Fixed Interest Securities and Derivatives - Literature review Example

Fixed Interest Securities and Derivatives A. Introduction Investigating relationships between yields of diverse maturities was one of the first purposes of co-integration analysis (Campbell and Shiller, 1987; and Engle and Granger, 1987). Hall et al. (1992) extended the original Bivariate approach to the multivariate case. The analysis focused on a set of short-term maturities and discovered one regular tendency. This was conceived to substantiate the expectations theory of the term structure. The expectations theory states that a longer-term bond rate is only the mean of anticipated one-period rates for the period of the bond with addition of some fixed term premium. Based on this theory, the spreads amongst diverse maturities constitute the co-integrating vectors. If there was found only one general trend, it was resolved that the term premia then must be mean-returning if not constant. Shea (1992) studied a more extensive set of yields, which included the long-term maturities up to 25 years. The results of his study supported the verdicts of Hall et al. (1992) for the short end of the yield curve but eliminated fixed spreads which comprised the longer-term maturities. Working up on Shea (1992), other investigators discovered three common trends when they included yields of longer maturities. Zhang (1993) established this for US data while Carstensen (2003) for German data. Yield Curve There are a variety of hypotheses that can describe any slope which the yield curve may take. The simplest theory is the pure expectations theory. The use of the expectations theory in the study of the yield curve can be deciphered as far back as that Fisher (1896). The Expectations Theory presumes that all financial tools on the yield curve are absolutely substitutable. In this the forward rates solely correspond to the predictable future rates. As these rates either rise or fall for any time period, the shape of the yield curve can be either upward sloped or downward for that particular period. Peterson (2001) had actually attempted to make clear the inaccuracy of the Expectations Theory. He states that “there is a rational bias for investors to go ‘with the crowd.’ Specifically, he shows that an institutional investor going against the crowd has a high degree of visibility to one’s superiors. The risk / reward calculation is biased toward not ‘sticking one’s neck out.’ If he goes against the crowd and rightly predicts the market, he gains some positive recognition. However, if he goes against the crowd and wrongly predicts the market’s movements, then it could be the end of his career.” Consequently, the estimates are logically coloured to go along with the crowd. These activities skew the yield curve and develop results that contravene the Expectations Theory. Next is the liquidity preference theory. This theory asserts that capitalists never like uncertainties and thus have to be offered a higher rate of return when they opt for bonds with longer term of maturity. Consequently, the forward rate replicates not only opportunities about future interest rates but also a “liquidity” premium which has to be higher for securities which have a longer period of maturity. Ceteris paribus which is a rising liquidity premium entails that the shape of the yield curve will be sloping upward. Matthews (1963, p.201) submits, “If asset-owners dislike risk, the possibility of a capital loss will discourage them from holding bonds, even though they consider a capital gain no less likely than a capital loss. The demand for money arising from this source will be interest elastic, because asset-owners have to weigh the riskiness of bonds against their yield.” The preferred habitat theory also follows the opinion that the term structure speculates the anticipation of the future path of interest rates and a risk premium. On the other hand, the preferred habitat theory disapproves the affirmation that the risk premium must grow consistently with maturity. The preferred habitat theory maintains that to the level the demand and supply of finances in a given maturity ambit does not correspond, some loaners and recipients will be stimulated to change over to maturities depicting the reverse instabilities. Nonetheless, they will have to be covered by a suitable risk premium whose size will reproduce the degree of aversion to either price or reinvestment risk. Thus the shape of the yield curve based on this theory is decided by both anticipations of future interest rates and a risk premium. The shape may be positive or negative, to stimulate market players to change their favoured habitat. Therefore the yield curve can be sloped up or