Financial Markets Blog > Bond Math For Dummies

As we get older the conventional logic has been to shift assets out of higher risk stocks and into lower risk bonds. With central bank’s (the “Fed” in the US) unprecedented market intervention the boring, low risk bond market is no longer boring and is no longer low risk.
The bond market (aka debt market, credit market) is a financial market where participants can either issue new debt securities or buy and sell existing debt securities. When you purchase a bond the issuer of the bond promises to pay you a coupon payment (usually twice a year) during the term of the bond and the bond’s face value at the end of the term. For example if you purchase a $1000 corporate bond with a term of 10 years and a coupon rate of 4% the issuer of the bond promises to pay you a $20 coupon payment (1000 x 0.04 x ½ year) every six months for 10 years and the bond’s face value ($1000) at the end of ten years. If the bond does not default then you can expect to receive the following over the life of the bond…
NO DEFAULT SCENARIO #1: 20 coupon payments plus face value = 20 x $20 + $1000 = $1400
If the issuer defaults on the bond at some point during the 10 year period then you can expect to receive coupon payments over the time period prior to default and a fraction of face value at default. The average amount recovered on a bond default is approximately 40% of face value. Using our example above if the bond defaults at the end of year 5 then you can expect to receive the following over the life of the bond…
DEFAULT SECARIO #2: 10 coupon payments plus the recovery amount = 10 x $20 + $1000 x 40% = $600
The yield to maturity (YTM) is the overall interest rate you earn on the bond assuming that the bond will be held until maturity and the issuer does not default. We can view YTM as the market interest rate plus a credit spread. So for example the current yield on the 10 Year Treasury is 1.48%. Treasuries are considered to be risk-free because there is no perceived risk that the issuer will default (scenario #2 is not possible). For corporate bonds there is a possibility of default (scenario #2 is possible) so the YTM will be the 10 Year Treasury yield of 1.48% plus a credit spread. The price of our bond today is equal to our scenario #1 payments above discounted at the YTM. If the credit spread is say 1.00% then the YTM is 2.48% and the price of our bond is…
During the time that you hold the bond YTM will change due to a number of factors. If YTM increases then you will lose money (a capital loss) because the payments promised to you over the life of the bond are now discounted at a higher rate. If YTM decreases then you will make money (a capital gain) because the payments promised to you over the life of the bond are now discounted at a lower rate. Bond price moves in the opposite direction of the change in YTM in that an increase in YTM means a decrease in price and a decrease in YTM means an increase in price.
YTM can increase or decrease via Fed intervention where the Fed sets rates higher or lower than what market rates were when you purchased the bond. If the Fed increases rates then YTM increases and you lose money (a capital loss) for the reasons above. If the Fed decreases rates then YTM decreases and you make money (a capital gain) for the reasons above.
YTM can increase or decrease because market views as to the probability that the issuer will default change. The higher the credit rating assigned to a bond the lower the probability of default. Investment grade bonds are rated AAA to BBB and non-investment grade bonds (i.e. junk bonds) are bonds with ratings of BB and below. When a bond’s credit rating changes this is a signal to the market that the probability of default has changed and the bond will be priced accordingly. If the bond’s credit rating is downgraded then YTM increases and you lose money (a capital loss). If the bond’s credit rating is upgraded then YTM decreases and you make money (a capital gain).
YTM can increase or decrease based on inflation expectations. If inflation expectations increase then bond investors will demand a higher rate of return so YTM increases and bond price decreases (a capital loss). If inflation expectations decrease then bond investors will lower their return requirements so YTM will decrease and bond price will increase (a capital gain). We should always think in terms of real returns, which are actual market rates minus the rate of inflation. For example in our case the annual real rate of return on our bond given that it does not default is YTM minus the inflation rate. So if inflation is expected to be 1.50%, which is approximately what it is today, then the real rate of return on our bond is 2.48% minus 1.50% = 0.98%.
Market Observations:

Market yields are so low that after subtracting the inflation rate the real rate of return on a Treasury bond is probably zero or negative. The only way to make money in the bond market is via capital gains, which are realized if market rates decrease further.

Many bond funds use leverage (i.e. the carry trade) where the fund borrows short-term and invests long-term. This strategy magnifies gains in good times and magnifies losses in bad times.

Over the past decade or so the Fed has decreased interest rates so bond funds have done quite well due to realized capital gains (as rates decrease bond price increases). There was a lot of money to be made by front running the Fed (i.e. buying bonds at today’s rates knowing that the Fed will decrease rates tomorrow).

The historical 10 Year Treasury rate is approximately 6.00% versus today’s market rate of 1.48%. If the Fed loses control and rates rise towards their historical average then there will be large losses in the bond market. The Fed controls the short end of the yield curve and has “psychological” control over the long end (no need to worry because the Fed will always have my back). The Fed could lose control if the massive amount of money printing ends up causing inflation greater than target, the economy deteriorates and credit spreads widen, the economic damage due to low and negative rates becomes too obvious to ignore, EU bank failures lead to contagion, etc.

Many investors who are getting a near-zero or negative real rate of return in the bond market are substituting dividend paying stocks for bonds because the dividend yield is greater than the prevailing rate of interest. In the mind of the naïve investor a bond yielding 3% is the same as a stock with a dividend yield of 3%. What investors don’t realize is that this strategy entails taking a lot more risk because whereas in the bond market there may be a low probability of a loss of principal (due to default) with dividend paying stocks there is a high probability of loss via normal volatility.

Most important – The Fed may be caught in a trap where it can’t increase rates because of the massive damage caused to the bond market (and stock market) if rates rise but at the same time it knows that keeping rates at below market levels may cause massive unanticipated damage to the economy. At the end of the day the economy is the 800 pound gorilla and will eventually get its way and the central banks will most likely lose control at some point (To quote the song: I fought the law and the law won).

An investor who seeks to minimize risk (at the expense of return) may want to shorten duration (as bond term increases so does the negative effect of an increase in rates) and replace junk bonds (which will be the first to suffer credit rating downgrades if the economy deteriorates) with high quality corporate bonds.