Thursday, June 19, 2014

Fixed Income, Part I: Relationship Between Interest Rates & Bond Prices

With interest rates at historic lows, and the Fed saying they will keep short rates low for an “extended time,” there is much confusion among financial pundits as to where interest rates and bond prices are headed in the coming years. With so much disagreement among the experts, many of our clients have asked that we provide an in-depth discussion of our views on inflation and interest rates, and the path these rates may follow in the coming years.

Although we regularly answer these questions in our client meetings, using our blog allows us to quickly explain our current views and strategies to a larger audience.

This particular series of blogs focuses primarily on the bond market; beginning with the basics before tackling the more complicated issues.

The format is Q&A. The first installment is a brief analysis of the fundamentals of bond investing, which we hope will build a solid foundation of understanding as we move forward. Nathan Winklepleck, co-editor of the blog, has assembled a list of our most frequently asked questions. He will serve as the moderator for the Q and A and will ask Joe Zabratanski our Senior Fixed Income Manager and Greg Donaldson our Chief Investment Officer to provide answers and commentary.

Q: Nathan: We have received several questions from clients about the impact of changing rates on bond prices.  Could you explain the relationship between interest rate fluctuations and fixed income prices?  How and why does one influence the other? 

A: Joe: The relationship between interest rates and fixed income prices is like a teeter totter.  On one side you have the bond’s price and on the other you have the bond’s yield.  One cannot go up without the other going down.  In a manner of speaking, they are “hardwired.”  

The reason they move in opposite directions has to do with a bond’s “fixed” qualities.  Most bonds have a fixed interest rate and a fixed maturity date.  Thus, when interest rates go up or down, it causes a fairly predictable change in bond prices to achieve a new equilibrium level.  Thus, it is changes in interest rates that drive bond prices, not the other way around, as so many people believe.

For example, if you were to buy a 30-year U.S. Treasury bond with a “par value” of $1,000 and an interest rate of 3.5%, you would pay $1,000 today and receive $35 per year for the next 30 years and then get your original principal back. If you are planning to hold the bond to maturity, you know on the purchase date what rate of return you will earn for the next 30 years. The question we get asked most often is:”What happens to the value of my bond if interest rates change?”  At first glance, this follows a simple formula.  
Fast-forward 3 years; let’s say interest rates on 30-year U.S. Treasury bonds have risen from 3.5% to 4.5%.  To find the price of a bond with a fixed interest rate of 3.5% in a market where new bonds are yielding 4.5%, we return to the formula and solve for the unknown price, represented by the variable X. We can do this because the other two parts of the formula are known. 
Investors are now requiring a 4.5% yield on long bonds, and we know our bond is paying $35 per year. To solve for the unknown price (X), we know from high school algebra to multiply both sides of the equation by X.  This creates a new formula:
Re-arranged, the formula becomes:

In summary, today’s 30-year bonds are yielding about 3.5%.  If interest rates were to rise by one percent over the next three years, the formula above shows that the bond’s price would fall to about $780, or nearly 22%.

Nathan: Wow, that’s quite a hit for a rather small increase in rates. I’m guessing that is the reason so many people are so confused about what to do with bonds?

Joe: Bonds are now at historically low yields, and thus, are very sensitive to changes in interest rates. But let’s remember, if we hold a bond to maturity, we will receive the full $1,000 par value, so in some way the example I just gave you is not as bad as it may seem at first glance.  The price loss the bond experiences in a rising interest rate environment is only a loss on paper, unless you were to sell it.  

Nathan: What if I said I’m going to sell the 3.5% bond and buy the 4.5% bond.  That way I can receive the new higher yield without the big paper loss on the first bond I bought?

Joe: There is nothing to be gained by doing this because; the market is very efficient in these repricings.  They happen very fast.

Nathan: In the example you provided, the bond’s maturity was 30 years in the future.  Would a bond with a shorter maturity be less volatile?

Joe: Yes, but it would also come with a heavy cost.  Today, 10-year Treasury bonds yield only about 2.5% and five year T-bonds are yielding a paltry 1.75%.

Nathan:  These low yields are just remarkable.  In the past, what have been the long-term averages yields of bonds with these maturity ranges?

Joe: 30-year T-bonds have averaged over 6%, 10-year and 5-year T-bonds have averaged 5% and 4%, respectively.

Nathan: It seems that returning to the long-term average yields would be very destructive to bond values, even if we held every bond to maturity.

Joe: Nathan, I’m going to save the strategy we are currently using in this environment for future blog discussions. Instead, let me share with you some of the general ways of diminishing risk in the fixed income market.  Earlier you asked if a bond’s volatility changed with its length of maturity.  That was a very good question, and I want to amplify my answer.
Bonds have two main risks.  The first risk is that the issuer of the bond will “default” on the loan, which means that he will be unable to make his interest payments or pay you back when your bond reaches maturity.  The second risk is that an increase in interest rates, usually driven by rising inflation concerns, will make your bond worth less than what you paid for it.

With a bond or other fixed income security, interest rate risk is measured by a term known as “duration”.  The higher the duration, the more interest rate sensitive a fixed income security will be. Using the teeter totter example, you can think of duration as the length of the bond price’s side.  

The two teeter totters above illustrate the impact duration can have on bond price volatility.  The longer the teeter totter on the duration side, the bigger of a swing bond prices will have.  Given the same increase or decrease in interest rates, a fixed income security with a longer duration will experience much greater price volatility.

The farther away a bond’s maturity, the longer its duration will be. That is why the interest rate on a 30-year U.S. Treasury is generally higher than the rate on a 10-year U.S. Treasury. Fixed income investors refer to this as the “yield curve”, which is shown below.

As you can see by the chart, the U.S. Treasury with the shortest maturity (1 month) is yielding near 0% while the Treasury with the longest maturity (30 years) is right at 3.5%. The increasing yield curve makes sense, as it indicates that investors are currently requiring more compensation for accepting a higher level of price and interest rate volatility.

Nathan: What kinds of factors go into calculating duration?

Joe: There is a subtle difference from the meaning of duration as it relates to analyzing bonds and its meaning in common mathematical use.  In the bond world, duration is actually a precise formula that tells us how volatile a bond is.  Importantly, this calculation takes into consideration the length of maturity of the bond, as well as the interest rate of the bond.

Let me give you an example.  When using a bond calculator to determine the actual volatility of the three bonds I mentioned earlier, we find that the precise level of volatility for a one percent change in yield for the 30 year bond is 19.8%, 8.8% for the 10-year bond, and 4.8% for the 5-year bond.  You can see that volatility falls dramatically as the length of maturity falls.  We still have to deal with the very low rates in shorter maturities, but that can be done with higher yielding securities in asset classes other than U.S. Treasuries.

Nathan: So you are saying that by using securities other than U.S. Treasury bonds, we can produce respectable returns with a more muted volatility?  If that is the case, then the fulcrum, or midpoint, of our teeter totter would shift its position along the board depending upon the interest rate and the length of maturity of the security in question?

Joe: That is correct.  In addition, almost all fixed income securities have a call provision that allows the issuer to pay off the bonds earlier than their maturity date.  In addition to these calls, there are mandatory sinking funds that can change the price risk of a longer bond.

I certainly do not want to say there is anything easy about investing in this bond market, but there is wiggle room here and there that we have found to provide our clients with reasonably attractive current yields and less volatility than long Treasury bonds.  

Next time we will discuss the relationship between inflation and interest rates.  Please contact us if you have any questions.