Below is a weekly update from our Chief Investment Officer, Dr. Scott Lummer. He co-hosts an audio segment entitled “Market Matters.” In this week's show, Scott discusses his view on interest rates, and why investors with moderate and long-term time horizons should not be overly concerned with interest rate rises. He also explains how the effect of both mathematics means investors of individual bonds and bond mutual funds are protected from the impacts of interest rate increases. Each week he covers a different piece of investment news focusing on recent events in the capital markets, and relates them to Savant Investment Group’s perspective on investing.
Addendum to show Calculations:
I’m going to start with an assumption that is an approximation, but isn’t exactly true – that the percentage that the price that a bond decreases because of an increase in interest rates is equal to the percentage interest change multiplied by the maturity of the bond. That means if interest rates increase by 2%, the price of a three year bond will fall by 6% (2% x 3), the price of a five year bond will fall by 10% (2% x 5), etc.
Let’s look at what happens to the price of a relatively simple bond fund when interest rates change. The fund has five $100,000 bonds, maturing in one year, three years, five years, seven years, and nine years. Let’s suppose interest rates are currently 3%. If you are holding the bond fund for five years, and the manager of the fund invests in new bonds when the old bonds mature (at an interest rate of 3%), over the next five years you will get $15,000 (3% x $500,000) of interest each year plus the $500,000 principal back in five years. Now, let’s assume interest rates increase by 2%, to 5%, next month. The new price of the fund, using my assumption, will be:
The value of the fund fell by $50,000, or 10%, which also is the amount of the interest rate change multiplied by the average maturity of the fund of five years – that’s why in analyzing bond funds, we are always concerned with average maturity.
Now let’s look at what happens in five years. The bond manager was able to hold the one-year, three-year, and five-year bonds to maturity and get the face value of $100,000 each. The manager took those proceeds and reinvested them in $100,000 bonds, now earning 5%. The original seven-year and nine-year bonds will have two years and four years remaining on them, and, assuming interest rates stay at the new level of 5%, we can use the assumption to calculate their value.
So it looks like you would lose $12,000 on the bond fund. But, we need to account for the fact that the one-year bonds and three-year bonds matured, and were re-invested at the higher interest rate – higher by 2%. For the one-year bond, you received an extra $2,000 in interest a year for four years, or $8,000. For the three-year bond, you received an extra $2,000 in interest each year for two years, or $4,000. The extra interest you receive of $12,000 exactly offsets the capital loss on the bonds.
As I said, the assumption of the price change was an approximation. In actuality, the price change on a bond is equal to the interest rate change multiplied by the “modified duration” of a bond, instead of its maturity. The modified duration is a somewhat complicated mathematical calculation that is related to the maturity, but adjusts for the fact that an investor receives interest payments before the maturity date, and takes those payments into account in calculating the true average maturity of a bond – for example, a five year bond actually has a modified duration of about 4 ½ years. So the example I used works for a bond fund with a modified duration of five years instead of an average maturity of five years.
Daphne: Welcome to Market Matters, a weekly discussion about investing in today’s capital markets. I’m Daphne Feng and, as always, I’m joined by the Chief Investment Officer of Savant Investment Group, Dr. Scott Lummer. Scott, several of our clients have asked if interest rates are expected to rise over the next couple of years, why should they invest in bonds?
Scott: That’s a great question – many investors have the same concern.
Daphne: First of all, do you believe interest rates will rise in the future?
Scott: Absolutely. Interest rates, at least those on Treasury bonds, will almost certainly rise over the next couple of years. They have been held to artificially low levels by the Federal Reserve bond buying program to stimulate the economy. But the Fed has been tapering that program, and the Fed’s own forecast is that rates will be rising over the next two years. The only questions are how much rates will rise and how fast the rise will occur.
Daphne: And of course, that increase in interest rates will cause the prices of Treasury bonds to fall.
Scott: That’s correct. Although it’s your job to ask the questions, and my job to appear to be smart in answering them.
Daphne: That leads me to the main question. If you believe rates will rise, and that increase will hurt bond prices, why should investors continue to invest in bonds?
Scott: I understand the concern. But we have to understand how bond pricing works. When a bond price rises or falls because of interest rate movements, that change is only temporary. As long as the bond doesn’t default, the investor gets paid back in full regardless of what happens to interest rates. So, if you need $500,000 in five years, and you invest solely in five-year bonds, you will get your $500,000 principal back even if interest rates rise, or fall, in the interim.
Daphne: What if you need the money later than that, suppose in seven years?
Scott: Then you actually should be hoping that interest rates rise. Yes, the rise will cause the prices of bonds to fall initially. But then you will get your $500,000 in five years, and you’ll be able to invest that money for another two years at a higher rate of interest. So it’s a bonus.
Daphne: And what if rates increase and you need the money in three years?
Scott: Then you would lose money on your investment. Which is why, if you need much of your investment over the next few years, you should not invest in five year bonds – you should choose shorter-term bonds.
Daphne: O.K. That explains what happens with buying individual bonds. But most of our clients invest in bond mutual funds. Won’t that have a different effect?
Scott: The math is a little more complicated, but the net result is the same. Let’s create a simple bond fund, comprised of five $100,000 bonds – maturing in one year, three years, five years, seven years, and nine years. That means it has an average maturity of five years. If interest rates rise, and you need the money in five years, you will break even on the bond fund in five years
Daphne: I can understand breaking even on the three bonds that mature in the first five years, but won’t the interest rate increase cause the seven-year and nine-year bonds to be sold at a loss in five years?
Scott: Yes. But you’re forgetting one thing. The bonds that matured in one year and three years can now be re-invested at a higher interest rate than before. That extra amount of interest exactly offsets the loss on the two longer term bonds. That’s why the concept of “average maturity” is important.
Daphne: How do you know that offset is exact?
Scott: You can trust me. But also, I posted on our blog, at www.savantig.com, the calculations and assumptions for the example.
Daphne: And what about if the investor needs the money in seven years … or in three years?
Scott: The situation is the same as with the single bond example. If the money in needed in seven years and interest rates increase, the investor is ahead. If the money is needed in three years, the investor is behind. Again, investors with short-term needs should invest in shorter term bonds.
Daphne: That’s Market Matters for this week. Thanks to all of you for listening. Please join us next week Scott and I will talk about investing in the smart phone age.