixed Income Management
Navigating Rising Rates with Active, MultiSector Fixed Income Management 2 With bond yields near 60year lows and expected to rise, U.S. core bond investors are increasingly questioning how to mitigate
More informationFixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
More informationETF Investment Solutions How to Target the Bond Market s Sweet Spot with Crossover Bonds
ETF Investment Solutions How to Target the Bond Market s Sweet Spot with Crossover Bonds CONTENTS I. ASSET CLASS BACKGROUND What Are Crossover Bonds? II. CHARACTERISTICS OF CROSSOVER BONDS What Are the
More informationFixed Income Attribution. The Wiley Finance Series
Brochure More information from http://www.researchandmarkets.com/reports/2216624/ Fixed Income Attribution. The Wiley Finance Series Description: Fixed income attribution is by its very nature a complex
More informationChapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.)
Chapter 6 Interest Rates And Bond Valuation Learning Goals 1. Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. 2. Review the legal aspects of bond financing
More informationPerspectives September
Perspectives September 2013 Quantitative Research Option Modeling for Leveraged Finance Part I Bjorn Flesaker Managing Director and Head of Quantitative Research Prudential Fixed Income Juan Suris Vice
More informationInterest Rates and Bond Valuation
Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean
More informationUnderstanding duration and convexity of fixed income securities. Vinod Kothari
Understanding duration and convexity of fixed income securities Vinod Kothari Notation y : yield p: price of the bond T: total maturity of the bond t: any given time during T C t : D m : Cashflow from
More informationThe Empirical Approach to Interest Rate and Credit Risk in a Fixed Income Portfolio
www.empirical.net Seattle Portland Eugene Tacoma Anchorage March 27, 2013 The Empirical Approach to Interest Rate and Credit Risk in a Fixed Income Portfolio By Erik Lehr In recent weeks, market news about
More informationA guide to investing in highyield bonds
A guide to investing in highyield bonds What you should know before you buy Are highyield bonds suitable for you? Highyield bonds are designed for investors who: Can accept additional risks of investing
More information20. Investments 4: Bond Basics
20. Investments 4: Bond Basics Introduction The purpose of an investment portfolio is to help individuals and families meet their financial goals. These goals differ from person to person and change over
More informationNATIONAL STOCK EXCHANGE OF INDIA LIMITED
NATIONAL STOCK EXCHANGE OF INDIA LIMITED Capital Market FAQ on Corporate Bond Date : September 29, 2011 1. What are securities? Securities are financial instruments that represent a creditor relationship
More informationMadison Investment Advisors LLC
Madison Investment Advisors LLC Intermediate Fixed Income SELECT ROSTER Firm Information: Location: Year Founded: Total Employees: Assets ($mil): Accounts: Key Personnel: Matt Hayner, CFA Vice President
More informationANZ Debt Indices  Descriptions
ANZ Debt Indices  Descriptions Publication Frequency The ANZ Debt Indices are calculated and published daily, after the close of trading, on all days on which banks are open for general banking business
More informationIntroduction. example of a AA curve appears at the end of this presentation.
1 Introduction The High Quality Market (HQM) Corporate Bond Yield Curve for the Pension Protection Act (PPA) uses a methodology developed at Treasury to construct yield curves from extended regressions
More informationAnswers to Review Questions
Answers to Review Questions 1. The real rate of interest is the rate that creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual
More informationYIELD CURVE GENERATION
1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A
More informationLiquidity of Corporate Bonds
Liquidity of Corporate Bonds Jack Bao, Jun Pan and Jiang Wang MIT October 21, 2008 The QGroup Autumn Meeting Liquidity and Corporate Bonds In comparison, low levels of trading in corporate bond market
More informationChapter 3. Fixed Income Securities
IE 5441 1 Chapter 3. Fixed Income Securities IE 5441 2 Financial instruments: bills, notes, bonds, annuities, futures contracts, mortgages, options,...; assortments that are not real goods but they carry
More informationChapter. Investing in Bonds. 13.1 Evaluating Bonds 13.2 Buying and Selling Bonds. 2010 SouthWestern, Cengage Learning
Chapter 13 Investing in Bonds 13.1 Evaluating Bonds 13.2 Buying and Selling Bonds 2010 SouthWestern, Cengage Learning Standards Standard 4.0 Investigate opportunities available for saving and investing.
