Bonds Flashcards
Bond Certificate
states the terms of the bond
Maturity Date
the date of the final repayment of the bond
Term
the time remaining until the repayment date
Coupon
the promised interest payment
Face Value
the amount that will be repaid at maturity
Coupon Rate
the amount of each coupon payment expressed as APR
Coupon Payment Equation
Coupon Rate x Face Value/ Numbe
Yield to Maturity
the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond
Suppose we have a zero-coupon bond that matures in one year. It has a face value of $100,000 and is currently selling for $96,618.36. What is it’s yield to maturity?
Suppose we have a zero-coupon bond that matures in one year. It has a face value of $100,000 and is currently selling for $96,618.36. What is it’s yield to maturity?
PV = -96618 FV = 100000 N = 1 I/Y = ? = 3.5
Its yield to maturity is 3.5%.
Determine the yield to maturity of the following $100 face value bonds with the present values listed below:
98.04, 95.18, 91.51, 87.14
find the ytms for each which are
2, 2.5, 3, 3.5
Spot interest rates
the yield on a default-free zero coupon bond
Zero-Coupon yield curve
a plot of the yields of risk-free zero-coupon bonds as a function of the bond’s maturity
Yield Curve
a curve with the interest rates on the y axis, and the term in years on the x axis
Coupon Bonds
bond that pay their investors their face value at maturity and also pay regular coupon interest payments
(1-10 years)=treasury notes
(10 years or greater)= treasury bonds
ten year bond $1000 bond 4 percent coupon semi-annual coupon payments what cash flows will you receive if you hold the bond until maturity
(4%x$1000)/2=$20 twice per year and then you will receive the $1000 ace value of the bond in ten years
YTM of coupon bonds
YTM= the single discount rate that makes all of the bonds future payments equal to the bond’s present value
5 year $1000 bond 5% coupon rate semiannual coupons trading for $957.35 YTM=?
YTM=6%
multiply the YTM by 2 since there are 2 periods per year, this gives us the annual rate
$1000 par semi annual bond
7 years until maturity
9% coupon rate
price is currently 1080.55
YTM=3.75X2=7.5
5 year 1000 semi-annual bond 5% coupon rate YTM=6.3 price=?
divide everything by 2 except the interest rate which you multiply by 2
Clean Price v.s. Dirty Price
Clean price is the price quoted on the bond, if the bond is sold immediately after the coupon payment is made then the clean price is the price which is paid for the bond
Dirty Price: clean price plus the accrued interest
Calculating Dirty Price and the accrued interest formulal
Accrued Interest=coupon amount x (Days since last coupon payment divided by the days in the current coupon period
Calculating the Coupon Rate
10 year $1000 bond annual coupons currrent price is $900 YTM is 6%
find the payment of the bond and then divide that payment by the face value of the bond
Discount, Par, and Premium Bonds
Discount- bonds are selling for less than there face value
Par- bonds are selling for exactly their face value
Premium- bonds are selling for more than their face value
3 Bond Relationships
Coupon>YTM= Premium
Coupon=YTM=Par
Coupon
Factors Affecting Bond Prices
1) As market interest rates change, bonds YTM and prices change
2) Holding market interests constant, as bonds move closer to maturity there present value changes
Bond Relationships Pt. 2
There is an inverse relationship between interest rates and bond prices
- the sensitivity to changes in interest rate is called Duration
- bonds with high duration are highly sensitive to changes in interest rates
- bonds with low duration are less sensitive to changes in interest rates
Duration Relationships
shorter maturity zero- coupon bonds are less sensitive to interest rate changes than longer term zero-coupon bonds
bonds with higher coupon rates are less sensitive to interest rate changes than bonds with lower coupon rates
Calculate the Rate of Return on Bonds
1) Calculate the initial price
2) calculate the ending price of the bond
3) Divide the ending price by the initial price and raise it to the power of one over the number of years it has been held and then subtract 1
purchase 15 year
zero coupon bond
with a YTM of 8%
hold the bond for five years
1) bond’s yield to maturity is 8% when you sell it, what is the IRR
2) ytm is 9%, when you sell it, what is the IRR of the investment
long solution on slides
On the run bonds
treasury bonds that are the mosg recently issued
use a bunch of zero coupon bonds to find the interest rate on a default free coupon bond
on slide
Forward interest rate
interest rate that can be guaranteed today for a loan or investment in the future