Transcript Price Elasticity of Bonds

•Reffered from: www.moneypa.com/post/Bond-Basics-Yield-Price-And-Other-Confusion.aspx
•www.investorwords.com/521/bond.html
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•A debt instrument issued for a period of more than one year with the purpose of
raising capital by borrowing.
•The Federal government, states, cities, corporations, and many other types of
institutions sell bonds.
•Generally, a bond is a promise to repay the principal along with interest (coupons) on
a specified date (maturity).
•Some bonds do not pay interest, but all bonds require a repayment of principal.
•However, the buyer does not gain any kind of ownership rights to the issuer, unlike in
the case of equities. On the hand, a bond holder has a greater claim on an issuer's
income than a shareholder in the case of financial distress (this is true for all
creditors). Bonds are often divided into different categories based on tax status, credit
quality, issuer type, maturity and secured/unsecured (and there are several other
ways to classify bonds as well).
•U.S. Treasury bonds are generally considered the safest unsecured bonds, since the
possibility of the Treasury defaulting on payments is almost zero. The yield from a
bond is made up of three components: coupon interest, capital gains and interest on
interest (if a bond pays no coupon interest, the only yield will be capital gains)
•A bond might be sold at above or below par (the amount paid out at maturity), but
the market price will approach par value as the bond approaches maturity. A riskier
bond has to provide a higher payout to compensate for that additional risk. Some
bonds are tax-exempt, and these are typically issued by municipal, country or state
governments, whose interest payments are not subject to federal income tax, and
sometimes also state or local income tax.
Bond Yield, Price And Other Confusion
Understanding the price fluctuation of bonds is probably the most confusing part of this lesson. In fact, many new
investors are surprised to learn that a bond's price changes on a daily basis, just like that of any other publiclytraded security. Up to this point, we've talked about bonds as if every investor holds them to maturity. It's true that
if you do this you're guaranteed to get your principal back; however, a bond does not have to be held to maturity.
At any time, a bond can be sold in the open market, where the price can fluctuate - sometimes dramatically. We'll
get to how price changes in a bit. First, we need to introduce the concept of yield
Measuring Return With Yield
Yield is a figure that shows the return you get on a bond. The simplest version of
yield is calculated using the following formula:
yield = coupon amount/price.
When you buy a bond at par, yield is equal to the interest rate. When the price
changes, so does the yield. Let's demonstrate this with an example. If you buy a
bond with a 10% coupon at its $1,000 par value, the yield is 10% ($100/$1,000).
Pretty simple stuff. But if the price goes down to $800, then the yield goes up to
12.5%.
This happens because you are getting the same guaranteed $100 on an asset that is worth
$800 ($100/$800).Conversely, if the bond goes up in price to $1,200, the yield shrinks to
8.33% ($100/$1,200).
Yield To Maturity
Of course, these matters are always more complicated in real life. When bond investors refer to yield,
they are usually referring to yield to maturity (YTM). YTM is a more advanced yield calculation that
shows the total return you will receive if you hold the bond to maturity. It equals all the interest
payments you will receive (and assumes that you will reinvest the interest payment at the same rate as
the current yield on the bond) plus any gain (if you purchased at a discount) or loss (if you purchased
at a premium).
Knowing how to calculate YTM isn't important right now. In fact, the calculation is rather
sophisticated and beyond the scope of this tutorial. The key point here is that YTM is more accurate
and enables you to compare bonds with different maturities and coupons.
Putting It All Together: The Link Between Price And Yield
The relationship of yield to price can be summarized as follows: when price goes up, yield goes down
and vice versa. Technically, you'd say the bond's price and its yield are inversely related.
Here's a commonly asked question: How can high yields and high prices both be good when they can't
happen at the same time? The answer depends on your point of view. If you are a bond buyer, you want
high yields. A buyer wants to pay $800 for the $1,000 bond, which gives the bond a high yield of 12.5%.
