Analysis of U.S. savings bonds

U.S. savings bonds are complex contracts. Financial planners have traditionally paid little attention to savings bonds, in part because they often offer below-market interest rates. However, they sometimes offer above-market interest rates, especially when one learns how to view and value their option features. All savings bonds contain put options that protect the investor against a rise in interest rates. Thus, they can be viewed as short-term, intermediate-term, or long-term bonds. The EE bonds also offer several tax options. We show how savings bonds can be used to beat the kiddie tax, to finance postsecondary education, and in retirement planning.     

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

A new characterization of the American-style option is proposed under a very general multifactor Markovian and diffusion framework. The efficiency of the proposed pricing solutions is shown to depend only on the use of a viable valuation method for the corresponding European-style option and for the transition density of the model’s state variables. Under a Gauss-Markov stochastic interest rates setup, these new American option pricing solutions are shown to offer a much better accuracy-efficiency trade-off than the approximations already available in the literature. This result is also used to price callable corporate bonds under an endogenous bankruptcy structural approach, by decomposing the option to call or default into a European put on the firm value plus two early exercise premium components.     

Modeling term structures of defaultable bonds

This article presents convenient reduced-form models of thevaluation of contingent claims subject to default risk, focusingon applications to the term structure of interest rates forcorporate or sovereign bonds. Examples include the valuationof a credit-spread option.     

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.     

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.     

The nominal duration of TIPS bonds

This paper studies the price responsiveness (effective duration) of U.S. government issued inflation-indexed bonds, known by the acronym TIPS (Treasury Inflation-Protected Securities), to changes in nominal interest rates, real interest rates, and expected inflation. Using the TIPS pricing formula derived by Laatsch and Klein [Q. Rev. Econ. Finance 43 (2002) 405], we first confirm that TIPS bonds have zero sensitivity to changes solely in expected inflation. By changes solely in expected inflation, we mean that the real rate remains unchanged and the nominal rate changes in accordance with the established Fisher [Publ. Am. Econ. Assoc. 11 (1896)] effect. We show that the first derivative of the TIPS price is zero whenever the real rate is held constant. Thus, the first partial derivative of the TIPS bond pricing formula with respect to expected inflation is zero and the first partial derivative of the TIPS bond price with respect to nominal rates is also zero, given, in each case, that we hold the real rate constant. We then temporarily shift the analysis to zero-coupon TIPS bonds and zero-coupon ordinary Treasury bonds. We prove that the nominal duration of zero-coupon TIPS bonds equals that of zero-coupon ordinary Treasury bonds when the real rate changes but expected inflation is held constant.However, if expected inflation changes and the change in the nominal rate does not yield a constant real rate, zero-coupon TIPS prices will change and they will change by a smaller percentage than will zero-coupon ordinary Treasury bonds. We analyze TIPS responsiveness to changes in nominal rates under such conditions. We derive an approximation to effective duration that demonstrates that the effective durations of various maturity zero-coupon TIPS bonds are approximately linear functions in time to maturity of the effective duration of the one-year zero-coupon TIPS bond, ceteris paribus.Nominal effective duration of TIPS bonds is certainly of interest to fixed income portfolio managers that might have a desire to include such bonds in their portfolio. After all, the greater portion of a typical fixed income portfolio is in traditional, noninflation protected bonds whose major risk exposure is to changes in nominal rates. To properly assess the role of TIPS bonds in the portfolio, portfolio managers need information as to how TIPS bonds respond to the changes in nominal rates that are driving the price behavior of the bulk of the portfolio's assets. Prior to concluding the paper, we demonstrate how portfolio managers can calculate the nominal durations of coupon TIPS bonds using the zero-coupon duration formula we derive.     

The determinants of the return on index bonds

The investor holding an index-linked bond is guaranteed a given real income irrespective of the prevailing inflation rate. The holding-period return (HPR) on such a bond should, therefore adjust to realized inflation; this is the firsthypothesis tested. The value of the bond may also change due to anticipated changes in the real interest rate which should themselves be related to uncertainty about future inflation; hence HPRs on linked bonds may vary with inflation uncertainty (second hypothesis). Furthermore, for bonds with long periods of time to maturity the effect of uncertainty about future inflation rates may be rather small so that as we approach maturity, the effect of inflation uncertainty should increase (third hypothesis). These three hypotheses are tested on a sample of eight Israeli index-linked bonds with maturities three months apart. The first hypothesis is supported by the data but the last two are not.     

Binary interest rate sensitivities of emerging market corporate bonds

We develop a framework to assess interest rate sensitivities of emerging market corporate debt. Our analysis, based on yield indexes, is applied to investment grade and high yield portfolios. We reach beyond correlation-based analyses of interest rate sensitivity and keep our scope centered at capital gains of emerging market corporates and U.S. government bonds portfolios. Our empirical analysis spans over the period 2002–2015. We address interest rate sensitivity of assets during the ignition, apogee, and the aftermath of the global financial crisis. Based on historical data series, we evidence that the emerging market corporate bonds exhibit two different regimes of sensitivity to interest rate changes. We observe switching from a positive sensitivity under the normal market conditions to a negative one during distressed phases of business cycles and provide economical explanations of such phenomena. We show that emerging market corporate bonds, which on average could appear rather insensitive to the interest rate risk, in fact, present binary interest rate sensitivities. This research sheds light on how financial institutions may approach interest rate risk management including the downside risk hedge. Our findings allow banks and financial institutions to optimize economic capital under Basel III regulatory capital rules.     

