Bonds (Week 3)

Question 1

What are bonds?

Answer 1

Security, sold by governments or corporations, that promise future fixed payments to investors (called bondholders).

Question 2

What is a maturity date?

Answer 2

Bonds are rarely perpetual (such as consols); the final date of payments is called the maturity date.

Question 3

What are the two types of payments bondholders can receive?

Answer 3

1. Coupons - interest payments
2. Principal repayments

Question 4

What is a principal repayment?

Answer 4

The principal (also called the face value) is the amount used to calculate the interest.

Question 5

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 P_B to buy this bond and in one year you will receive £1000.

How much are you willing to pay for this bond?

Answer 5

Clearly P_B <1000. To compute the value of the bond:

V_B = 1000/1+k_B

k_B is the dicount rate applicable to the bond’s cash flows. Because this bond is risk free, then k_B = k_f.

So, if the risk-free rate is 5%, then V_B = £952.38. In efficient markets, P_B = V_B = £952.38.

Question 6

What is the yield to maturity?

Answer 6

The implied return based on the promised repayment.

Question 7

What is the Yield to Maturity of a one-year, zero coupon bond?

Answer 7

Question 8

What is the equation for the value of a risk-free bond?

Answer 8

Question 9

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?

Answer 9

Question 10

What is another term for coupon rate?

Answer 10

Promised yield

Question 11

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?

Answer 11

Question 12

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?

Answer 12

Question 13

What is the Yield to Maturity when a bond is risk free?

Answer 13

The YTM is the same as the discount rate.

Question 14

What does it mean if a bond is priced at par?

Answer 14

The value of the bond is the same as the face value (P_B = F).

Question 15

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.

Answer 15

Question 16

If the bond is priced at par and there is no default risk, what is the YTM, promised yield and discount rate?

Answer 16

YTM = Promised Yield = Discount Rate (= 3%)

Question 17

The YTM of a bond priced at par is ______ lower than the discount rate.

Answer 17

The YTM of a bond priced at par is never lower than the discount rate.

Question 18

The YTM is a _____ approximation for the expected returns on a bond that has a high probability of default and/or low recovery rates.

Answer 18

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.

Question 19

Despite there being a risk of default, we have used the risk-free rate (3%) to discount the bond cash flows. Is this correct?

Answer 19

Only if bond cash flows carry no systematic risk (=zero beta). In practice, bond betas (systematic risk) are close to zero, but not exactly.