Geeky Bond Math Made (somewhat) Simple.

In the universe of capital market investments, it seems there’s no area more confounding than the ‘debt markets’.  Clients and advisors alike project a look of semi-understanding when bonds and all of their quirky dynamics come into the equation.

Bonds are easy, as long as we remember one thing:  they’re debt.  We’re pretty comfortable with debt as a society – we use it to purchase big-ticket items, like homes, cars and education.   In these cases, we’re the borrower, with banks usually serving as lenders.  But just as frequently, we ‘flip the script’, don’t we?  When we put money into a bank account, WE are the lender and the bank is the borrower (that’s why they pay us interest).

So, when companies need to borrow to raise capital for growth, or when states and towns need to raise money to build roads, schools, hospitals and stadiums, we lend them money by purchasing bonds.  Just like when we borrow money, there are a number of different payback arrangements that can be agreed upon.  And, the higher the credit rating of the borrower, generally the lower the interest costs.

Up to that point, things are very basic.  The part that confuses people arises when we, as bondholders (creditors) entertain the thought of transferring the debt to another creditor.

Let’s say, for example, I purchased a 30-year US Treasury Bond (so, I’m lending money to the US government… looks a lot like a mortgage).  The agreement is that interest payments (called ‘Coupon’) will be 4% per year.  Unlike most mortgages, this will be interest-only for the life of the loan, and at the end of the 30 years (called the Maturity Date), the whole amount is due to me.   What if, 10 years later, interest rates increase?  Is that a good thing or a bad thing?  Answer:  BOTH

• It’s a good thing, because when I receive the interest payments, I can invest them at a higher rate of return, so I’m making more money in the long run.
• It’s a bad thing, because if I want to sell the bond to someone else, they won’t want to pay me full value for it – because they can buy a new bond at a higher rate of interest, instead of mine. I’d have to discount the price (the Market Price) in order to convince them to buy the bond.  The buyer of my bond would continue to receive the regular coupon payments, same as I did, and would receive the face value (or Par Value) at the maturity date, like I would have.  But, since she paid me less than par value for the bond, she’ll make money not just through the coupon payments, but also from the price appreciation since she paid less than par value.  The combination of these two factors (interest and price appreciation – or depreciation) is called the bond’s yield.

In the previous example, what if I needed to set money aside for something and I needed that 4% yield to reach my goal?

There are two ways to get there:

• Obviously, I can buy a bond that matures at my ‘goal date’. But, that’s imperfect, because I may or may not get the same rate of return (yield to maturity) when I reinvest the interest payments along the way.
• I might not have to wait until maturity – since the “good” and “bad” impact of a rate change partially offset each other. There is a ‘magic number’ of years it will take for this to happen and that number of years is called a bond’s Duration.

Bond Duration is technically the dollar-weighted average of time to receive cash flow on a bond.  Bonds with substantial interest payments have durations that are shorter than the time to their maturity dates because we get some of the investment back before maturity through coupon payments.  We don’t really need to worry too much about how duration is calculated, but it helps to know two things about duration:

1. It’s the ‘sweet spot’ where we can reasonably predict the number of years holding a bond and investing the interest proceeds to get the yield we’re aiming for, and
2. Duration is also a pretty reliable indicator of the market price movement of a bond in response to interest rate changes. In our previous example, let’s say the going rate on 30-year bonds went up from 4% coupon rate to 6% coupon rate.  That’s a 2% rate increase and we know that the impact of the rate increase is that the market value of my bond went down.  If the duration of my 4% bond was, say, 12 years, I’d multiply that 12 by the rate change (2%) and expect that the change in my bond’s value would be 12 * 2% = 24% loss in value because of this increase in rates (and it would be a similar gain in value if there had been a decrease in rates).

You can see why bond duration is much more valuable to us (and to folks like pension managers) than bond maturity in planning for obligations down the road.

And, with this investment of 10 minutes of your time, you’re now conversant in the following, formerly complicated, bond terms:  Par Value, Market Value, Coupon, Yield, Maturity and Duration.  Congratulations, you newly-minted bond geek!