down or it can be either flat, or humped. Culbertson (1957) merges the Liquidity-Preference Theory with the proposal of segmented markets to deliver a substitute to the Expectations Theory. Modigliani and Sutch (1966) were the first to merge the different theories and generate the Preferred-Habitat Theory. Even though their theory is capable of answering the three experimental facts of the yield curve, the Preferred-Habitat Theory similar to the Expectations Theory, has grave defects. It presumes a fundamental interest rate and does not succeed to describe the source of this initial rate. The market sectionalisation theory also discerns that capitalists have favoured habitats determined by the character of their indebtednesses. This theory also suggests that the main cause for the shape of the yield curve dwells in asset-liability direction restraints and/or borrowers limiting their financing to particular maturity sectors. Still, the market division theory disagrees from the favoured habitat theory in that it presumes that neither capitalists nor receivers are willing to change from one maturity sphere to another. This aids investors to take advantage of chances developing from deviations between expectations and forward rates. Therefore the shape of the yield curve of the segmentation theory is ascertained by supply of and demand for securities amongst each maturity sphere. Hakim and Rashidian (2000) indicate that when there is a proportional change in the supply of one security, it may have the outcome of “twisting the yield curve.” They also explain that the monetary power can have an outcome on the yield curve further than expectation and liquidity consequences. But, the impact of the financial authority decreases across the term structure, i.e., the effect becomes strongest for short- and medium-term securities. Seo (2003) presents a new direction for the Segmented Markets Theory. He indicates that the markets may be sectioned due to transaction costs. Investment will not take place if the transaction costs are more than the profit to be made through the investment process. The author detects that there are substantial transaction costs that cut back the strength of the arbitrage procedure and thus the market segments. Modern Contributions to Yield Curve Theory Recent approaches in yield curve theory centre on the relationship amongst the yield and macroeconomic variables like development, inflation, and future interest rates. The yield curve is frequently applied as an index of the kind of monetary policy being followed (IMF Staff Paper, 1994). The Expectations Theory contributes to the proposal of the yield curve as a forecaster of future inflation, stating that long-term rates are established on the capitalists’ expectations of future interest rates and thus inflation. An augment in present long rates suggests that capitalists anticipate future short rates to step-up. A number of authors have detected substantial proof of a relationship between the yield curve and inflation (Browne and Manasse 1989). Each of the yield curve theories discussed above on its own, either is not able to meet the three experimental concepts of the yield curve or betrays to respond the essential question. The Expectations Theory describes why long and short rates incline to move together, but does not account for a constantly positive slope and cannot elucidate why long rates incline to stay steady in relation to short rates. The Liquidity Preference theory describes the affirmative slope and elucidates why long and short rates have a tendency to move unitedly, but the theory neglects to describe the cause why long rates incline to remain more static than short rates. The Segmented Markets Hypothesis fails to conform to any of the 3 pragmatic facts. In spite of these defects, each of these theories brings up matters that must be covered in a full theory of the yield curve. Ireland (1996) indicates the risk premium is fairly small when equated to the expectations result. Thus the expectations consequence can intermittently control the liquidity-preference, and it is potential to witness reversed yield curves in the real world. While exogenous components determine the anticipations of entrepreneurs, expectations are basically an internal element of the entrepreneur. Entrepreneurs’ conclusions are made at their own, individual borders. Thus, expectations have to be taken into account as an endogenous element. In a study of this association, Fleming and Remolona (1999) scrutinise the consequences of surprise proclamations made by the Federal Reserve and the US Treasury. They conclude that “the announcement effects are relatively weak for the short maturities and strong for the intermediate