More informationRisks and Rewards in High Yield Bonds
Risks and Rewards in High Yield Bonds Peter R. Duffy, CFA, Partner, Senior Portfolio Manager Navy Yard Corporate Center, Three Crescent Drive, Suite 400, Philadelphia, PA 19112 www.penncapital.com 1 What
More informationCanadian Life Insurance Company Asset/Liability Management Summary Report as at: 31Jan08 interest rates as of: 29Feb08 Run: 2Apr08 20:07 Book
Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31Jan08 interest rates as of: 29Feb08 Run: 2Apr08 20:07 Book Book Present Modified Effective Projected change in net present
More informationCALL VOLUME FORECASTING FOR SERVICE DESKS
CALL VOLUME FORECASTING FOR SERVICE DESKS Krishna Murthy Dasari Satyam Computer Services Ltd. This paper discusses the practical role of forecasting for Service Desk call volumes. Although there are many
More informationVariance swaps and CBOE S&P 500 variance futures
Variance swaps and CBOE S&P 500 variance futures by Lewis Biscamp and Tim Weithers, Chicago Trading Company, LLC Over the past several years, equityindex volatility products have emerged as an asset class
More informationBonds and preferred stock. Basic definitions. Preferred(?) stock. Investing in fixed income securities
Bonds and preferred stock Investing in fixed income securities Basic definitions Stock: share of ownership Stockholders are the owners of the firm Two types of stock: preferred and common Preferred stock:
More informationINTERACTIVE BROKERS DISCLOSURE STATEMENT FOR BOND TRADING
INTERACTIVE BROKERS DISCLOSURE STATEMENT FOR BOND TRADING THIS DISCLOSURE STATEMENT DISCUSSES THE CHARACTERISTICS AND RISKS OF TRADING BONDS THROUGH INTERACTIVE BROKERS (IB). BEFORE TRADING BONDS YOU SHOULD
More informationIndustry Environment and Concepts for Forecasting 1
Table of Contents Industry Environment and Concepts for Forecasting 1 Forecasting Methods Overview...2 Multilevel Forecasting...3 Demand Forecasting...4 Integrating Information...5 Simplifying the Forecast...6
More information1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
More informationA guide to investing in highyield bonds
A guide to investing in highyield bonds What you should know before you buy Are highyield bonds suitable for you? Highyield bonds are designed for investors who: Can accept additional risks of investing
More informationChapter 4 Valuing Bonds
Chapter 4 Valuing Bonds MULTIPLE CHOICE 1. A 15 year, 8%, $1000 face value bond is currently trading at $958. The yield to maturity of this bond must be a. less than 8%. b. equal to 8%. c. greater than
More informationImpact of rising interest rates on preferred securities
Impact of rising interest rates on preferred securities This report looks at the risks preferred investors may face in a risinginterestrate environment. We are currently in a period of historically low
More informationFNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
More informationHedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies
Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies Drazen Pesjak Supervised by A.A. Tsvetkov 1, D. Posthuma 2 and S.A. Borovkova 3 MSc. Thesis Finance HONOURS TRACK Quantitative
More informationAnnual Treasury And Investment Portfolio Update for 2015
Item No.: 7d_Supp Meeting Date: March 8, 2016 Annual Treasury And Investment Portfolio Update for 2015 Commission Briefing Presented by Diane Campbell March 8, 2016 Treasury Management Update Background
More informationPricing and Strategy for Muni BMA Swaps
J.P. Morgan Management Municipal Strategy Note BMA Basis Swaps: Can be used to trade the relative value of Libor against short maturity tax exempt bonds. Imply future tax rates and can be used to take
More informationSensex Realized Volatility Index
Sensex Realized Volatility Index Introduction: Volatility modelling has traditionally relied on complex econometric procedures in order to accommodate the inherent latent character of volatility. Realized
More informationA GUIDE TO FLOATING RATE BANK LOANS:
Contact information: Advisor Services: (631) 6294908 Email: info@catalystmf.com Website: www.catalystmf.com A GUIDE TO FLOATING RATE BANK LOANS: An Attractive Investment for a Rising Interest Rate Environment
More informationGlobal Financial Management
Global Financial Management Bond Valuation Copyright 999 by Alon Brav, Campbell R. Harvey, Stephen Gray and Ernst Maug. All rights reserved. No part of this lecture may be reproduced without the permission
More informationLOS 56.a: Explain steps in the bond valuation process.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction
More informationThe US Municipal Bond Risk Model. Oren Cheyette
The US Municipal Bond Risk Model Oren Cheyette THE US MUNICIPAL BOND RISK MODEL Overview Barra s integrated risk model includes coverage of municipal bonds accounting for marketwide and issuerspecific
More informationGoals. Bonds: Fixed Income Securities. Two Parts. Bond Returns
Goals Bonds: Fixed Income Securities History Features and structure Bond ratings Economics 71a: Spring 2007 Mayo chapter 12 Lecture notes 4.3 Bond Returns Two Parts Interest and capital gains Stock comparison:
More informationC(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900$. The yield to maturity will then be the y that solves
Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of longterm fixed income securities are federal government bonds, corporate
More informationSaving and Investing. Chapter 11 Section Main Menu
Saving and Investing How does investing contribute to the free enterprise system? How does the financial system bring together savers and borrowers? How do financial intermediaries link savers and borrowers?
More informationDistinguishing duration from convexity
Distinguishing duration from convexity Vanguard research May 010 Executive summary. For equity investors, the perception of risk is generally straightforward: Market risk the possibility that prices may
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationA Flexible Benchmark Relative Method of Attributing Returns for Fixed Income Portfolios
White Paper A Flexible Benchmark Relative Method of Attributing s for Fixed Income Portfolios By Stanley J. Kwasniewski, CFA Copyright 2013 FactSet Research Systems Inc. All rights reserved. A Flexible
More informationZeroCoupon Bonds (Pure Discount Bonds)
ZeroCoupon Bonds (Pure Discount Bonds) The price of a zerocoupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
More informationIntroduction to Convertible Debentures
Introduction to Convertible Debentures Intro to Convertible Debentures March, 2009 Convertible debentures are hybrid securities which offer advantages of both bonds and equities. Like ordinary bonds they
More informationInvestment insight. Fixed income the what, when, where, why and how TABLE 1: DIFFERENT TYPES OF FIXED INCOME SECURITIES. What is fixed income?
Fixed income investments make up a large proportion of the investment universe and can form a significant part of a diversified portfolio but investors are often much less familiar with how fixed income
More informationINTEREST RATE SWAPS September 1999
INTEREST RATE SWAPS September 1999 INTEREST RATE SWAPS Definition: Transfer of interest rate streams without transferring underlying debt. 2 FIXED FOR FLOATING SWAP Some Definitions Notational Principal:
More informationGuggenheim Investments. European HighYield and Bank Loan Market Overview
Guggenheim Investments European HighYield and Bank Loan Market Overview August 2015 European HighYield & Bank Loan Market Overview Please see disclosures and legal notice at end of document. 2 August
More information