Bonds (Week 3) Flashcards
What are bonds?
Security, sold by governments or corporations, that promise future fixed payments to investors (called bondholders).
What is a maturity date?
Bonds are rarely perpetual (such as consols); the final date of payments is called the maturity date.
What are the two types of payments bondholders can receive?
- Coupons - interest payments
- Principal repayments
What is a principal repayment?
The principal (also called the face value) is the amount used to calculate the interest.
Imagine a zero-coupon bond (a bond that does not pay interest - this does not exist irl). It is a one-year, risk-free, zero-coupon bond with face value £1000.
Today you pay PB to buy this bond and in one year you will receive £1000.
How much are you willing to pay for this bond?
Clearly PB <1000. To compute the value of the bond:
VB = 1000/1+kB
kB is the dicount rate applicable to the bond’s cash flows. Because this bond is risk free, then kB = kf.
So, if the risk-free rate is 5%, then VB = £952.38. In efficient markets, PB = VB = £952.38.
What is the yield to maturity?
The implied return based on the promised repayment.
What is the Yield to Maturity of a one-year, zero coupon bond?
What is the equation for the value of a risk-free bond?
Suppose that two years ago you bought a five-year £100 UK gilt, with promised annual coupon rate 2%.
If the current risk-free rate is 0.25%, what is the present value?
What is another term for coupon rate?
Promised yield
Consider a one-year bond with a promised yeild of 5%. The bond has face value of £1000. There is 20% probability of default. In such a case, the bond only pays £500. The risk-free rate is 3%.
What is the value of this bond?
Consider a one-year bond with a promised yeild of 5%. The bond has face value of £1000. There is 20% probability of default. In such a case, the bond only pays £500. The risk-free rate is 3%.
Current price is £912.62
What is the Yield to Maturity?
What is the Yield to Maturity when a bond is risk free?
The YTM is the same as the discount rate.
What does it mean if a bond is priced at par?
The value of the bond is the same as the face value (PB = F).
For the same face value F = £1000.
There is a 0.2 chance of default, in which case the payment is £500.
The discount rate is 3%.
Find the coupon you need to pay at par and the YTM.
If the bond is priced at par and there is no default risk, what is the YTM, promised yield and discount rate?
YTM = Promised Yield = Discount Rate (= 3%)
The YTM of a bond priced at par is ______ lower than the discount rate.
The YTM of a bond priced at par is never lower than the discount rate.
The YTM is a _____ approximation for the expected returns on a bond that has a high probability of default and/or low recovery rates.
The YTM is a poor approximation for the expected returns on a bond that has a high probability of default and/or low recovery rates.
Despite there being a risk of default, we have used the risk-free rate (3%) to discount the bond cash flows. Is this correct?
Only if bond cash flows carry no systematic risk (=zero beta). In practice, bond betas (systematic risk) are close to zero, but not exactly.
