Short-maturity bonds

There is another reason not to write off new investments in bonds Investors have some control over the pain they would suffer in a rising rate environment. To minimize losses, they can pick funds holding intermediate- or even short-maturity bonds, which fluctuate in price far less than the longest-maturity bonds. 

Maturity Generally default spreads are larger for longer date bonds and narrow for short-term bonds. 

The segmented markets hypothesis, first described in Culbertson (1957), seeks to explain the shape of the yield curve. It states that different types of market participants, with different requirements, invest in different parts of the term structure. For instance, the banking sector needs short-dated bonds, while pension funds require longer-term ones. Regulatory reasons may also affect preferences for particular maturity investments. 

Being short a bond is the equivalent to being a borrower of funds. Assuming that these positions are held to maturity, the resulting cash flows are those shown in FIGURE 7.1. 

Step-up recovery FRNs, whose coupons are fixed against comparable longer-maturity bonds, i.e., bonds with longer maturities than those of the FRNs in question. These notes enable investors to maintain exposure to short-term assets while capitalizing on a yield curved with positive slope. 

In contrast to the situation in most strip markets. Treasury strips with very short maturities do not trade expensive relative to the curve. When the yield curve is positive, short strips are often in demand because they enable investors to match liabilities without reinvestment risk and at a higher yield than they could get on coupon bonds of the same maturity. The Treasury strip yield curve, on the other hand, has been inverted from before there was a market. In other government strip markets, such as Frances, however, short maturities of up to three years are often well bid. 

But first, you should know what types of bonds are available. Among the types of bonds you can choose from are U.S. government securities, municipal bonds, corporate bonds, mortgage and asset-backed securities, federal agency securities and foreign government bonds. There are also many short-maturity options such as Treasury bills, bank certificates of deposit and commercial paper. 

Catalytic RNAs, or ribozymes, are RNAs, which catalytically cleave covalent bonds in a target RNA. The catalytic site is the result of the conformation adopted by the RNA-RNA complex in the presence of divalent cations. Shortly thereafter, Altman and colleagues discovered the active role of the RNA component of RNase P in the process of tRNA maturation. This was the first characterization of a true RNA enzyme that catalyzes the reaction of a free substrate, i.e., possesses catalytic activity in trans (Guerrier et al. 1983). A variety of ribozymes, catalyzing intramolecular splicing or cleavage reactions, have subsequently been found in lower eukaryotes, viruses, and some bacteria. 

We can define forward rates in terms of the short rate. Again for infinitesimal change in time from a forward date TitoT (for example, two bonds whose maturity dates are very close together), we can define a forward rate for instantaneous borrowing, given by... 

A short-rate model can be used to derive a complete term structure. We can illustrate this by showing how the model can be used to price discount bonds of any maturity. The derivation is not shown here. Let P t, T) be the price of a risk-free zero-coupon bond at time t maturing at time T that has a maturity value of 1. This price is a random process, although we know that the price at time T will be 1. Assume that an investor holds this bond, which has been financed by borrowing funds of value C,. Therefore, at any time t the value of the short cash position must be C,= —P(t, T) otherwise, there would be an arbitrage position. The value of the short cash position is growing at a rate dictated by the short-term risk-free rate r, and this rate is given by... 

So, now we have determined that a short-rate model is related to the dynamics of bond yields and therefore may be used to derive a complete term structure. We also said that in the same way the model can be used to value bonds of any maturity. The original models were one-factor models, which describe the process for the short-rate r in terms of one source of uncertainty. This is used to capture the short-rate in the following form ... 

This model incorporates mean reversion, which is not an imrealistic feature. Mean reversion is the process that describes that when the short-rate r is high, it will tend to be pulled back towards the long-term average level when the rate is low, it will have an upward drift towards the average level. In Vasicek s model, the short-rate is pulled to a mean level 6 at a rate of a. The mean reversion is governed by the stochastic term odW which is normally distributed. Using Equation (3.24), Vasicek shows that the price at time t of a zero-coupon bond of maturity T is given by ... 

The Ho-Lee (1986) model was one of the first arbitrage-free models and was presented using a binomial lattice approach, with two parameters the standard deviation of the short-rate and the riskpremium of the short-rate. We summarise it here. Following Ho and Lee, let ( ) be the equilibrium price of a zero-coupon bond maturing at time T under state i. That is F( ) is a discount... 

The price of a zero-coupon discount at time t is defined in terms of the short-rate r at time t and the current term structure. The price function is not static, and the price of a bond at time t that matures at time T is a function of the short-rate, as we have noted, and separately of the time f. 

Like the bond price function, the yield on a zero-coupon bond is a function of the short-rate r and follows a normal distribution the yield curve is a function of the short-rate r, the time t and the time to maturity T. The Imig-run average future interest over the time to maturity (t, T) is normally distributed and given by ... 

In seeking to develop a model for the entire term structure, the requirement is to model the behaviour of the entire forward yield curve, that is, the behaviour of the forward short-rate/(f, T) for all forward dates T. Therefore, we require the random process f(T) for all forward dates T. Given this, it can be shown that the yield R on a T-maturity zero-coupon bond at time t is the average of the forward rates at that time on all the forward dates s between t and T, given by Equation (4.1) ... 

In an environment of interest-rate uncertainty, from previous chapters we know the price today of a zero-coupon bond of maturity T to be a function of the expectation of future short rates, which at time t are not known this is given in Equation (7.1) ... 

As introduced, the reference rate represents the interest rate or index used to obtain the linkage. In the European market, the major parts of floating-rate note issuances are linked to the Euribor and the remaining to the constant maturity swap. In the US and UK markets, they are tied to the Libor and short-term treasury bonds. 

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