On the other hand, if you already own a bond, you've locked in your interest rate, so you hope the price
of the bond goes up. This way you can cash out by selling your bond in the future
Price In The Market
So far we've discussed the factors of face value, coupon, maturity, issuers and yield. All of
these characteristics of a bond play a role in its price. However, the factor that influences a
bond more than any other is the level of prevailing interest rates in the economy. When
interest rates rise, the prices of bonds in the market fall, thereby raising the yield of the
older bonds and bringing them into line with newer bonds being issued with higher
coupons. When interest rates fall, the prices of bonds in the market rise, thereby lowering
the yield of the older bonds and bringing them into line with newer bonds being issued
with lower coupons
Why Bonds Fluctuate in Price
Many are the factors that influence directly price fluctuations of bonds. These factors
include the relation among prices of bonds, coupon rates, market yields, maturities and
risk assessment.
The following axioms illustrate this relation:
•The coupon rate relative to market rates of interest. When the rate of interest boosts in
the market, and surpass the coupon rate of a bond, the price of such bond will fall so as
to resemble the current yield at the market’s interest rate. When the rates of interest
drop, prices of bonds go up. While lesser the coupon rate of a bond, greater will price
fluctuations be. ( M.I
B.P , M.I
B.P )
• The length of time to maturity. While greater the maturity (principal), more volatile will
price fluctuations be.
•For a given change in a bond’s yield. A longer time to maturity of the bond greater will
the magnitude of changes in a bond’s yield be.
•For a given change in a bond’s yield. The size of the shifts in prices of bonds increase
at a decreasing rate depending on the time to maturity of the bond.
•For a given change in the bond’s yield. The magnitude of the prices of bonds are
inversely related to the bond’s yield.
•For a given change in the bond’s yield. The magnitude of the price increase caused by
a decrease in yield is greater than the price decrease caused by an increase in yield.
•Changes in risk assessment by the market. While lower the quality of a bond, lower is
the price. While higher the quality of the bond higher the price. The greater the risk of
the bond, the more volatile will be the bond’s price fluctuations.
Bonds:
Interest Rate Sensibility
The price of bonds can vary, but not every bond is affected
in the same way when circumstances change. If the typical
market interest rate drops, market price will fall for all
bonds, but not at the same rate. We will look at the reasons
for this, while taking a look at the duration of bonds, which
will show us the remaining average lifetime of a bond. The
point of this is to be able to compare different bonds with
each other.
Elasticity
Elasticity is a statistical concept, but is widespread in economics, and we will now
take a look at it in this context. We can determine the interest elasticity of the market
price using the following:
The numerator is the current price change in percentage, and the denominator is
the interest rate change in percentage. The result will be in percentage format and
the way we interpret it is (if E=4,5) that: If the interest rate changes by 1% that will
induce a 4,5% change in the current price.
Elasticity is not actually used in finance because it only gives a rough estimate and is
not a good base for comparison. What we use in reality is duration and modified
duration.
Duration
Duration was first developed by Frederick Macaulay in 1938, and is used widely since 1952 when F.M Reddington
alerted financial corporations of its importance. This just shows how recent some concepts are in finance.
Duration is officially the measure of the average (cash-weighted) term-to-maturity of a bond. Practically it means
how much an investor has to wait for his investment to break even (on average). It has a large formula, but do
not be swayed, it is not difficult.
The numerator is really the maturity of the cash-flows weighed with the present value of the
respective cash-flows. The denominator is actually the current price of the bond (the present
value of the cash flows).
We can observe some important laws about duration:
•Every bond which has any other cash flows than the repayment of the face value has a
smaller duration than the time to maturity.
•If two bonds have the same time to maturity the one with the larger duration has a
lower coupon rate.
•If two bonds have the same coupon rate, the one with the longer time to maturity will
have a higher duration. So with longer maturity time comes growing duration, although
this growth is a slowing growth, a bond with a ten year maturity will not have twice the
duration of a five year bond.
•If two bonds have equal time to maturity and coupon rates the one with the lower yield
expected by investors will have a higher duration.
•Zero coupon bond’s duration equals their time to maturity
Modified duration
To determine how prices react to interest changes we use modified duration. It will show us exactly
what elasticity has showed us, but more precisely.