maturities of one to five years. When plotted by maturity, these effects form hump-shaped curves.” B. Introduction According to Fabozzi & Ramsey (1999: p.21) “The starting point in evaluation of any financial asset is estimation of its expected cash flow.” The principal prepayments entails that the cash flow of a pass-through cannot be recognised with firmness. Therefore the rate of principal prepayments is the overriding feature involving the measure of pass-throughs. Prepayment Benchmark Conventions “Estimating the cash flow from a pass through requires making an assumption about future prepayments” (Fabozzi & Ramsey 1999:p. 21).During the past there have been quite a lot of conventions applied as a benchmark for prepayment rates. Although some of them are not used any more the pre-dominant one is the Public Securities Association (PSA) prepayment benchmark. PSA Prepayment Benchmark Frank (1991) states: “The cash flow for each class of CM0 can be derived only by assuming some prepayment rate for the underlying mortgage collateral. The prepayment benchmark used by mortgage backed securities dealers to quote CM0 yields is the PSA (Public Securities Association) standard prepayment model.” The PSA (Public Securities Association) prepayment benchmark was initially brought in to allow for a standard criterion for pricing Collateralized Mortgage Obligations (CMO) supported by 30-year fixed-rate. It was used for fully amortising mortgages, and it is a creation of a research by the PSA that measured the transience rates of residential loans assured by the FHA. The PSA committee examined data and it seemed like the mortgages got ‘seasoned’ meaning prepayment rates inclined to level off after 29 months during which time the conditional prepayment rate (CPR) inclined to oscillate at more or less 6%. Founded on this, the PSA formulated its prepayment standard through premises similar to an additive gain in CPR from month 1 to month 30 and other reductions. Even though many shrewd money managers acknowledged the utility of CPR for citing yield and/or price, the CPR has many restrictions in finding out the measure of a pass-through. Fabozzi and Ramsey (1999: p.33) state “The message is that money managers must take care in using any measure that is based on the PSA prepayment benchmark. It is, only a market convention”. Prepayment premises, that is, figures established on significant prepayment rates for each specific type of mortgage loan under different economic conditions from different geographic areas, are factored into the bidding price, “yield,” and market measure of a CMO. The fruition of the mean life and yield forecasts reckons on the accurateness of the prepayment premises. The PSA prepayment standard is showed as a monthly sequence of yearly prepayment rates. This benchmark is generally denoted as a prepayment model, signifying that it can be utilised to calculate approximately prepayments. Depiction of this benchmark as a prepayment model is unsuitable. It is only a market principle of prepayment behaviour. The PSA benchmark presumes that prepayment rates are low for recently developed security interest and then will speed up as the security interest become seasoned. The PSA benchmark accepts the following CPRs for 30 year mortgages: i. A CPR of 0.2% for the I month, augmented by 0.2% per year per month for the next 30 months when it attains 6% per year and ii. A 6% CPR for the outstanding years. This bench mark is referred to as “100% PSA” of simply “100 PSA”. Mathematically, 100 PSA can be showed as follows: If t ≤ 30: CPR = 6% (t/30) If t > 30: CPR = 6%; Where t is the number of months since the mortgage originated. Slower and faster speeds are denoted as some percent of PSA. For instance, 50 PSA entails one-half the CPR of the PSA benchmark prepayment rate or 150 PSA means 1.5 times the CPR of the PSA benchmark prepayment rate. The requirement of assumptions and prepayment presumptions is planned to be an active operation, under the power of insurance governors. Attaining a balance between ease and an illustration series of results is mainly difficult here. Literature on Prepayment Two kinds of models have been conceived for modeling prepayments. Downing et al., (2005) qualify them as cut down-form and structural models. The structural approach presumes that mortgage terminating is the optimal reaction of a noetic recipient to alterations in the measures of variables like interest rates, housing prices, etc. It was first initiated by Dunn and McConnell (1981) who presented a model established on standard dependent claim pricing theory. In their model, prices of mortgage endorsed securities and prepayment behaviour are fixed together. They accept the Cox