Interest Interest

Rates I:Rates I:

Money & Banking - ECO 473 - Dr. D. Foster

The The BasicsBasics

What is interest?What is interest?

Payment made to savers to compensate them for foregoing consumption.

“The most powerful force in the universe is compound interest.”

Interest rates embody our expectations of the future.

What affects interest? Who What affects interest? Who cares?cares?

Time value of money

Liquidity

Risk

Savers

Borrowers

Policymakers

Forecasters

Calculating InterestCalculating Interest

Nominal yield: iiNN = C/F = C/F

Current yield: iiCC = C/P = C/P

Yield to maturity (YTM) . . . interest return if bond held to maturity

ii = nominal interest = nominal interest raterate

Getting from bond purchases to interest ratesGetting from bond purchases to interest rates

Face value (FV)

$$$

mm/yyyy

$ $ $ $ $ $

Bond

Maturity date(in n

years)

Coupons & value

(C)

When the Fed buys bonds, their prices will ___ and interest rates will ___.sells

• Usually, we talk of annual coupons• Market price of the bond = present value of income

stream discounted at interest rate i :

Using interest rates to price Using interest rates to price bondsbonds

Relates to discounting into present valuespresent values

PV = $X/[(1+i)PV = $X/[(1+i)nn]]

PV is the market price, or . . . . .set equation = price and solve for i (which is the YTM)

Special case: Perpetuity Price = C/iPrice = C/i

YTM if P=$950, C=$60, YTM if P=$950, C=$60, n=3?n=3?

$1 today is worth more than $1 tomorrow

PV shows the “discounted” value of future $

FV show the “compounded” value of present $

$X$X today = $X$X··(1+i)(1+i)nn in n years You have $1000 now; i=5%, n=18. What is FV? You get $1000 in 9 years; i=7%. What is PV?

Present & Future ValuesPresent & Future Values

Price = PV (expected earnings):

P = EP = E11/(1+i) + E/(1+i) + E22/(1+i)/(1+i)22 + E + E33/(1+i)/(1+i)33 + ... + ...

Dividends = Earnings in the long run. P = PV(expected dividends)

Using interest rates to price Using interest rates to price stocksstocks

Expectations:Expectations: “Rational Expectations” - use

available information and understanding of markets.

P due to E and/or i.

Interest Rates & RiskInterest Rates & Risk

Default risk

(Il)liquidity risk

“Risk premium” = i - iT-Bill where the T-Bill is the riskless (“safe”) rate.

How do you distinguish default from liquidity risk?

Bond Price will Bond Price will interest rate interest rate

Monetary policy:

Fed buysbuys bonds - price rises - interest rates fall - spending rises - GDP GDP

Fed sellssells bonds - price falls - interest rates rise - spending falls - Inflation Inflation

Some simple bond pricing Some simple bond pricing problemsproblems

1. A bond has a face value (FV) of $1000, will mature in 2022 and has an annual coupon of $74 and the market rate of interest is 8.1%.a) What is the current market price of this bond?

b) Suppose that the current market interest rate falls to 6.54%. What will be the new market price for this bond?

c) Suppose that when the bond was first sold, it’s market price was $1000. What must have been the market rate of interest then?

2. Consider a bond with FV=$1000, maturity = 2024, C=$81 and i=7.25%a) What is the current price of this bond?

b) If the Fed jumps into the bond market, even though it just buys U.S. Treasuries, it will affect all interest rates to some extent. If they buy lots of bonds and interest rates fall to 6.88%, what will happen to the price of your bond?

3. The bond in #2 was given to you by your kindly aunt. She told you it matures in 2024, but her eyesight isn’t so good. You take a close look at the bond and see that it matures in 2020. Market i=7.25%.a) What is the price of this bond? Why is it different than what you calculated in #2a?

Quick HitsQuick Hits

A wide spectrum of interest rates: Federal Funds rate Prime rate 30 year bond rate

Real interest rate (r)= i - Note, this can only be calculated for past. Note, i = r + e (real return + exp. infl.)

Real and Nominal Interest Rates, 1960-2007

Interest Interest

Rates I:Rates I:

Money & Banking - ECO 473 - Dr. D. Foster

The The BasicsBasics