I
Features of Debt Contract
Fixed maturity
Specified payment schedule
Fixed income obligations paid before equity holder get paid

1. term to maturity
number of years during which the borrower has promised to meet the conditions of the debt
2. Principal: the amount that will be repaid
3. Bullet maturity
   The entire principal can be repaid at the maturity date
4. Balloon payment
  Various amount of the principal can be paid over the life of the debt
5. Par value (maturity value, face value)
  Amount paid at maturity
6. coupon: the periodic interest payment (United States every six months)
7. Zero coupon bonds (instrument)
Deep discounted
Principal and interest paid at maturity
8. Price of most debt contracts are quoted as percent of par value
Example :  par value            1000
                        Price quote         91 ¾ %
                        Price in dollar    1000 X 0.9175 = $917.50
 
 
 

II
basic valuation principles
General formula measuring every securities with different interest rate
 

a1                    a2                                                                              an nP0 = ----------- + ---------------- + ……………………….+ --------------------------------              (1 + r1)      (1 + r1)(1 + r2)                                             (1 + r1)(1 + r2)…..........(1 + rn)  where a1 = cash flow              n = maturity             r1 = one period return Price = the sum of present value (PV) of payments

 
 

III
Return from a bond : YTM measure
How to compare the rate of return of instruments having different cash flows (CFs) and different maturity?
-- YTM (Yield to Maturity)
Definition: the interest rate that makes the PV of CFs equal to the market value (price) of the instrument
 

C1              C2                                                                 Cn Price = ---------- + ---------- + ……………………………+ -----------------              (1 + y)        (1 + y)2                                                          (1 + y)n -- IRR (Internal Rate Return) earned from holding the bond to maturity Assumption  1. Investor will hold the bond to maturity 2. All CFs can be reinvested at the calculated YTM Weakness 1. assume a flat yield curve 2. assume future rates are known

Notes : bond equivalent (annualize yield) – doubling the semiannual yield
 
 
 

IV
Reasons why a bond price will change
 

positive relationship if C increased, P increased value of bond depends on coupon (C), interest rate (Y), maturity (t)

1. A change in the level of interest rate in the economy
Example : if interest rate increased, price decreased
                 If interest rate decreased, price increased
(negatively relationship)
2. Price converges to par at maturity
Overtime, price of discount bond rises
Overtime, price of premium bond declines
3. For a  non-treasuries
Change in yield spread – change in required yield
Risk premium also effect the bond price
4. Change in the perceived credit quality at issue
 
 

IV
Premium par yield

If coupon rate > YTM  -- sell at premium     (P > 100)
If coupon rate < YTM -- sell at discount      (P<100)
If coupon rate = YTM -- sell at par              (P = 100)
 
 

VI
Reinvestment of CFs and yield
-- risk associated with holding bonds

1. Interest rate risk (Price risk)
The risk that a bond will have to be sold at a lose if the bond is not hold to maturity
If the general level of interest rate rises, the price of a bond falls
i increased – price decreased
Negative relationship between interest rate and price
2. Reinvestment risk
Future interest at which the coupon can be reinvested will be less than the YTM – (Future i < YTM)
(YTM assumption : all CFs reinvested at YTM)
Interest on interest and depends on the prevailing i level at the time of reinvestment
higher interest rate is good news for reinvestment
Note: zero coupon bond: no investment risk
i increased – price increased
Positive relationship between interest rate and price
 
 

VII
Bond Price volatility

1. Review of Price / Yield
Bond price changes in the opposite direction from the change in yield
 

non linear (not 450), asymmetric and convex

2. Measure of Price volatility
The price sensitivity of a bond to a change in yield
Duration

Duration
(a) weighted average term to maturity to the components of a bond CFs in which the time of receipt of each payment is
     weighted by the PV of that payment
(b) weighted average term to maturity where the CFs are in term of their PV

Properties of Duration
1. Coupon
Bond with higher coupon rate has a shorter duration (more weight is being given to coupon payment)
2. Duration of band < time to mature
3. Yield
As market yield increased, duration decreased (weighting of CFs will be more heavily placed on the early CFs – duration
   decreased)
 
 
 

Definition
measure of the weighted average life of a bond (the approximately percent change in price for small change in Y)
 
 

FACT

LT bond -- D decreased
coupon increased -- D decreased (more weighted to coupon)
yield increased -- D decreased

lower weight on CFs in the far future

Limitation
local approximation
assume parallel shift in Y.C