Bonds

Companies as well as governments very often need to borrow money in order to finance their growth. This could be done by taking out a loan from a specific lender, issuing equity (companies only), and issuing debt. Fixed income securities are created with the issuance of debt. Fixed income securities can be structured in various forms such as discount bonds like treasury bills. Other types of fixed income structures include:- amortizing bonds, convertible bonds and floating rate notes. In this article we will concentrate on regular bullet bonds and their various derivatives.

The descriptive part of a regular bond consists of the:
Coupon:- This is the payment the issuer makes to the holder of the bond. It is expressed as a percentage of the face value of the bond.
Payment:
Frequency: - This is the number of times per year the coupon is paid. For example a semi-annual paying coupon pays twice a year.
Interest:-Accrual Date:- This is the date the bond is issued to the market
Maturity:- This is the date the bond expires and the notional amount is returned to the holder of the bond.
Other important variables include, day count type, notional amount outstanding as well as security identification number, but we will not concentrate on these concepts in this introductory article.

Once a bond arrives at the secondary market it very often trades away from its par value of 100%. For example a one unit increment of a bond is sold for 1000 dollars, otherwise known as par. This price will often be different once it trades. If it trades at less than par, it is said to be trading at a discount and if it is priced at higher than par it is sold at a premium. A very important metric in fixed income is known as yield. This is the rate of return of the bond. The simplest method of calculating the crude yield of a bond is by dividing the coupon of the bond by the traded price. This means that the higher the price of the bond, the lower the resulting yields. Yield is however calculated in a much more sophisticated method known as yield to maturity. The yield to maturity is a variable which is solved after knowing what the inputs for price, maturity, coupon and payment frequency are. The market price of a bond is given by

Market Price=

We know the price of the bond, which is determined by the market, we know the maturity and coupon as well as the payment frequency, given on the description of the bond. Given the known we can imply the unknown yield to maturity (YTM) of the bond by working backwards. Simply put, the price of a bond varies inversely with yield. As the price of the bond rises the coupon becomes a smaller proportion of the bond price and therefore by the above formula the yield will drop as well. In terms of relating this to the interest rate market. If I am a holder of a 5% 5 year treasury bond, if the FED decides to raise rates to 5.25% then my bond will drop in price so that the yield will match the current equilibrium rate of interest rate, adjusted for risk (will discuss later). Below is the price-yield relationship of a bond.

The above chart represents the relationship between the price of a bond to its yield. As the yield rises the price goes down and vice versa. This chart however represents a single bond with a single maturity. What is even more important to fixed income practitioners is the yield curve. This like the above chart has yield on the Y axis but instead of price has maturity or term structure on the X axis. The chart simply represents how the yield varies with maturity. Conventionally as the maturity increases the yield or the expected return increases as investors in long term bonds are faced with greater risk.

Below you can see the current US on the run/off the run yield curve. As the chart below demonstrates the US does not currently have the conventional upward sloping yield curve. This is due to the economy having a high rate of inflation as well as the future expecting a slowdown in the economy, especially the housing market. The explanation as to why this would cause the below shape of the yield curve is beyond the scope of this article and will be discussed at a later stage.

Bond Risks

Bonds have two main types of risks 1. Interest rate risk and 2. Credit Risk. Other types of risks exist amongst more exotic bond structures like prepayment risks but these concepts are beyond the scope of plain bullet bonds. As described above there is an inverse relationship between price and yield, but the relationship needs to be defined more accurately. A common risk metric is duration. This is the sensitivity of the bond price to changes in yield. In its simplest form the risk varies as one moves along the price to yield chart. To calculate the risk or one picks a point on the curve and draws a tangent to it. The slope of the tangent is the duration. Logically therefore at very low yields the yield changes very little relative to price changes in the bond. At very high yield the duration increases. The longer the maturity of the bond the higher the duration. To understand this one has to think about opportunity costs. If I were to invest 100 dollars at a 3% rate of interest for 1 year I would get 3 dollars at the end of the year. If rates rise to 5% after that 1 year I can reinvest my 103 dollars at 5% and receive 5.15 USD of interest. If my previous 3% interest investment was actually for a 5 year bond, I would only get a 3.09 dollar interest and I would be tied in to this lower interest for the next 3 years after that. Point being that the longer the maturity of the bond the higher the risk because an adverse effect on interest rates would mean that the investor is tied up with this rate for a longer time and thereby potentially loose out on a higher yielding investment. The reverse is also true if interest rates drop. The long term bond holder would be protected from a low yield for a longer time and as a result the price of his bond would increase at a greater amount than a high yielding bond with a shorter maturity. Another known sensitivity gauge is known as convexity. This is the rate at which duration varies with price. This is simply the slope of a point of the duration versus price chart. In mathematical terms it is the second derivative of yield with respect to price.

A second type of common risk is known as credit risk. Credit risk will not really be prevalent in government bonds of developed economies like the treasury bonds but they would be in more economically risky economies like. They are even more commonly considered in corporate bonds. The more risky a company the greater the rate of return expected by the investor to compensate for the risk. An investment bank originating a corporate bond for a company will need to price the coupon to take into account the perceived credit risk of default by the company as well as the interest rate environment.

The bond has a credit rating of B1 by Moody’s and B by S&P. The coupon value was set in according to this credit rating. The bond was actually issued in 1999 when interest rates were much lower. A 5.8% coupon is relatively high compared to a risk free treasury with the same maturity and issue date.  To calculate the yield of a bond to changes in price Bloomberg has a yield analysis screen which allows one to override yield and price to recalculate corresponding values. It also allows one to determine the duration, and convexity of a bond.