# What is Bond Duration and What Does it Mean?

When looking through a fund or ETF fact sheet, depending upon the country of domicile, the features, terms, and statistics of the fund can be rather extensive, and even a bit intimidating to the new investor.  Reading through fact sheets on a regular basis will also likely involve your coming across new terms, and new performance metrics necessitating further research.

However, as is the case in most situations, sticking to fundamentals and tried and tested methods will take you the majority of the distance when making a decision. In evaluating a bond fund or ETF, in addition to the standardized credit ratings of the underlying holdings (think Moody’s and Standard and Poor’s), one of the key metrics in understanding a bond fund and how it could impact your portfolio is the fund’s average duration.

## How to Calculate Bond Duration

In simple terms, a bond’s duration is the weighted average amount of time it takes to receive the expected cash flows; and is a function of the bond yield and the term. Luckily this fact is not very difficult to remember, as the name “duration” stems from the idea that it is simply a measure of the duration of time.  The formula itself, however, is not so simple.

Whereby:

• PVi is the Present Value of the ith cash flow
• t i  is the time in years until the ith payment will be received
• V is the present value of all future cash flows

More specifically, the above use of duration with bonds is what is called Macaulay’s Duration, named after the Canadian economist Frederick Macaulay.  There is in fact another formula for duration, called the modified duration.  Although the root formula for calculating modified duration is slightly different and can yield slightly different results, for example, when measuring a bond with a fixed coupon and assuming a continuously compounded interest, both formulas will yield the same results. It too has a formula a bit intimidating for anyone other than those with a specific interest in mathematics, but it also happens to have a rather nice shortcut formula as well, which can be used if you already have the Macaulay’s Duration:

Whereby:

• yk is the yield to maturity
• k is the compounding frequency per year

## How does bond duration affect my portfolio?

When discussing duration with your advisor or when duration is referenced on a bond fund factsheet, the Modified Duration is typically what they are talking about.  This is because the modified duration is a specific calculation for the price sensitivity of your bond or bond fund to movements in interest rates.  As an investor, this is a very important metric.  A common misconception about bonds and bond ETFs is that they are risk free, or very low risk.  Although a strong case can be made that they are usually lower risk that stocks or stock funds; bonds certainly come complete with their own share of risks.  Among the primary risks involved in bond investment are credit risk and interest rate risk, the former dealing with how confident investors are with an institution’s ability to make their interest payments and repay principal.

Interest rate risk, however, can be a slightly more difficult topic to wrestle with for new investors. Credit risk primarily has to do with the country or company itself, and so naturally that would have a direct impact on the value of the company’s bonds.  Interest rate risk, however, deals primarily with changes happening in the outside world, and how that then impacts the value of the company’s outstanding bonds relative to other bonds and newly-issued bonds.

The rule of thumb to remember is that when interest rates go up, the value of bonds go down, and vise-versa. In other words, they are negatively correlated.  Of course, at first glance this seems counter-intuitive.  “If interest rates go up, is that not a good thing for bonds?  Doesn’t that mean they are paying more interest”.  Yes, that is correct for newly-issued bonds, or perhaps some sort of floating rate investment product.  However, for investment bonds, they typically have a fixed coupon rate.  So, for example, when market interest rates go up (which can be caused by a great many factors, the most famous being actions taken by central banks), newly-issued bonds will have their coupons set accordingly, and older bonds will go down in value, and vise-versa.

For example, take two companies with a similar credit risk.  Company A issued bonds 3 years ago at a 5% coupon.  Since then market interest rates have gone up, and Company B, with the exact same credit risk, issues bonds at 7%. Because the two companies are exactly the same with regard to credit risk, for their bonds to now be equal investments in the eyes of the market, the secondary market value of Company A’s old bonds would need to decrease, to make up for their less-attractive 5% coupon.  Or else, who would buy it?  Who would pay the same price for something that pays less interest?

## A bond’s duration is the measure of how heavily impacted a bond will be from changes in interest rates.

For example, a bond with a long duration will experience a much larger impact from changes in interest rates than a bond with a short duration.

## What does duration mean for my portfolio, today?

Markets have been in a period of low interest rates for nearly a decade now following the financial crisis.  Central banks are hinting at a gradual increase of lending rates, and the market is currently pricing in all such possibilities.  However, when looking at the history of interest rates, the record is quite clear, once interest rates go low they can very easily stay low for a very long time.  This was true throughout the 20th century, and has many examples looking all the way back to antiquity.  Given the possibility of both a jump upward in interest rates, and potential for the current low-interest state of affairs to continue dragging on; it would behoove the prudent investor to keep a close watch on the average duration of the fixed income portion of their portfolio.

- Bond Price Volatility and Term to Maturity: A Generalized Respecification-  Michael H. Hopewell and George G. Kaufman, The American Economic Review, Vol. 63, No. 4

- Duration and Risk Assessment for Bonds and Common Stocks - John Boquist, The Journal of Finance, Vol. 30 Issue 5

- Macaulay's Duration: An Appreciation - Roman L. Weil, The Journal of Business, Vol. 46, No. 4