duration basics

7/31/2019 Duration Basics

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PREPARED BY-

HARSHITA CHATURVEDI

DURATION BASICS


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DEFINITION

It is a measure of a bond's sensitivity to interestrate changes.

The higher the bond's duration, the greater itssensitivity to the change and vice versa

most commonly used measure of risk in bondinvesting.

It incorporates a bond's yield, coupon, finalmaturity and call features into one number,expressed in years.


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Rising interest rates mean falling bond prices,

while declining interest rates mean rising bondprices.

For example, a 5 year duration meansthe bond will decrease in value by 5%if interest rates rise 1% and increase in value by5% if interest rates fall 1%.

If an investor expects interest rates to fall duringthe course of the time the bond is held, a bondwith a long duration would be appealing.


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HOW IT WORKS

There is more than one way to calculate duration,depending on one's compounding assumptions,but the Macaulay Duration is the most common.

Macaulay Duration.

Developed in 1938 by Frederic Macaulay, thisform of duration measures the number of years

required to recover the true cost of a bond,considering the present value of all coupon andprincipal payments received in the future.


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where:

t = period in which the coupon is received

C = periodic (usually semiannual) coupon payment

y = the periodic yield to maturity or required yieldn = number periods

M = maturity value (in $)

P = market price ofbond


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EXPLANATION

Duration = Present value of a bond's cash flows,weighted by length of time to receipt and dividedby the bond's current market value.

For example, let's calculate the duration of a

three-year, $1,000 Company XYZ bond with asemiannual 10% coupon.


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Company XYZ Macaulay duration = $5,329.48 /

$1,000 = 5.33

As we know duration can help understandsensitivity of a bond to changes in prevailinginterest rates, thus multiplying a bond's duration bythe change, we can estimate the percentage pricechange for the bond.

For example, the Company XYZ bonds with aduration of 5.53 years. If market yields increasedby 20 basis points (0.20%), the approximatepercentage change in the XYZ bond's price wouldbe:

-5.53 x .002 = -0.01106 or -1.106%


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FACTORS AFFECTINGDURATION

six things affect a bond's duration:

Bond's Price: if the bond in the above examplewere trading at $900 today, then

duration=$5,329.48 / $900 = 5.92. If $1,200today, then duration =$5,329.48 / $1,200 = 4.44.

Coupon: The higher a bond's coupon, the moreincome it produces early on and thus the shorter

its duration. The lower the coupon, the longer theduration (and volatility). Zero-coupon bonds,which have only one cash flow, have durationsequal to their maturities.


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Maturity: The longer a bond's maturity, the

greater its duration (and volatility). Durationchanges every time a bond makes a couponpayment. Over time, it shortens as the bond nearsmaturity.

Yield to Maturity: The higher a bond's yield tomaturity, the shorter its duration because thepresent value of the distant cash flows (whichhave the heaviest weighting) become

overshadowed by the value of the nearerpayments.

Sinking Fund: The presence of a sinking fund

lowers a bond's duration because the extra cash


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Call provision: Bonds with call provisions also

have shorter durations because the principal isrepaid earlier than a similar non-callable bond.

LIMITATIONS OF MACAULAYS DURATION:

The formula assumes a linear relationshipbetween bond prices and yields even though therelationship is actually convex. Thus, the formula isless reliable when there is a large change in yield.


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WHY IS IT IMPORTANT

An investor benefits from duration in 2 ways:

Speculating on interest rates: Investors whoanticipate a decline in market interest rates would

try to increase the average duration of their bondportfolio. Likewise, investors who expect a rise ininterest rates would want to lower their averageduration.

Matching risk to your tastes: When selecting

from bonds of different maturities and yields, orcomparing bond mutual funds, duration allows youto quickly determine which bonds are moresensitive to changes in market interest rates, and

to what degree.


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CONCLUSION The Securities Industry and Financial Markets

Association, a trade group of financialprofessionals, has posted an article titled Risksof Investing in Bonds, which offers further

information on duration risk. Regent School Press, an academic publisher,

offers a technical analysis of bond durationina PDF file.

Karvy, a financial services company, providesa calculatorfor figuring how to use bond durationto hedge risks in other investments.

duration basics

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