Callable Bonds: Better Value Than Advertised?

Callable bonds allow issuers to manage interest rate risk in the sense that if rates decline, the bonds can be redeemed and replaced with lower‐cost debt. Investors demand a coupon premium for giving issuers this option; and when deciding whether to issue callable or noncall‐able bonds, the issuing companies must determine whether it's worth paying the coupon premium. This article addresses two main questions about the structuring and refunding of callable bonds. The first concerns the value of the call option: At the time of issuance, does it make sense to accept the coupon premium for the option being acquired? The second concerns the optimal timing of a refunding: At refunding, do the cash flow savings provide adequate compensation for the option that is being exercised and hence given up? In perfect markets with no taxes or transactions costs, the average corporate issuer should be indifferent between issuing callable bonds or their noncallable equivalent. But corporate taxes, together with risk management considerations, can lead some issuers to prefer callable bonds, possibly with coupons that otherwise would be unacceptably high. Refunding decisions should be made using the concept of “call efficiency,” which compares the savings (net of transactions costs) from calling to the loss of option value. The latter should also account for any option that is built into the replacement issue. Transaction costs that occur when refunding diminish the value of the call option, and their effect should be factored in at the time of issuance. One way of avoiding such costs is to issue “ratchet” bonds—essentially one‐way floaters that automatically reset lower when rates decline, thus delivering the benefits of callable bonds while eliminating transaction costs.     

The Choice of Call Provision Terms: Evidence of the Existence of Agency Costs of Debt

An examination of the provisions of bond issues reveals that most bonds prohibit firms from calling the issue during the initial years, after which time the bond can be called at the option of the firm. A substantial number of firms, however, also reserve the right to call the issue during this initial period for purposes other than refinancing at a lower coupon rate. The additional flexibility which accompanies the option of early redemption can be used to reduce the agency costs of debt associated with future investment opportunities, informational asymmetry, and the risk incentive problem. Using a sample of newly issued bonds, statistical tests are performed to show that there are, in fact, differences between firms which do and do not reserve the right of early redemption. This paper shows that these differences provide empirical evidence which is consistent with the hypothesis that firms use the option of early redemption to reduce agency costs.     

EXACT FORMULAS FOR PRICING BONDS AND OPTIONS WHEN INTEREST RATE DIFFUSIONS CONTAIN JUMPS

I develop Heath‐Jarrow‐Morton extensions of the Vasicek and Jamshidian pure‐diffusion models, extend these models to incorporate Poisson‐Gaussian interest rate jumps, and obtain closed‐form models for valuing default‐free, zero‐coupon bonds and European call and put options on default‐free, zero‐coupon bonds in a market where interest rates can experience discontinuous information shocks. The jump‐diffusion pricing models value the instrument as the probability‐weighted average of the pure‐diffusion model prices, each conditional on a specific number of jumps occurring during the life of the instrument. I extend the models to coupon‐bearing instruments by applying Jamshidian's serial‐decomposition technique.     

YIELD VOLATILITY OF DISCOUNT COUPON BONDS

In this research, the yield volatility of coupon-taxable discount bonds is analyzed. The relationship of before-tax yield changes on discounts as compared with changes in new, par issue (market) yields is developed in the form of a net yield factor (NYF). Also, the behavior of the NYF as dependent upon parameters such as maturity, coupon, market yield, and tax rates is examined. Then, the incorporation and impact of the NYF on price volatility are shown. Finally, results of empirical tests are reported, which validate the usefulness of NYFs in the measurement of yield volatility for discount bonds.     

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.     

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.     

Municipal bonds: a contingent claims perspective

The purpose of this paper is to provide an overview of the municipal bond market with an emphasis on the numerous embedded contingent claims. Embedded contingent claims include the standard call features, sinking funds, the advance refunding option, the synthetic advance refunding option, the credit risk option (default risk), marketability, and the numerous tax-related events. Municipal bond investors must carefully assess the relative value of these contingent claims before investing in municipal bonds. Also, due to unique risk premiums within the municipal bond market, it is important to carefully structure the municipal bond holdings, paying particular attention to duration, within the context of an overall financial plan. There appears to be a benefit to lengthening the duration of the municipal bond portion of the portfolio.     

