1. Understanding interest rates
The Economics of Money, Banking, and Financial Markets Mishkin, 7th ed. Chapter 4
Understanding interest rates

2. Present value
The present value of a given future payment is smaller when:
the interest rate is higher, and/or
the payment is further in the future.

3. 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

4. Types of credit market instruments
Simple loan
Fixed-payment loan
Coupon bond
Discount (zero coupon) bond

5. Yield to maturity
Yield to maturity for a debt instrument = the interest rate at which the present value of the payment stream equals the current price of the instrument, i.e., interest rate that equates today’s value with present value of all future payments

6. Yield to maturity – simple loan (i =10%)
$110 – $ $10
i = = = 0.10 = 10%
$ $100

7. Yield to maturity – fixed-payment loan (i =12%)

8. Yield to maturity – coupon bond

9. Yield to maturity – coupon bond
When bond is sold at face value, the yield to maturity = coupon rate
Price of bond and yield to maturity are inversely related
Yield to maturity is greater than the coupon rate when bond price is below the face value

10. Consol (perpetuity)

11. Yield to maturity – discount bond

12. Overview
Current bond prices and interest rates (yields to maturity) are inversely related for all types of bonds.

13. Bond Page of the Newspaper (a)
Current yield=C/P
Change on bid price from yesterday
Both coupon bonds
bond:Maturity>10yrs
note: Maturity<10yrs
For long-term bonds, the YTM is almost the same as current yield, but this is not true for short-term bonds.
Differences represent dealer’s profits

14. Bond Page of the Newspaper (b), (c)
Both discount yields=
((F-P)/F)*(360/days to Mat.)
True discount yield=
((F-P)/P)*(365/days to Mat.)
discount bonds
Maturity<1yr
Change on asked yield from yesterday
Current yield=C/P
Coupon rate 5 5/8
138*$1,000
Mature at 2031

15. Other measures of interest rates
Current yield: ic = C/P ...(7)
P=price of the coupon bond, C=yearly payment
Only accurate for consols
A reasonable approximation to the yield to maturity for bonds with a maturity of 20+ years.
Relatively poor approximation to the yield to maturity for short-term bonds.
A better approximation when the bond price is close to the face value.
Changes in current yield are always in the same direction as changes in the yield to maturity.

16. Other measures of interest rate
idb: yeild on a discount basis, F: face value
P: purchase price of the discount bond
Always understates the yield to maturity since:
this formula uses F instead of P(<F) in denominator
a year (=365 days) has more than 360 days
Changes in the same direction as the yield to maturity. (larger days to maturity has smaller i-idb )

17. Interest rates and rate of return
Rate of return includes capital gains and losses as well as current interest receipts

18. One-year returns on 10%-coupon-rate bond

19. Maturity and the Volatility of Bond Returns
Key Findings from Table 2
1. Only bond whose return = yield is one with maturity = holding period
2. For bonds with maturity > holding period, i  P implying capital loss
3. Longer is maturity, greater is % price change associated with interest rate change
4. Longer is maturity, more return changes with change in interest rate
5. Bond with high initial interest rate can still have negative return if i 
Conclusion from Table 2 Analysis
1. Prices and returns more volatile for long-term bonds because have higher interest-rate risk
2. No interest-rate risk for any bond whose maturity equals holding period

20. Bond prices and rate of return
Rate of return = initial yield to maturity if a bond is held to maturity
Bond prices decline as interest rates rise, leading to capital losses
Long-term bonds exhibit more variability in price in response to interest-rate changes
Longer-term bonds experience more capital gains and losses when interest rates change (interest-rate risk)
A negative return can occur for bonds when the interest rate rise.

21. Real and nominal interest rates
Fisher equation:

22. U.S. Real and Nominal Interest Rates

23. Financial innovation
In January 1997, the U.S. Treasury introduced indexed bonds. Interest and principal payments are adjusted for changes in the price level.