Lecture 12 Flashcards
Term structure of interest rates =
Structure of interest rates for discounting cash flows of different maturities
Yield curve displays
Relationship between yield and maturity > plots YTM as a function of time to maturity
Yield curve implies
Information on the expected future short term rates
Bonds of different maturities sell at
Different yield to maturities
Long term bonds sold at
Higher yields than short term bonds
As interest rates increase/ decrease, bondholders experience
Capital gains/ losses
If the market rate falls below the coupon rate
The bond is attractive, therefore investors would pay > the par value
If the market rate exceeds the coupon rate
Investors will pay below the par value
Duration is a measure of
The average maturity of a bond’s promised cash flows. The number of years required to recover the true cost (price) of the bond.
Duration is a guide for
The sensitivity of a bond to interest rate changes
Duration =
The weighted average of times until each payment is received. Weights are proportional to the present value of each payment.
Duration is shorter than the maturity for
All bonds, except zero coupon bonds (= for zero coupon)
Long term bonds more sensitive to interest rate movements
Than short term. Duration quantifies this
Duration rules (5)
- Duration of zero-coupon bond = time to maturity
- Holding maturity constant, a bond’s duration is higher when the coupon rate is lower
- Holding the coupon rate constant, a bond’s duration increases with time to maturity
- Holding other factors constant, the duration of a coupon bond is higher when the bond’d YTM is lower
- Duration of a level perpetuity = (1 + y) / y or 1 + (1/y)
Duration is an independent coupon rate only for
Perpetuities
Is there a linear relationship between bond prices and yield, as duration suggests?
No
Duration rule is a good approximation when
There are only small changes in bond yields
Bonds with greater convexity have
Increased curvature in the price-yield relationship
Duration approximation (straight line) always
Understates the value of the bond
Underestimates the increase in bond price when yield falls
Overestimates the decline in the price when the yield increases
Bonds with increased convexity see
Greater price increase and smaller price fall when interest rates fluctuate by large amounts
If interest rates are volatile
Investors prefer convexity
For greater convexity, investors must
Pay higher prices and accept lower yields to maturity
