us treasury: dfimarket valuations duration

8/14/2019 US Treasury: dfimarket valuations duration

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The need for Market Valuation of yourportfolio….

SFFAS 1 – Accounting for Selected Assets andLiabilities

72. Disclosure of market value. For investments

in Market-based and marketable Treasurysecurities, the market valuation should bedisclosed.

FEDE RAL ACCOU NTING STAN DARDS ADVIS ORYEDE RAL ACCOU NTING STAN DARDS ADVIS ORYBOAR DOAR D



Once you choose the price file you use the Endof Day price to calculate your market value.



Duration



• We also know that longer maturity debtsecurities tend to be more volatile inprice.

– For a given change in interest rates, theprice of a longer term bond generallychanges more than the price of a shorterterm bond.

• We know:

– An increase in interest rates causesbond prices to fall, and a decrease ininterest rates causes bond prices torise.



• Two bonds with the same term to

maturity do not have the sameinterest-rate risk.

– A 10 year zero coupon bond makes all

of its payments at the end of theterm.

– A 10 year coupon bond makespayments before the maturity date.



• When interest rates rise, the pricesof low coupon securities tend to fallfaster than the prices of highcoupon securities.

• Similarly, when interest ratesdecline, the prices of low couponrate securities tend to rise faster

than the prices of high coupon ratesecurities.



• The new measure permits analyststo construct a linear relationshipbetween term to maturity andsecurity price volatility, regardlessof differing coupon rates.

• Knowledge of the impact of

varying coupon rates on securityprice volatility led to thedevelopment of a new index of maturity other than straightcalendar time.



Duration is measured in years; however,do not confuse it with a bond’s maturity.For all bonds, duration is shorter thanmaturity except zero coupon bonds,whose duration is equal to maturity. Thisis because all cash flows are received atmaturity.

is the measure of the price sensitivity of

a fixed-income security to an interestrate change of 100 basis points. Thecalculation is based on the weighted

average of the present values for allcash flows.

Duration…



The term “duration,” having a special meaning in the context of bonds, isa measurement of how long in years it takes for the price of a bond to berepaid by its internal cash flows. It is an important measure for investorsto consider, as bonds with higher durations are more risky and havehigher price volatility than bonds with lower durations.

For each of the two basic types of bonds the duration is the following:

1. Zero-coupon bond – Duration is equal to its time to maturity.

2. Straight bond – Duration will always be less than its time tomaturity.

Here are some visual models that demonstrate the properties of durationfor a zero-coupon bond and a straight bond.



Duration of a Zero-Coupon Bond

The red lever above represents the four-year time period it takes for a zerocoupon to mature. The money bag balancing on the far right represents thefuture value of the bond, the amount that will be paid to the bondholder atmaturity. The fulcrum, or the point holding the lever, represents duration,which must be positioned where the red lever is balanced. The fulcrumbalances the red lever at the point on the time line when the amount paidfor the bond and the cash flow received from the bond are equal. Since the

entire cash flow of a zero-coupon bond occurs at maturity, the fulcrum islocated directly below this one payment.



Duration of a Straight Bond

Consider a straight bond that pays coupons annually and matures in five years.Its cash flows consist of five annual coupon payments and the last payment

includes the face value of the bond.

The moneybags represent the cash flows you will receive over the five-year period. To balance the red lever (at the point where total cash flows equal the amountpaid for the bond), the fulcrum must be further to the left, at a point beforematurity. Unlike the zero-coupon bond, the straight bond pays coupon payments

throughout its life and therefore repays the full amount paid for the bond sooner.



Factors Affecting DurationIt is important to note, however, that duration changes as the coupons arepaid to the bondholder. As the bondholder receives a coupon payment, theamount of the cash flow is no longer on the timeline, which means it is nolonger counted as a future cash flow that goes towards repaying thebondholder. Our model of the fulcrum demonstrates this: as the firstcoupon payment is removed from the red lever (paid to the bondholder), thelever is no longer in balance (because the coupon payment is no longer

counted as a future cash flow).



Duration increases immediately on the day a coupon is paid, but throughout

the life of the bond, the duration is continually decreasing as time to thebond’s maturity decreases. The movement of time is represented above asthe shortening of the red lever: notice how the first duration had five paymentperiods and the above diagram has only four. This shortening of the timeline,however, occurs gradually, and as it does, duration continually decreases. So,in summary, duration is decreasing as time moves closer to maturity, butduration also increases momentarily on the day a coupon is paid and removed

from the series of future cash flows – all this occurs until duration, as it doesfor a zero-coupon bond, eventually converges with the bond’s maturity.

The fulcrum must now move to the right in order to balance thelever again:



Coupon rate and Yield also affect the bond’s duration. Bonds with highcoupon rates and in turn high yields will tend to have a lower durationthan bonds that pay low coupon rates, or offer a low yield. This makessense, since when a bond pays a higher coupon rate the holder of thesecurity received repayment for the security at a faster rate. Thediagram below summarizes how duration changes with coupon rate andyield.

Duartion – Other factors:



MacaulayDuration The formula usually used to calculate a bond’s basic duration is the

Macaulay duration, which was created by Frederick Macaulay in 1938 butnot commonly used until the 1970s.

Macaulay duration is calculated by adding the results of multiplying the presentvalue of each cash flow by the time it is received, and dividing by the total priceof the security. The formula for Macaulay duration is as follows:

n = number of cash flowst = time to maturity

C = cash flow

i = yield to maturity

M = maturity par value

Let’s go through an example:



If you hold a five-year bond with a par value of $1,000 and a coupon rate of 5%.For simplicity, assume that the bond is paid annually and that interest rates are3% (yield).

n = number of cash flows

t = time to maturityC = cash flow

i = yield to maturity

M = maturity par value

Fortunately if you are seeking the Macaulay duration of a zero-coupon bond, the

duration would be equal to the bond’s maturity, so there is no calculationrequired.



Therefore… Therefore…the lower the coupon rate, the

higher the duration of the bond.



Coupon Bonds: duration is shorter thanmaturity Discount bonds (yield is greater thancoupon): duration increases at a decreasing

rate up to a point, after which it declines

Par value bonds: duration increases withmaturity.

Premium bonds (yield is less than coupon):duration increases throughout but at a lesserrate than with a par value bond.



Duration depends on yield-to-maturity.

The higher the yield the shorter the

duration, other things being equal.



In Treasury bonds, the only source of risk stems from interest ratechanges.

Duration is a measure of this sourceof risk.

Duration allows bonds of different

maturities and coupon rates to bedirectly compared.



@DURATION(settlement;maturity;coupon;yield;[frequency];[

basis]) calculates the annual duration for a security thatpays periodic interest.

Example

A security has a July 1, 1993, settlement date and aDecember 1, 1998, maturity date. The semiannual couponrate is 5.50% and the annual yield is 5.61%. The bond has a30/360 day-count basis.

To determine the security's annual duration:

@DURATION(@DATE(93;7;1);@DATE(98;12;1);0.055;0.0561;2;0) = 4.734591



http://www.investopedia.com/calculator/MDuration.aspx



Email [email protected] if you would

like to receive either or both of the reports.

Include which report (Market Valuation and/orDuration) you would like to receive, the

Account Fund Symbol(s), and a date for whichyou want the information.

Questions?

us treasury: dfimarket valuations duration

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