Holding a Bond to Maturity
The basic measures for evaluating bonds are rate of return, also called yield, and risk. Most people have some notion of yield and risk; however, to properly use these measures for fixed-income investment decisions, you need to understand their limitations and pitfalls. In this article, I’ll explain what they measure, their limitations and alternative measures that overcome their limitations.
The yield on a bond or on any investment is a measure of the rate of growth between an initial investment value and its final value. Bond risk is a measure of the volatility of the future cashflow of a bond measured to some horizon date and then converted to a yield. It is important to realize that the interest rate risk of holding a bond to maturity is only reinvestment risk, namely the uncertainty of the cashflow generated by reinvesting interest payments during the life of the bond. There is no interest rate risk for the maturity payment as it is guaranteed. Of course, there is the risk of defaults which we will ignore in our discussion as it is separate from interest rate risk.
Reinvestment Risk
Consider a 10-year US Treasury Bond that has a coupon rate of 10% annually and pays interest semi-annually. We’ll buy $10,000 of the bond priced at par (100% of redemption value). We’ll buy the bond on the date it was issued. The yield-to-maturity of the bond using the industry standard calculation is 10% which assumes each interest payment is reinvested at 10%.
Here are the investment details:
• The initial investment is $10,000, the cost of purchase.
• The future value of 20 interest payments of $500 or $10,000
• The redemption payment of $10,000.
• The interest gained from reinvesting the interest payments.
To see the difference the reinvestment assumption makes on future cashflow and therefore on yield, let’s consider four different interest rate scenarios for interest reinvestment as shown in the table below.
This table shows the importance of future interest rates on the rate-of-return and future cashflow of a bond held to maturity. In the case of a 10% yield to maturity over 10 years, the reinvestment cashflow represents 33% of the ultimate cashflow received by an investor, a significant contribution. In general, reinvestment interest is a significant contributor to yield when bonds are held for more than several years. The one exception to this rule is zero coupon bonds which have no interest rate risk because they have no interest payments.
We can get a good idea of the degree of reinvestment risk by comparing the sum of interest payments to the difference between the price paid and redemption value, which is the capital gain or loss. Together they account for the total income received. If most of the total income is due to interest, then the bond has more reinvestment risk, if most of the total income is capital gain or loss then it has less reinvestment risk. You can use the ratio of interest payments to total income to get a sense of the degree of interest rate risk.
When comparing bonds of similar maturity and credit risk we must also consider income taxes. Taxes will differ depending on the split between interest income and the capital gain or loss. When the price paid is less than redemption, the bond is said to be purchased at a discount resulting in a capital gain, when the price paid is more than redemption amount the bond is said to be purchased at a premium, resulting in a capital loss. In evaluating bonds, yield and future cashflow should be calculated on an after tax basis using the state and federal tax rates of the investor.
Horizon Analysis
So far, we have discussed yield and interest rate risk when a bond is held to maturity. But what if the bond may be sold prior to maturity? In this case, it is not meaningful to use yield-to-maturity since it applies only to the bond’s maturity date. The standard industry measure used for interest rate risk is called duration. Duration measures the percentage change in price for a percentage change in yield given the current yield and maturity date. It measures the price sensitivity to an instantaneous change in current market yield and assumes the bond is held to maturity. But we are assuming that the bond may be sold prior to maturity, so duration is not useful in this case and can even be misleading. Both yield-to-maturity and duration need to be replaced by more meaningful measures.
To determine a meaningful measure of bond interest rate risk and yield, we need to estimate a bond’s future value and yield on a series of future dates not just at maturity. Using several points in time gives us a picture of how the bond behaves as it ages. Duration does not take account the bond’s movement is time nor does yield-to-maturity. It is the journey of the bond through time that represents the possible rates of return and interest rate risk of the bond. A more meaningful measure of return and risk is to determine the yield of the bond and the future cashflow variation at one or more future dates, say every 3 months for the next year or two. Once we have estimated rates-of-return and its variation through several time periods, we can plot risk and return vs time to better compare different bonds.
The Yield Curve
One way to measure the future cashflow and market value of a bond is to use the yield curve obtained on bond exchanges and from the US Treasury yield curve as supplemented by a credit spread curve to factor in the default risk premium. The points on the yield curve represent the current market yield for a single cashflow on any given future date. Using a market yield curve, we can then determine a forward interest rate curve which represents the current market’s estimate of the future yield curve. Using a set of forward rate curves, we can calculate the bond’s market value on any future date along with interest payments and reinvestment interest. To estimate the variability of the forward rate curve, we can use the recent short, medium and long-term interest rate volatilities and use cubic spline or regression interpolation to determine the volatility of each interest rate at any point along the forward rate curve. Using the standard deviation of recent yield curve volatility, we can determine the expected future cashflow and yield and their volatilities at each date of interest over time.
In summary, we have seen that the standard method of measuring interest risk using duration and yield-to-maturity is very limited. A more accurate approach is to use available market data and horizon analysis to construct a profile of the risk vs return of a bond throughout its life. Doing so gives a portfolio manager a more accurate way to compare bonds. This approach is extremely helpful in constructing a bond maturity ladder. Every bond can be considered a bullet bond on any cashflow date so that all bonds with similar credit worthiness can be considered as a cashflow generator on any ladder date based on its estimated future cashflow, yield and interest rate risk regardless of its maturity date.
Software Solution
DataVerse System’s BasisPoint analytical software implements the risk vs return methodology outlined above. It also provides the same analytics as Bloomberg and matches Bloomberg results. Click the link below to find out more.