PORTFOLIO MANAGEMENT NOTES:
Term Structure of Interest Rates:
Fixed-coupon bonds are not risk free, and there is an assumption that future interest payments can be reinvested at the same rate.
We face a problem when it comes to measuring expected return when the investor’s investment horizon does not match the time to maturity. For example, if we have a two-year investment horizon, there are multiple options:
Roll over two one-year bonds
Buy and hold a two-year bond to maturity
Buy an n-year bond and sell after two years
We need to compare the ‘expected return’, as opposed to the yield to maturity. This is called the Holding Period Return.
In order to calculate the RHS, we need to be able to estimate future market interest rates.
Deriving Spot Rates from Fixed-Coupon Bonds
By looking at the yield curve for different fixed-coupon bonds, we can infer the expected rates in the market. For example:
A one-year 12.5% bond with YTM = 5.5% could be considered as a one-year zero-coupon bond with a face value of $112.50. Therefore y(1) = 5.5%
A two-year 10.5% coupon bond with YTM = 6.8% can be considered as a combination of:
A one-year zero-coupon bond with face value of $10.50
A two-year zero-coupon bond with a face value of $110.50
So….
y(2) = 6.8670%
Deriving Forward Rates for Fixed-Interest Bonds
Let f(n,t) be the YTM of an n-period bond t-periods ahead. For simplicity, we restrict n to 1. So, f(1) is the YTM of a one-year bond in one years time, and f(2) is the YTM of a one-year bond in two years time.
So, if we want to infer f(1), i.e. the YTM of a one-year bond in one-years time, then we look at the pricing of a two-year bond. Given a YTM of 6.8% for a 2-year 10.5% coupon bond, we can calculate the price as being:
Alternatively, the bond price can be determined by discounting the coupon payment by the current YTM for a one-year bond, and by discounting the final payment by both the current rate and the expected rate:...