Chapter 6 - Bonds Flashcards
How large is the US bond market?
Approximaltey the same as the US equity market actually. There is a great amount invested in both treasury and regular bonds
Why do we study bonds?
1) Bond prices can be used to determine the risk free interest rate. This allows us to create the yield curve. This yield curve is important predictor of future sentiment.
2) Firms typically issue bonds to raise funds for their own investments. Understanding the bonds is necessary to understand the firm’s cost of debt.
3) Easy understanding of how securities are priced in a compattiive market
Recall the definition of a bond
A bond is a security sold by governments and corporations in order to raise money that will fund projects. It is an obligation that force the issuer to return some promised future payment.
what is the final repayment date of a bond typically called?
Maturity date
What is the bond certificate?
bond certificate holds the details of amounts and dates of the payments.
What do we call the time remaining of a bond, until the maturity date?
The term of the bond
What payments do bonds typically pay?
2 types.
coupons and the principal.
The coupon is the promised interest payment.
The principal, also called FACE VALUE, is the amount we use to compute the coupons.
Usually, the face value is payed at maturity.
When we say “a $1000 bond”, what do we mean?
A bond with a face value of $1000.
elaborate on how the coupon is computed
We need the coupon rate and the face value. The coupon rate is set by the issuer of the bond. It is stated on the bond certificate.
Coupon rate is by convention APR.
We compute the coupon by the following formula:
coupon = (coupon rate x FaceValue) / (CPNs each year)
What is the simplest type of bond?
Zero coupon bonds
Name an exmapel of a zero coupon bond
US treasury bills.
Us treasury bills are zero coupon bonds with a time to maturity of up to one year.
Why are zero coupon bonds simple?
They dont have a coupon. Instead they have a face value, and will typically (most likely) trade at a price the is below the face value (discount, in other words).
Recall IRR
Internal rate of return is the discount rate that makes the present value of the cash flows equal to 0.
Requires at least one negative initial investment
What is YTM?
Yield to maturity.
It is a special name given to bonds. It is actually the same as IRR, but for bonds. It is also commonly just called “yield”.
Formally: The yield to maturity of a bond is the discount rate that sets the present value of the promised payments equal to the current market price of the bond.
Given a zero coupon bond with a time to maturity of several years, how do we find the yield to maturity?
The YTM is solved by transforming the IRR equation:
Price = FV / (IRR ^n)
IRR = (FV / (Price)) ^{1/n}
This is basically derived from the IRR formula AND the law of one price. we use the law of one price to say that the bonds market price should be exactly equal to the present value of its cash flows.
Therefore, if the bonds YTM is unknown, we use the current market price as well as the bond certificate to find the YTM.
If YTM is known, but the price is not, we can derive the price easily by using the established assumption of law of one price.
What perticular benefit can we use the zero coupon default-free bonds with time to maturity at date n for?
They are suitable at determining the risk free interest rate for various periods.
Since the zero coupon bond dont pay coupons, they are easily used to compute YTM. Then we use the law of one price to establish the fact that YTM of the zero coupon bond MUST be the same as the risk free rate for the same period.
This is something we can do because of the same level of risk, and same cash flows. This allows us to use the law.
What is the yield curve?
The yield curve is a function that maps a time to maturity to an interest rate. Risk free interest rates speciically.
Because of the relationship between risk free interest rate, yield curve, zero coupon US treasury bonds, we often refer to the yield curve as the ZERO COUPON YIELD CURVE.
What is spot interest rate?
Spot interest rate is the yield for some specific time to maturity on a zero coupon risk-free bond.
We can find it by using the YTM formula established earlier.
Elaborate on coupon bonds
Same as the zero coupon bonds, they too pay the face value at maturity. However, they also pay coupons during the timebetween.
Two types of US Treasury coupons currently active?
1) US treasury notes
2) US treasury bonds
The difference is the time frame. They differ in terms of hte original time to maturity.
The notes originally have a time to maturity of one to ten years.
The bonds have 10 years to 30 years typically, but the only formality is that they have longer than 10 year maturity.
Why is coupon bonds slightly tricky to work with?
They may have cash flows at intervals that makes it difficult, at least more difficult than the zero coupon bonds.
If we want to find the yield, or the market price, we must use the cash flows at all the various times and discount them correctly.
How do we go about when trying to find the YTM of a coupon bond?
We make use of the fact that bonds typically are annuities. Because of this, we can use the annuity formula, and smack the face value with the same discount rate at the end as well.
This requires the coupons to be the same always. However, they typically are because they are computed using the face value. The face value will not change, which means that the annuity formula is perfectly valid.
Again, the YTM is equal to the discount rate that would equate the current market price with the promised cash flows of the bond.
P = CPN x 1/y (1 - 1/ (1+y)^n) + FV/(1+y)^n
The formula for finding the market price of the coupon bond has one signifcant drawback….?
Because the equaiton is transcendental, there is no way to solve for the YTM without without using a trial-and-error apporahc, or solving numerically. Because of this, I suppose it would be more common with tasks that is given the YTM and the case is to compute the price.
Elaborate on whats going on ehre
Shows how the bond prices change with the passage of time for a variety of coupon rates.
The YTM remains the same: 5%. Recall that if the bonds are US treasury, then they are risk free, and a risk free investment cannot earn a larger return one place compared to the other place, so they need to have the same ROI. Therefore, all of these bonds have the same YTM.
As we can see, the zero coupon bond shows a smooth line, indicating that time is the only thing affecting its price.
FOr the couupon bonds, there are soemthing causing the zig zags, whcih is the coupon effect.
The upper bond has a coupon of 10%, which is higher than the YTM of 5%. Because of this larger coupon, the bond price will trade at a premium. Therefore, its price is higher than the others, but will converge towards the par face value (and final coupon value) as time pass by.
The bond with YTM = Coupon rate has no time effect, in terms of percentage of face value.
Do not confuse zero coupon bonds and coupon bonds. It is very important to understand that the coupons cause a bond to trade at a price higher than its equivalent zero coupon bond. This is because coupon bonds produce more cash flows, which naturally makes its price higher.