Don't Waste a Free Lunch: Managing the Advance Refunding Option

A callable municipal bond issue funding a new project is usually eligible for “advance refunding”—that is, refunding between the issue date and the call date. Such refunding is accomplished by issuing new bonds, and investing the proceeds in an escrow portfolio of Treasury securities whose cash flows pay off the outstanding issue until the call date, when the old bonds are retired. Under favorable market conditions, advance refunding enables a municipality to lock in lower interest rates prior to the call date; waiting until that date would expose the issuer to the risk of higher rates. The right to advance refund is an option whose value depends not only on the issuer's borrowing rate, but also on Treasury rates, which determine the cost of the escrow portfolio. What makes this option (referred to by the authors as the “ARO”) unusual is that it is effectively a free lunch for the issuer. While investors pay a lower price for a callable bond, the price is not affected by the bond's eligibility for advance refunding. The free lunch is demonstrable when the yield of the escrowed Treasuries is higher than the issuer's funding rate to the call date. In such cases, the present value of the cash flows to the call date (which is how the market prices a deep‐in‐the‐money callable bond) exceeds the cost of the escrow. This excess effectively enables the issuer to retire the bonds below their fair market value. Another manifestation of the free lunch offered by advance refunding transaction occurs when the savings exceed the expected value of waiting—that is, when the value of the call option is less than the currently realizable savings. One important consideration when deciding whether and when to advance refund is that the ARO can be exercised only once in an issue's refunding life‐cycle. If an issue is advance refunded, its replacement cannot be. But if an issue is refunded once it becomes callable, the ARO stays alive in the replacement issue. In this article, the authors develop an analytical framework to help issuers deal with this problem. First, they explore how the value of the ARO depends on coupon, maturity, time to call, and prevailing Treasury rates. Then they use the results to make a recommendation about the advance refunding decision: act now or wait? To answer this question, the authors extend the standard measure of refunding efficiency to incorporate the ARO of the replacement issue. Incorporating the ARO of the replacement issue slows down the signal to advance refund, whereas failure to do so could lead to a suboptimal decision. Near the call date, issuers may be better off locking in savings with a hedge rather than sacrificing the eligibility of the replacement issue for advance refunding.     

Bond pricing with a surface of zero coupon yields

We present a new method for consistent cross‐sectional pricing of all traded bonds in the fixed income market. By applying thin plate regression splines ( Wood, 2003 ) to bootstrapped zero coupon bond yields ( Hagan and West, 2006 ), the method decomposes traded yields into a risk‐free component plus premia for credit and liquidity risks, where the decomposition is consistent with the market valuations and underlying cash flows of the bonds. We apply the framework to end of quarter yield data from 2008 to 2011 on Australian dollar denominated semi‐government, supranational and agency (SSA) bonds, and find that the surface provides an excellent fit to the underlying zero coupon yield curves. Further, the decomposition of selected yield time series and cross‐sections demonstrates how credit premia increased for Australian SSA bonds through the Global Financial Crisis (GFC), but were counterbalanced by liquidity discounts as investors sought safe haven securities.     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

THE BALANCED CAPITAL STRUCTURE

At leading companies, financial executives are becoming business partners rather than just scorekeepers. In this environment, capital structure can be a source of competitive advantage, and financial strategy issues are critical: Should your company buy back shares or issue stock, grow internally or join the M & A boom, issue fixed-rate debt or stay floating? These decisions must be addressed one company at a time, balancing the competing priorities of cost, risk, and flexibility. The most important issue, target leverage, depends on the company's desired risk profile, growth plans, and debt cost considerations. But market conditions are also very important: Can the company access the equity market? How will a repurchase announcement be interpreted? Market conditions also affect the raising of debt capital. Rather than maintaining a constant mix of fixed- to floating-rate debt, companies should shift the mix during high- or low-yield environments. Many other financing issues will effectively be decided by market convention. For example, meeting a company's needs with respect to seniority, maturity structure, call flexibility, and financial covenants is often accomplished simply by choosing the market that most closely matches the firm's cost and risk preferences.     

