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Some investors might initially believe that they will hold their bonds to maturity, but unforeseen circumstances may develop. Even more likely, an investor may want to either sell their existing low yield investment to obtain a higher yield or to change their asset allocation to increase their equity exposure. A risk adverse conservative investor might be surprised to incur a significant loss on the sale of their “safe” investment. Current interest rates are at historically low levels and the realistic expectation is that they cannot go any lower and may increase in the near future. Hence, fixed income investments are not necessarily as safe and less volatile as they had been in the past. Bond funds also present a different challenge for investors than holding individual bonds. Individual bond investors can hold their bonds and receive the par amount at maturity assuming the bonds do not default. However, bond funds are typically structured as short-term, intermediate term (typically 5-7 year maturity) and long-term (typically ten or more years’ maturity). The bond funds’ managers will routinely purchase new bonds as existing ones mature in order to maintain the target average maturity so most bond funds never mature.


The Financial Industry Regulatory Authority (FINRA) was established in 2007 by Congress to protect investors. FINRA has cautioned investors who own bonds or bond funds that the one number an investor should know is duration. On February 14, 2013 FINRA issued a new investor alert called “Duration: What an Interest Rate Hike Could Do To Your Bond Portfolio” which warned investors that duration could cause GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 175 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 their bond or bond portfolios to decline in value if interest rates were to rise. Thomas S.Y. Ho (1992) states in his paper entitled Key Rate Duration: Measures of Interest Rate Risks, that “identifying interest rate exposure is central to active and structured portfolio management.” Key rate duration is defined as “holding all other maturities constant, this measures the sensitivity or the value of a portfolio to a 1% change in yield for a given maturity.” Investopedia. T. Ho further states (2013) that “key rate duration gives us a measure to enable us to manage our yield curve risk”. F. R. Macaulay (1938) first defined the definition of duration basically as the “essence of the time element of a loan”. Cox, Ingersoll and Ross (1979) examines in their paper, Duration and Measurement of Basis Risk, the traditional measurement of duration and the conditions under which it is valid to use in risk comparisons. Their findings were that the Macaulay method of interest calculation was a pure bond discounting and too theoretical. Hence their findings supported a modified or effective duration calculation.

How Can an Investor Determine Their Interest Rate Risk?

The most widely accepted measure of interest rate risk for the average investor is something called duration, which is a measure of the sensitivity of bond prices to changes in interest rates. Duration is a number that at a particular point in time will tell an investor approximately what percentage a non-callable bond will change in value given a 1 percent change in interest rates. With a known bond or bond fund’s duration, an investor can estimate, all else being equal, how the investment will react to a change in interest rates and make an informed decision based on his expectation of future interest rates. The time to maturity for a given bond may provide a general sense of its interest rate sensitivity, but duration is a much more accurate measure. An example is Vanguard’s Intermediate Term Treasury Bond Fund (VBILX), which has an “effective maturity” of 7.2 years but an “average duration” of 6.5 years. Generally the higher the duration number of a bond, the more sensitive the bond is to interest rate changes. Investors who are expecting higher interest rates might wish to invest in bonds with shorter durations or maturities to limit their potential losses.

How is Duration Calculated?

Duration is the number of years it would take an investor to recoup the full cost of their bond or bond fund considering the present value of all interest and principal payments to be received. Hence, a bond’s cash flow payments for both interest and principal are discounted at current market interest rates divided by the current market value of the bond. In general, the greater the duration of the bond, the more sensitive that bond will be to interest rate changes. It should be noted though that duration is generally accurate for small changes in interest rates. Utilization of duration for large interest rate changes requires taking into account a concept known as convexity which measures the change in duration as interest rate changes become more significant. The market value of a bond will generally decline less for larger interest rate increases.

Convexity depending on the characteristics of the bond or bond fund can be both negative and positive, which means that the duration can actually decrease or increase based on the degree of interest rate change.

Thus the correlation between a change in interest rates and their effect on bond prices is not necessarily symmetric. This paper will not address convexity however; but investors should be aware that it may impact their investment decisions if there are large changes in interest rates.

An example of how duration can be applied: Assume an investor puts $10,000 into a bond fund which has an average duration of 5. Generally, a 2 percent across the board increase in interest rates will result in approximately a 10 percent (5 duration x 2%) or a $1,000 decline in the fund’s value to $9,000, all else being equal. However, if that same $10,000 had been invested in a fund with duration of 10 with this same 2 percent interest rate increase, the investment would have decreased 20 percent (10 duration x 2%) or $2,000 and now be worth $8,000. Conversely, a 2% decrease in interest rates could result in the fund increasing in value by 20%.

GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 176 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 Figure 1: Illustration of How a 2% Increase in Interest Rates Reduces a $10,000 Bond's Value Based on its Duration

–  –  –

$12,000 $9,600 $10,000 $9,000 $8,000 $8,000 $6,000 $6,000 $4,000 $2,000

–  –  –

Figure 1 illustrates the theoretical impact of a two (2%) interest rate increase for bonds with different durations. An example of a bond fund with a high duration is the Schroder Long Duration Investment Grade Bond Fund (STWLX) which has a duration of 14.79 as of September 2015.

How Does Duration Impact Investment Decisions: The level of interest rate risk that an investor may take is a function of their overall risk tolerance, time horizon and their expectation of future interest rate changes.

