文档介绍：Chapter 4
Understanding
Interest Rates
1
Four Types of Credit Instruments
1. Simple loan
2. Fixed-payment loan
3. Coupon bond
4. Discount (zero coupon) bond
Concept of Present Value
Simple loan of $1 at 10% interest
Year 1 2 3 n
$ $ $ $1x(1 + i)n
$1
PV of future $1 =
(1 + i)n
Present Value
2
Yield to Maturity: Loans
Yield to maturity = interest rate that equates today’s value with present value of all future payments
1. Simple Loan (i = 10%)
$100 = $110/(1 + i)
$110 –$100 $10
i = = = = 10%
$100 $100
2. Fixed Payment Loan (i = 12%)
$126 $126 $126 $126
$1000 = + + + ... +
(1+i) (1+i)2 (1+i)3 (1+i)25
FP FP FP FP
LV = + + + ... +
(1+i) (1+i)2 (1+i)3 (1+i)n
3
Yield to Maturity: Bonds
4. Discount Bond (P = $900, F = $1000), one year
$1000
$900 =
(1+i)
$1000 –$900
i = = = %
$900
F – P
i =
P
3. Coupon Bond (Coupon rate = 10% = C/F)
$100 $100 $100 $100 $1000
P = + + + ... + +
(1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10
C C C C F
P = + + + ... + +
(1+i) (1+i)2 (1+i)3 (1+i)n (1+i)n
Consol: Fixed coupon payments of $C forever
C C
P = i =
i P
4
Relationship Between Price and Yield to Maturity
Three Interesting Facts in Table 1
1. When bond is at par, yield equals coupon rate
2. Price and yield are negatively related
3. Yield greater than coupon rate when bond price is below par value
5
Current Yield
C
ic =
P
Two Characteristics
1. Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond
2. Change in current yield always signals change in same direction as yield to maturity
Yield on a Discount Basis
(F – P) 360
idb = x
F (number of days to maturity)
One year bill, P = $900, F = $1000
$1000 –$900 360
idb = x = = %
$1000 365
Two Characteristics
1. Understates yield to maturity; longer the maturity, greater is understatement
2. Change in discount yield always signals change in same direction as yield to maturity
6
Bond Page of the Newspaper
Distincti