信用债流动性视角下的货币政策传导效果

企业债券是社融存量规模中仅次于贷款的一个重要组成部分,其利率的变化直接关系到实体经济的融资成本,文章通过实证研究指出,近年来基准利率与信用债二级市场成交收益率和一级市场发行票面利率相关性逐步提升,反映出通过债券路径的货币政策传导效果在逐步增强,而债券市场成交活跃度提升是其重要推手。文章进而提出进一步提升市场流动性的相关政策建议。     

Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of the term structure

Solutions are presented for prices on interest rate optionsin a two-factor version of the Cox-Ingersoll-Ross model of theterm structure. Specific solutions are developed for caps onfloating interest rates and for European options on discountbonds, coupon bonds, coupon bond futures, and Euro-dollar futures.The solutions for the options are expressed as multivariateintegrals, and we show how to reduce the calculations to univariatenumerical integrations, which can be calculated very quickly.The two-factor model provides more flexibility in fitting observedterm structures, and the fixed parameters of the model can beset to capture tie variability of the term structure over time.     

The determinants of bond call premia: A signalling approach

A signalling model is presented that provides an additional explanation for the determination of call premia on corporate bonds. It is shown that firms may signal their exclusive information about their probability of default by the choice of their call premia. Stockholders of safer firms (i.e., those that have a lower probability of bankruptcy) have a higher incentive for providing a low call premium. This occurs because the call option will be valuable only if the firm survives by the first call date. This event, however, is more likely for the safer firm. The safer firm will therefore be more willing to sacrifice some current revenues (or equivalently, to provide a higher coupon than it would otherwise have to pay in order to sell the bond at par) by determining a lower call premium. The model therefore predicts a negative correlation between safety and call premia, a correlation that has been empirically confirmed by Fischer, Heinkel, and Zechner (1989). This correlation provides support to the signalling theory vis-à-vis the alternative explanation of taxes determining the call premia. Another contribution of this model is that it ties the call premium decision with expectations of future interest rates. Such expectations are considered important by practitioners, but were rarely considered in previous research.     

Differential taxation and the equilibrium structure of interest rates

Equilibrium coupon bond pricing relationships given differential taxation are derived under uncertainty assuming that both corporate and municipal bonds were originally issued at par but are currently selling at a discount. The impact of differential taxation upon the term structure and coupon structure of interest rates is investigated, while the tax structure of interest rates is uniquely characterized. Differential taxation substantially alters the prevailing equilibrium structure of interest rates.     

A Long‐Term Perspective on the Determinants of Treasury Bond Stripping Levels

We examine the proportion of individual Treasury bonds held as strips over the entire history of the STRIPS program. First, we document a secular decline in the Treasury bond stripping levels from 1985 to 2010, coincidental with the long‐term decline in the interest rates. This pattern suggests that investors purchase strips to avoid reinvestment risk and to lock in the high interest rates in the 1980s and 1990s. Second, higher coupon and longer maturity bonds are shown to be more heavily stripped. Third, the suspension of new issues of 30‐year bonds from 2001 through 2006 created a gap in the maturity structure of Treasury bonds and induced heavy stripping of 30‐year bonds issued post 2006. Our findings suggest that stripping is motivated by several factors, including interest rate risk management, tax concerns and market completion.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

Are embedded calls valuable? Evidence from agency bonds

This paper examines the call option values embedded in callable agency bonds. For FHLB, FNMA, and SLMA bonds, call value estimates range from 1.23% of par to 1.47% on average, which are between those for the treasury and corporate debt securities. FHLMC bonds, on the other hand, have an average call value estimate of 2.85%. Call values are significantly larger for bonds with a longer remaining maturity and greater default risk. Most interestingly, call values in the call protection period are significantly larger than those in the callable period except for the SLMA bonds, whereas previous studies on corporate debt find no significant difference in call values between these two periods.     

Bond Selection for Managed Portfolios

Abstract:   Investors in coupon bonds evaluate them based upon financial considerations such as coupon rate, time‐to‐maturity, callability, convertibility, and financial condition of the issuer. These investors regard promised yield as only a rough measure of the reward a bond offers to compensate them for the pure time‐value‐of‐money and the financial risks to which they are exposed. Hence, they need a more meaningful measure of reward to facilitate comparisons among coupon bonds. The purpose of this paper is to describe an alternative heuristic approach to the task of making such comparisons. The approach produces a simple ordinal measure of reward, called the 'indifference spread,' that considers implicitly the potential sources of return to, as well as many of the risks associated with, investment in coupon bonds. For any coupon bond, the indifference spread method permits assessment of relative reward offered for the combined exposures to price and call risks, while also reasonably accommodating possible sale anytime prior to maturity. Once an investor (e.g., money manager) identifies indifference spreads for all bonds under consideration as of any moment in time, he/she can then draw conclusions regarding their relative values at that time based, in large part, on these spreads.