Topic 02

Question 1

What is yield to maturity?

Answer 1

Yield to maturity is the interest rate that equates the present value of an instrument with its value today.

For simple loans, simple interest rate = YTM

Numbers needed to calculate:

1. PV of debt instrument
2. future payment schedule

Question 2

What is the yield to maturity of a simple loan with PV $100 and cashflow in one year of $110.

Answer 2

100 = 110 / (1 + i)^n
(1+i)*100 = 110
1+i = 110/100
YTM = i = 10%

Question 3

How do you calculate YTM for a fixed payment loan?

Answer 3

LV = loan value
FP = fixed yearly payment
n = number years until maturity

LV = FP/(1+i) + FP/(1+i)^2 + FP/(1+i)^3 + FP/(1+i)^4 + …. + FP/(1+i)^n

Question 4

How do you calculate the YTM for a coupon bond?

Answer 4

P = price of coupon bond
C = yearly coupon payment
F = face value of bond
n = number years until maturity

P = C/(1+i) + C/(1+i)^2 + C/(1+i)^3 + …. + F/(1+i)^n

Question 5

What is a consol?

Answer 5

A consol is a perpetual bond that pays a coupon in perpetuity, has no maturity, therefore no principal repayment.

Question 6

How do you calculate the YTM for a consol?

Answer 6

P = C / i_c
P_c = price of consol
C = yearly coupon
i_c = YTM

i_c = C / P_c

*** This will give you the current yield for a coupon bond

Question 7

What are the key findings about maturity and the volatility of bond returns?

Answer 7

1. only bond whose return = yield is one with maturity = holding period
2. for bonds with maturity > holding period, i GOES UP, P GOES DOWN implying capital loss
3. The longer the maturity, the greater the price change associated with interest rate change
4. The longer the maturity, the more return changes with change in interest rate
5. A bond with a high initial interest rate can still have a negative return if i GOES UP

Question 8

What is duration?

Answer 8

Duration is the weighted average of the maturities of cash payments.

Increase in coupon -> more weighted in earlier years

Increase in interest rate -> more weighted in earlier years

Question 9

What are the key findings for calculating duration?

Answer 9

1. ALL ELSE EQUAL, the longer the term to maturity of a bond, the longer its duration
2. ALL ELSE EQUAL, when interest rates rise, the duration of a coupon bond falls
3. ALL ELSE EQUAL, the higher the coupon rate on the bond, the shorter the bond’s duration