The key is that knowing the duration of a fixed income investment allows the investor to quantify their interest rate risk and make an informed decision. An example of such an evaluation process was expressed by the brokerage firm, Charles Schwab, on their website in September 2015. Their advice to clients who might be tempted to purchase longer-term bonds for a slightly higher yield was that the increased duration may not be worth the risk.

“We see limited value and higher risks in long-term funds today compared to intermediate-term funds. The benefits of a slightly higher rate aren’t well-balanced with the increased interest-rate risk, in our view, for funds with average maturities much greater than 10 years. An exception might be if you’re focused on income and income alone and won't need to sell, or if you believe that interest rates will fall. While we believe rates could stay lower longer than many investors expect, they will rise eventually. Also, pay attention to the fund's duration. Duration is a measure of interest rate sensitivity, but it can also be thought of as a measure of how long it takes to recover your initial investment. Funds with shorter durations will typically be less sensitive to increases in interest rates and you’ll generally recover your initial investment sooner if interest rates rise as compared to funds with longer durations. However, funds with shorter durations typically have lower yields.” C Schwab 2015.

Where does an investor find duration information? The duration for an individual bond may be obtained by contacting the bond issuer, a broker or by using an online bond duration calculator, which can compute a specific bond’s duration. With regard to bond funds (versus individual bonds), most fund issuers provide “fund facts” on their websites, which disclose their average duration as well as other information including yield, expense ratio and average maturity. Another excellent source of information on the duration of many GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 177 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 bond funds can be found at finance.yahoo. By inputting the fund’s ticker symbol and then selecting “holdings”, the duration, average maturity and credit quality are disclosed and can be compared to the relevant category averages.

Several Methods Are Utilized to Calculate Duration The Macaulay duration calculation is a commonly used method. It measures a bond’s sensitivity to interest rate changes by calculating the weighted average number of years the investor must hold a bond until the present value of the bond’s cash flows equals the amount paid for the bond. It is a pure discounting of the present value of a bond’s cash flows so tends to theoretical. (Cox et al). Modified duration is a modified Macaulay computation that directly measures price sensitivity. Effective duration, on the other hand, is often the calculation cited for bonds that may have special redemption features. Unlike Macaulay duration, effective duration takes into account the potential changes in cash flows which can occur from redemptions.

Redemptions can occur from prepayments and the exercise of call and put options. Understanding the formula calculation is not as important though as understanding that duration is a measure of risk in relation to interest rate fluctuations. However some bond funds, such as Blackrock, have their own proprietary method for calculating duration and in those instances financial websites may not show duration for those funds and direct you to the fund’s actual web site.

There are also some special circumstances that could affect duration. Duration assumes that for every movement in interest rates, there is an equal change in bond prices in the opposite direction. However, this is not always the case. For example, when interest rates drop, a residential mortgage-backed security (a bond backed by home loans) might not see an equal increase in the bond’s price because it might prompt homeowners to refinance their mortgages. This in turn may limit increases in the bond’s price as the underlying mortgages are being refinanced at lower interest rates.

Changes in the Slope of the Yield Curve

The yield curve refers to the graphical representation of interest rates over a specified time period. Generally interest rates increase as the time to maturity increases. However, there have been rare times when the yield curve has been “inverted”, meaning that shorter-term rates were higher than long-term rates. More importantly, the application of duration assumes that a given 1% change in interest rates occurs uniformly across the yield curve. The reality is that interest rate changes may not be the same for all maturities.

Consequently, the change in value of a bond or a bond fund is directly affected by its position on the yield curve and where interest rates are changing on that curve. Figure 2 illustrates both the 2008 and 2014 yield curves. One can see that interest rates may not stay at their current historically low levels and might revert to a more normal level in future years. Figure 2 also shows that actual shifts in the yield curve are not usually perfectly parallel when interest rates rise across the board. (Investopedia).

A Bond Fund’s Name is Not Always an Accurate Gauge of its Duration Level

It is not always possible to judge a bond fund by its name. U.S. News and World Report regularly publish a listing of “Best Mutual Funds” which includes a list of “Intermediate-Term Bond” funds. U.S. News does appropriately note that their list of intermediate-term bond funds have durations from 3.5 to 6 years, which represents a significant range of interest rate sensitivity. Investors cannot just rely on the name of bond funds to accurately judge their interest rate risk. A case in point are two well respected funds on this intermediate-term bond fund listing that have very different durations as of October 2015. The Loomis Sayles Intermediate Duration Bond Fund (LSDIX) has a duration of 3.87 which is below the category average of 4.93 for Intermediate-term bond funds and therefore is less sensitive to interest rate changes then the general category. At the other end of the spectrum on that same list is the Vanguard Intermediate-Term Bond Index (VBIIX) which has a duration of 6.49. This is 68% greater than the aforementioned Loomis GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 178 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 Sayles Fund, and is also 32% higher than other funds in this category average. Consequentially, Vanguard’s fund has a significantly higher interest rate risk. This does not mean that the Vanguard Fund is inferior to the Loomis Sayles Fund. In fact, the Vanguard fund has very high credit quality and half the annual expense ratio of the Loomis Sayles Fund. The two funds just have very different interest rate risk characteristics.

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