interest rate model, Cox et al. (1985), and initiate suboptimal prepayments as a Poisson events. Cox et al. (1985) used a non-arbitrage case and derived a partial differential equation which could be solved numerically for the cost of the security. Suboptimal prepayment behaviour was first recorded in their study. Other famous structural models are that of Timmis (1985), Dunn and Spatt (2005), and Stanton (1995). Stanton (1995) demonstrates a model that covers the option-theoretic approach. He models the dealing costs confronted by security interest bearers and supposes that prepayment choices take place at distinct times. This results in prepayment behaviour that is coherent with the alleged burnout effect and generally takes place after the mortgages begin to grow. If the interest rates lessen and portion of the fundamental loans fail to prepay makes up the burnout. In reality the receivers who did not refinance during this interest rate dip period are not likely to do so if the interest rates further drops. Reference Part A: 1. Browne, Frank, and Paolo Manasse, 1989. “The Information of the Term Structure of Interest Rates: Theory and Practice,” OECD, Working Papers no. 69. 2. Campbell, J.Y. and Shiller, R.J. 1987. "Co-integration and tests of present value models," Journal of Political Economy, 95: pp.1062-1088 3. Carstensen, K. 2003. "Nonstationary term premia and cointegration of the term structure," Economic Letters, 80: pp. 409-413 4. Culbertson, John, 1957. “The Term Structure of Interest Rates,” Quarterly Journal of Economics, 71(4): pp.485-517. 5. Engle, R.F. and Granger, C.W.J. 1987. "Co-integration and error correction: representation, estimation and testing," Econometrica, 55: pp.251-276 6. Fisher, Irving. 1896. “Appreciation and Interest,” Publications of the American Economic Association, 11(4): pp. 1-98. 7. Fleming, Michael and Eli Remolona, 1999. “The Term-Structure of Announcement Effects,” Federal Reserve Bank of New York, Staff Report, 76, 1-50. 8. Hakim, Sam, and Manochehr Rashidian, 2000. “Testing for Segmentation in the Term Structure: Operation Twist Revisited,” Quarterly Journal of Business Economics, 39(1): pp.3-21. 9. Hall, A.D., Anderson, H.M. and Granger, C.W. 1992. "A co-integration analysis of Treasury bill yields," The Review of Economics and Statistics, 74: pp. 117-126 10. IMF Staff, 1994. “Information Content of the Yield Curve,” World Economic Outlook, May, 89-92. 11. Ireland, Peter, 1996. “Long-Term Interest Rates and Inflation: A Fisherian Approach,” Federal Reserve Bank of Richmond, Economic Quarterly, 82 (1): pp. 21-35. 12. Matthews, R.C.O., 1963. “Expenditure Plans and the Uncertainty Motive for Holding Money”. The Journal of Political Economy, 71(3): pp. 201-218. 13. Modigliani, Franco, and R. Sutch, 1966. “Innovations in Interest Rate Policy,” American Economic Review, 56(1/2): pp. 178–197. 14. Peterson, Steven, 2001. “Rational Bias in Yield Curve Forecasts,” The Review of Economics and Statistics, 83(3): pp. 457-464. 15. Shea, G.S. 1992. "Benchmarking the expectations hypothesis of the interest-rate term structure: an analysis of co-integration vectors," Journal of Business and Economic Statistics, 10: pp. 347-366 16. Seo, Byeongseon, 2003. “Nonlinear Mean Reversion in the Term Structure of Interest Rates,” Journal of Economic Dynamics and Control, 27(11-12): pp. 2243-2265. 17. Zhang, H. 1993. "Treasury yield curves and cointegration," Applied Economics, 25: pp.361-367 Part B: 18. Cox, J. C., Ingersoll, J. E., and Ross, S. A. 1985. “A theory of the term structure of interest rates." Econometrica, 53(2): 385-407. 19. Downing, C., Stanton, R., and Wallace, N. 2005. “An Empirical test of a Two-Factor Mortgage Valuation Model: How much Do House Prices Matter?" Real Estate Economics, 33: pp.681-710. 20. Dunn, K. and McConnell, J. 1981. “Valuation of GNMA mortgage-backed securities." The Journal of Finance, XXXVI (3): 599-616. 21. Dunn, K. and Spatt, C. (2005). “The Effect of Refinancing Costs and Market Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts." Real Estate Economics, 33(4): 595-617. 22. Fabozzi, Frank J. and Chuck Ramsey. 1999. Collateralized Mortgage Obligations: Structure and Analysis. 3rd edition. Frank J. Fabozzi Associates, New Hope, Pennsylvania. 23. Fabozzi, Frank. 1991. “The Handbook of Fixed Income Securities”, Business One Irwin, Page 27. 24. Stanton, R. 1995. “Rational Prepayment and the Valuation of Mortgage-Backed Securities." Review of Financial Studies, 8(3): 677-708. 25. Timmis, G. C. 1985. “Valuation of GNMA Mortgage-Backed Securities with Transaction Costs, Heterogeneous Households and Endogenously Generated Prepayment Rates." Working Paper, Carnegie-Mellon University, Pittsburgh, PA. Read More