Transparency,idiosyncratic risk,and convertible bonds

We first investigate the relationship among a company's information transparency, idiosyncratic risk, and return of its convertible bonds. The effects of a company's idiosyncratic risk on its equity's value volatility and its credit risk are also examined. The findings indicate that when a company discloses a significant amount of information, it is likely to have a higher idiosyncratic risk and a lower credit risk, with no impact on returns on convertible bonds. The volatility of stock returns is positively related to returns on convertible bonds, and it is found that diversified strategies and returns on a company's equity help to improve its credit rating and that a better credit rating triggers an increase in returns on convertible bonds and idiosyncratic risk, indicating that evaluations of the value of convertible bonds must take pure bonds and equity (option) values into account. After excluding conversion values and estimating the idiosyncratic risk on daily, weekly, and monthly bases, this study suggests that there is a positive relation between returns on convertible bonds and information transparency when estimating idiosyncratic risk on a monthly basis and that a positive association also exists between credit rating, idiosyncratic risk, and returns on bonds.     

Impact of interest rate surprises on Islamic and conventional stocks and bonds

This paper studies the impact of interest rate news surprises on Islamic and conventional stock and bond indices, using a dataset which covers interest rate announcements and forecasts, as well as stock and bond indices in three Islamic and eight non-Islamic countris. We find that interest rate surprises tend to have a smaller impact on the returns and volatility of Islamic than conventional bonds because Islamic bonds are structured to avoid explicit interest rates. However, interest rate surprises have about the same or bigger impact on the returns and volatility of Islamic relative to conventional stocks, despite the low amounts of cash and debt holdings of firms comprising Islamic stock indices.     

Implied tax rates and the valuation of discount bonds

Discount bonds afford the investor the opportunity for capital gains. If for tax reasons the market is segmented on the demand side, investors in lower and lower tax brackets must be attracted when interest rates rise and the supply of discount bonds increases. Changes in the differential tax on capital gains and interest income also should affect relative demand. Testing these hypotheses with U.S. Treasury bond data, the implied tax rate is found to vary over time in a manner consistent with market segmentation and tax law changes.     

Term structure estimation and pricing of callable Treasury bonds

This article describes a methodology of term structure estimation incorporating callable Treasury bonds using a bond-option valuation model. This article also examines whether some simple approximation of the option value suffice for providing a useful estimation procedure. The authors find that the errors in estimating the option value can generate significant errors for estimating the discount function. A call provision on a Treasury bond is not negligible at least our framework. This procedure is consistent with two aspects of the Treasury market. First, it provides the discount function that best determines the prices of observed Treasury securities, and second, it obtains a discount function that explains callable Treasuries.     

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.     

An analytic approximation formula for pricing zero-coupon bonds

This paper presents an analytic approximation formula for pricing zero-coupon bonds, when the dynamics of the short-term interest rate are driven by a one-factor mean-reverting process in which changes in the volatility of the interest rate are a function of the level of the interest rate.     

Hedging bonds subject to credit risk

This paper provides a simple and practical approach to hedging bonds that are subject to credit risk. Three new hedge ratios are derived and tested and the roles of basis risk and diversification is investigated. Empirical tests reveal that basis risk is an important factor in hedging corporate bonds. These tests identify a need for new interest rate derivatives where the underlying asset is subject to credit risk.     

含期权债券利率风险的衡量

久期(Duration)和凸度(Convexity)是度量普通债券利率风险的常用指标。含权债券中内嵌的期权会改变债券价格变动和利率变动的关系,使债券面临更大的利率风险,但常用的久期和凸度无法体现这一影响。实际久期和实际凸度可以弥补这一缺陷,是衡量含权债券利率风险的有效指标。对国家开发银行发行的可赎回债券和可回售债券的模拟和实证分析表明,由于内嵌了期权,在有些情况下实际凸度解释了大部分的利率风险,因此建议在投资中使用实际久期和实际凸度来衡量含权债券的利率风险,而且在利率比较高或比较低时不可忽略实际凸度对利率风险的解释作用。     

The Effect of Interest Rates on the Value of Corporate Assets and the Risk Premia of Corporate Debt

A growing number of papers have applied option pricing techniques to the valuation of risky debt. This paper deals directly with how a firm's relationship to interest rates affects its debt. A sequential binomial model is used to price the zero-coupon bonds of a firm whose value is related to interest rate changes.The results show that the strength of the relationship between firm value and interest rates (interest-rate risk) can have a significant impact on the value of a firm's debt. The model produces its most powerful results when the volatility of firm value is high and the term structure has a steep (negative or positive) slope; there is no impact when the term structure is flat. Our results indicate that empirical studies of yield spreads may have severe shortcomings if the relationship of firm value to interest rate changes is ignored.     

A theoretical deficiency in accounting for bonds

Accounting for bonds payable issued at a premium or discount between interest payment dates poses some interesting theoretical problems. Nine Intermediate Accounting textbooks were examined, and only two were found to deal with the topic, neither at a theoretical level. When the theoretical value is calculated for a bond issued at a discount or premium between interest payment dates, the computed value includes the accrued interest. The usual approach is to record the collection of accrued interest separately from the bond proceeds. Unless the bond is recorded correctly the premium or discount does not amortize properly. This paper examines the recording of the accrued interest, and offers some suggestions for teaching this topic in courses beyond the introductory level.     

A MULTIFACTOR MODEL OF THE QUALITY OPTION IN TREASURY FUTURES CONTRACTS

The values of quality options in Treasury futures contracts are set relative to the prices of all coupon bonds in their respective deliverable sets. As a result, any model used to value the quality option should set its price relative to the set of observed bond prices. This requirement rules out the use of most simple equilibrium models that represent all bond prices in terms of a finite number of state variables. We use the two-factor Heath-Jarrow-Morton model, which permits claims to be priced relative to observable bond prices, to investigate the potential value of the quality option in Treasury bond and note futures. We show that the quality option has significantly more value in a two-factor interest rate economy than in a single-factor economy, and that ignoring it could lead to significant mispricing.