bonds 1 awad raheel. bond characteristics ◦ reading the financial pages interest rates and bond...
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Bond Characteristics◦ Reading the financial pages
Interest Rates and Bond Prices Current Yield and Yield to Maturity Bond Rates and Returns Corporate Bonds and the Risk of Default
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Terminology
Bond - Security that obligates the issuer to make specified payments to the bondholder.
Coupon - The interest payments made to the bondholder.
Face Value (Par Value or Principal Value) - Payment at the maturity of the bond.
Coupon Rate - Annual interest payment, as a percentage of face value.
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WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
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The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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ExampleWhat is the price of a 5.5 % annual coupon bond, with a Rs1,000 face value, which matures in 3 years? Assume a required return of 3.5%.
03.056,1
)035.1(
055,1
)035.1(
55
)035.1(
55321
RsPV
PV
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Example (continued)What is the price of the bond if the required rate of return is 5.5 %?
000,1
)055.1(
055,1
)055.1(
55
)055.1(
55321
RsPV
PV
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Example (continued)What is the price of the bond if the required rate of return is 15 %?
09.783
)15.1(
055,1
)15.1(
55
)15.1(
55321
RsPV
PV
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Example (continued)What is the price of the bond if the required rate of return is 3.5% AND the coupons are paid semi-annually for 3 years?
49.056,1
)0175.1(
50.027,1
)0175.1(
50.27...
)0175.1(
50.27
)0175.1(
50.276521
RsPV
PV
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Example (continued)Q: How did the calculation change, given
semi-annual coupons versus annual coupon payments?
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Example (continued) Q: How did the calculation change, given
semi-annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once doubles the
total number of cash flows to be discounted in the PV
formula.
Discount Rate
Since the time periods are now half years, the discount
rate is also changed from the annual rate to the half
year rate.12AWAD RAHEEL
Current Yield - Annual coupon payments divided by bond price.
Yield To Maturity – Interest/Discount rate for which the present value of the bond’s payments equal to its price.
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Calculating Current Yield Suppose you are purchasing 3 years bond with
coupon rate of 10%. How do you calculate the rate of return the bond offer?
Current Rate of Return = 100/1000 = 10%AWAD RAHEEL 14
Cash Paid to You in Year
You Pay 1 2 3 Rate of Return
Rs 1000 100 100 1100 10%
Now suppose that the market price of 3 years bond is Rs1136.16 with annual income of Rs100. What is the rate of return now?
So you pay 1136.16 and receive 100 annually. Income as proportion of initial outlay is 100/1136.16 = .088 = 8.8%
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Cash Paid to You in Year
You Pay 1 2 3 Rate of Return
Rs 1136.16
100 100 1100 ?
Calculating Yield to Maturity (YTM=r)If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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ExampleWhat is the YTM of a 5.5 % annual coupon bond, with a Rs1,000 face value, which matures in 3 years? The market price of the bond is Rs1,056.03.
03.056,1
)1(
055,1
)1(
55
)1(
55321
RsPV
rrrPV
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WARNINGWARNINGCalculating YTM by hand can be very tedious.
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
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Rate of Return – Earnings per period per rupee invested.
Rate of return =total income
investment
Rate of return =Coupon income + price change
investment
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880
900
920
940
960
980
1,000
1,020
1,040
1,060
1,080
0 5 10 15 20 25 30
Bo
nd
Pri
ce
Time to Maturity
Price path for Premium Bond
Price path for Discount BondToday
Maturity
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0
600
1000
1500
30
Bond shows interest rate risk as its price fluctuate with interest rate change.
Do all bonds get effected equally? Long term bonds are more sensitive to interest
rate than prices of short term bonds.
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-
500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$ B
on
d P
ric
e
30 yr bond
3 yr bond
When the interest rate equals the 5.5% coupon rate, both
bonds sell at face value
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Interest Rate (%)
Bon
d pr
ice
0
Bonds are also available with real interest rates.
If nominal rate is 3.5% and inflation rate is 2%, then real interest rate will be:
Real interest rate = 1.035 -1 =.0147 = 1.47% 1.02
As inflation rate is uncertain, so is real interest rate.
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1 real interest rate = 1+nominal interest rate1+inflation rate
In inflation indexed bonds real cash flows are fixed while nominal cash flows (interest and principal) are changed as CPI changes.
e.g. Real cash flow of 2 years indexed bonds at 3% would be:
Now suppose that inflation turns out to be 5% in year 1 and 4% in year 2. then nominal cash flow would be:
Here cash payments are justified to give 3% real interest rate
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Year 1 Year 2
Real Cash Flow
Rs 30 Rs 1030
Year 1 Year 2
Nominal Cash Flow
Rs 30x1.05=Rs 31.50
Rs 1030x1.05x1.04 =Rs 1124.76
Like governments, corporate also borrow money by selling bonds.
Credit risk – The risk that bond issuer may default on its bonds.
Default premium – The additional yield on a bond investor require for bearing credit risk.
Investment grade – Bonds rated BBB and above. (1% default rate of AAA since 1971)
Junk bonds – Bonds having grade less than BBB (about 50% bonds rated CCC by S&P defaulted within 10 yrs)
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StandardMoody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principalis very strong.
Aa AA Very strong likelihood that interest and principal will berepaid
A A Strong ability to repay, but some vulnerability to changes incircumstances
Baa BBB Adequate capacity to repay; more vulnerability to changesin economic circumstances
Ba BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over
sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.30AWAD RAHEEL
Zero coupons◦ No coupon offered and receive face value of bond
at maturity date. Floating rate bonds
◦ Rate can be pegged to some measure of current market e.g. T Bills plus 2%
Convertible bonds◦ Option to convert into shares latter.◦ Investor accept lower interest rates on convertible
bonds.
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Innovations are always in process for bonds e.g.
Catastrophe (or cat) bonds:◦ Offer high return but reduced when specific type of
disaster occurs. Longevity bonds:
◦ Bond payments get higher if more population survived extra year.
◦ Pension funds are common buyer of these bonds as they have to pay extra if life expectancy increases.
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