Tower Private Advisors
- Markets recap
- Bond math
Capital Markets Recap
On this pre-holiday weekend Friday you’re getting an abbreviated Weekly Recap & Outlook. And I wanted to focus on just one thing today, bond math, or the mathematics behind why bond prices change.
The August 26, 2013, issue of industry-rag Investment News featured a story with this headline: “Rising rates hurt bonds? That’s news to investors.” I’m not sure where Edward Jones found these people to survey, but I think that more than half of the 17 readers of this blog would know that rising rates do, indeed, hurt bond prices. In fact, the survey found that two-thirds of the respondents didn’t understand how rates would affect their bond holdings, and “24% of those surveyed admitted they ‘feel completely in the dark about the potential effects.’ ”
So, here are the gory mathematical details why rising interest rates hurt bond prices.
Let’s say an investor bought a seven-year bond that paid a 5% annual rate of interest; we call this the coupon. The then-current interest rate on similar seven-year bonds was 5%, so our investor was willing to pay face value for the bond. Had interest rates been lower than 5%, she would have paid more; higher, and she would have paid less. The coupon and the yield–really, the price-adjusted coupon–were both 5%.
Here’s our bond math after two years. Our now-five-year bond will produce ten cash flows; 1-9 will be semi-annual interest payments of $2,500, while the 10th will be the par/face value of $100,000 plus one last interest payment. To determine the price of the bond, each cash flow is discounted–adjusted to account for the time value of money–back to the present, using the formula immediately below.
Note that the sum of the discounted cash flows equals 100,000, which is equal to the face value of the bond. If we divide the former by the latter, we get the bond price, which is $100 or 100% of face value.
Now, let’s assume that the next day, the Fed Chairman says something about his cat having a urinary tract infection. Bond markets around the world panic because they fear what the Chairman might do in his feline quandry. Interest rates on five-year bonds jump to 7%.
Here’s the new math, which is different than the new math my parents complained about 30 years ago. Bond math has never changed.
Why did the price of our bond fall? The general reason is that new bonds could be had that 7%, so our bond has to fall because it’s worth less. Exactly how much less is a function of how much the present value of the cash flows declines. Each cash flow is worth less in present dollars, and in to to, the cash flows are worth $8,416.61 less, so our bond’s price falls by (-)8.32%.
Have a great holiday weekend.
Graig P. Stettner, CFA, CMT
Chief Investment Officer
Tower Private Advisors
Tags: interest rates