Chapter 6 - Bonds Flashcards
why do we need valuation of bonds?
There are several reasons.
First, the prices of risk free treasury bonds can be used to determine the risk free interest rates that produce the yield curve. The yield curve helps us predict future market movements.
Second, firms often issue bonds to fund their investments, and the returns that investors receive on those bonds is one factor determining the firm’s cost of capital.
What is a bond?
A bond is a way for someone to raise money by receiving money today against the promise of returning the money in the future. Can be coupon bond or zero-coupon bond.
The terms of a bond is called..?
Bond certificate.
The bond certificate includes things like time to maturity, and the dates of all payments, and the amount to be payed.
The maturity date is the final payment date.
What is a “term”?
Term is used to describe the time remaining until the final repayment date, also known as the maturity date.
The promised interest payments of a bond is called …?
Coupons
What is the face value of a bond?
The face value of a bond is the notional amount we use to compute the interest payments. Usually, the face value is repayed at the maturity date.
The amount of each coupon payment is called?
The coupon rate.
By convention, the coupon rate is set as APR. therefore, the amount of each coupon payment, CPN, is computed as:
CPN = (CouponRate x FV) / (Number of coupon payments in a year)
Why do we use APR and not EAR on bonds?
using EAR with bonds would be a little weird. If we have a bond that does quarterly payments, then it would be a little difficult for the issuer to express the EAR, as they have no clue what the investor will do with the money. They could make EAR based on their interest rate, but that would not be very good since the investor is not getting that rate on his coupon payments (since they are given to him, and not accumulated in the face value of the bond to grow). There is no compounding on a bond, so using EAR makes little since
What is the principal of the bond?
The same as face value.
It is NOT the price or the value of the bond.
What are zero-coupon bonds?
Zero coupon bonds are bonds that do not pay any coupons. no interest payment.
However, they will trade at a “discount”, which means that they are trading for less than their face value, or the amount that will be returned to the buyer at the maturity.
Zero-coupon bonds trade at a discount because the present value of a future cash flow is always smaller than the future value. As long as regular conditions apply at least. In other words, the bond trades lower than future value because it simply is not worth as much today as in the future. So, the buyer will be compensated for the time value of money.
US treasury bills (T-bills) are example of zero-coupon bonds.
What are T-bills
T-bills, short for Treasury bills, are zero-coupon bonds that lasts up to a year. They are issued by the US government.
People often talk about interest rates of the T-bill, but it is actually the difference between the discount value and the face value. So it is not an explicitly given interest rate, but rather implicit.
What is YTM?
Yield to maturity.
YTM is a special name given to bonds, and it specifically refers to the internal rate of return IRR that the investors get from buying the bond at the discount, and holding it until maturity.
IRR is the rate that ivnestors get that make the NPV of the cash flow equal to 0.
For zero-coupon bonds, this IRR is basically just the return they get.
But YTM, or sometimes just the yield, is more generalizable. we take the price the bond sells for, and equals it to its promised cash flow, and find the IRR. This IRR is the yield to maturity. REMEMBER: We only use present values.
Why are zero coupon bonds with N periods easy to calcualte?
No interest payment. Only face value, original discount price, and IRR, which we call the YTM.
What are coupon bonds?
Coupon bonds are bonds that pay interest in addition to the face value.
There are 2 types of US treasury securities trading today:
1) Treasury notes: one to 10 year original maturity.
2) Treasury bonds: 10 to upwards original maturity.
Precisely define YTM
Yield to maturity is the single discount rate that would equate the current value of the bond with the present value of the cash flows of the remaining bond.
Formula for YTM of a coupon bond
The annuity formula seems important af.
BUT, here we reach the IRR problem. We cannot solve it analytically.
What is important to remember about YTM
The YTM, or IRR, is a per-coupon rate. Not necessarily APR. It is common to convert the result to APR when done.
coupon bonds can trade at a discount and …
a premium, and a par.
The value is dynamic.
How can YTM exceed the coupon rate?
the bond must be a coupon bond, and trade at a discount
Define a bond that trades at a par
its yield to maturity is the same as the coupon rate. Its face value will be the same as its price
Elaborate on the effect of time on bonds
If the YTM remains unchanged, the less time there is to maturity, the smaller the discount will be. This means that as time move by, the price of the bond will most closer to the face value. This is because, since the YTM remains unchanged, and we have less time, the price of the bond must increase to balance the time vs constant YTM.
YTM remains unchanged is a sort of “lightspeed in vacuum” approach. The only goal here is to understand that as time pass by, and all other factors remain constant, the price/value of the bond will move closer to its face value.
Consider a coupon bond of 30 years with face value of 100. It has a coupon rate of 10%. If this bond has a YTM of 5%, what will it trade at?
How about right before the first coupon payment?
how about right after the first coupon payment?
We compute it using the present value of annuity, but we need to use the YTM as the interest.
P = (Coupon/YTM) x (1 - 1/(1+YTM)^30) + 100/(1+YTM)^30
To find the price right before/immediately before the first coupon payment, we can consider the payment as date 0, and add the coupon as the initial “investment”.
P = Coupon + (Coupon/YTM)x(1- …^29) + 100/(…)^29
To find immediately after the first payment, we can subtract the coupon, and keep the 29.
There are some intuition here as well. Consider the price for the bond immediately before the first coupon payment. We know that we skip the time value of money for one year, get the coupon, continue with the bond. We can use the IRR, or the YTM to find this value since the YTM tells us the interest we get EVERY DAMN PERIOD. Since we are about to value it one period forward in time, we multiple the original price by the YTM. NB: this is a method that actually only works when we ignore the cash payout times. It works if we have continuous coupon payments. It will give us the value of the bond one year (one period) forward in time.
elaborate on bond prices and itnerest rate changes
As interest rates and demand for bond yield rise, bond prices will fall, and vice versa.
elaborate on changes in interest rate and its impact on bond price sensititivty
Bonds that have maturity in the close future are not much impacted. This is because there are fewer years to see the interest change impact on.
However, bonds with longer time to maturity can have substantial changes in the price of the bond.
the same principle applies to bonds with higher frequency coupon payments. Because they pay more of the cash earlier, they will be less sensitive to changes in interest rate.
