Fundamentals of Bond Math

To truly understand bonds, you need to have an understanding of a few key metrics that will help you analyze a bond price more accurately. These analytics will be at the base of your analysis.

Cash Flows

Bonds generate cash flows from three key sources: coupon payments which can be paid anywhere from monthly to yearly, bond price appreciation or depreciation, and coupon re-investment, or interest on interest.

Simple Interest

Let’s start with the basics; simple interest is your coupon payment. For example, assume you have $100,000 invested in 10 year bonds at 6% yearly, paying you semi-annual coupon payments. In this scenario, assuming you hold the bond till its maturity date. you will receive 2 coupon payments of $3,000 each, for a grand total of 20 coupon payments for $60,000.

Coupon Calculation. Investment Amount * Yearly Interest Rate / # of Coupon Periods per year = $100,000 * 6% ( or .06) / 2 = $3,000

Based on this calculation, you can easily see that monthly coupon payments for 10 years would net you a $60,000 in interest income. $3,000 * 2 coupon payments/year * 10 years

Interest on Interest — Compounding

Now assume that you did not need to take the coupon payments out to pay bills off with them and that you could actually re-invest the coupon payment back into the bond thereby increasing your bond amount by the coupon each time it is paid. In this case, you will be earning interest on interest, thereby, increasing your interest income semi-annually. Here is an example that should illustrate this point:

Original Investment Amount: $100,000

First Coupon Payment: $3,000

Second Coupon Payment: $3,090 ( ($100,000 + $3,000) * 6% / 2)

Interest received on second coupon payment: $90

Year 1 Balance: $10,690

Your simple interest cash flows totaled $6,000 while your interest on interest totaled $90. While this number seems relatively small, the power of compounding takes time and after year 10, your aggregate interest income would yield, $180,611.12, or $60,000 in simple interest and an additional $20,611.12 in compounded interest. The longer the term of the bond, the more exponential your interest on interest becomes. In fact, it the term of this bond was, say 20 years, an investor would actually earn more interest on interest than the actual coupon payment in the middle of year 13. As you can see, compounding interest is the greatest thing since sliced bread.

Yield

When you are purchasing a bond, you will be quoted by your broker in terms of yield. There are three key yield measures which give you insight into the potential cash flows of the bond. We will now discuss, coupon yield, current yield , and yield to maturity .

Coupon Yield

Coupon yield refers to the interest rate paid by the bond. This interest rate is calculated as a percentage of the par value or the initial investment amount. For fixed rate bonds, this amount will never change. As we showed you in the simple interest calculation above, the coupon payment remains the same over the life of the bond.

Current Yield

Current yield gives you a snapshot of the relationship between the current price of the bond and the current coupon payment. Remember, from our bond introduction, once a bond is purchased, it immediately becomes part of the secondary market where prices can fluctuate daily. The current yield helps you understand the current situation of the bond but does not take into account two key components of cash flows earned; interest on interest as we just discussed above, and bond price fluctuations .

Yield to Maturity (YTM)

YTM is the most powerful yield measurement, as it aggregates all cash flows into one number providing you with an internal rate of return (IRR) which includes: coupon interest, interest on interest, and the difference between purchase price and redemption price. The formula to calculate the yield to maturity is far to complex to discuss here; however, a financial calculator will allow you to do the trick. What you need to know about yield to maturity is that it allows you to fully understand what your true rate of return will be after taking into account all your cash flows. Additionally, it allows you to compare bonds of differing terms, such as a 10 year bond paying 5% and a 30 year bond paying 6%.

Total Return

Most investors buy long term bonds and use the YTM as a measurement of expected return. While the YTM is a great yield analysis tool, it bases its calculation on the premise that the bond holder will not sell their bonds before maturity. Let’s face it, most of you will not be holding the bond till maturity and therefore will expose yourself to the risk of bond price appreciation and depreciation. Total Return takes interest income and investment gains/losses into account when determining the true return of the bond.

With the new accounting standards in the financial industry, large banks and other financial institutions must now manage their portfolio more closely to understand their risk to different types of shocks. The total return analysis is done daily by financial firms and this is known as marking-to-market . By marking their securities to market, bond traders are forced to take more accountability for their actions, not to mention that it is the cleanest form of analysis.

In a nutshell, total return allows you to do a thorough analysis on your potential returns by taking into account all the factors that can affect your returns; such as, commissions, dividends. simple interest, interest on interest, and change in investment bond prices.