Interest Rates I: Money & Banking - ECO Dr. D. Foster The Basics

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 cares? Time value of money Liquidity Risk Savers Borrowers Policymakers Forecasters

Calculating Interest i N = C/F Nominal yield: i N = C/F i C = C/P Current yield: i C = C/P Yield to maturity (YTM)... interest return if bond held to maturity i = nominal interest rate

Getting 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 bonds present values Relates to discounting into present values PV = $X/[(1+i) n ] PV = $X/[(1+i) n ] PV is the market price, or.....set equation = price and solve for i (which is the YTM) Price = C/i Special case: Perpetuity Price = C/i YTM if P=$950, C=$60, 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·(1+i) n $X today = $X·(1+i) n 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 Values

Price = PV (expected earnings): P = E 1 /(1+i) + E 2 /(1+i) 2 + E 3 /(1+i) Dividends = Earnings in the long run. P = PV(expected dividends) Using interest rates to price stocks Expectations: “Rational Expectations” - use available information and understanding of markets.  P due to  E and/or  i.

Interest Rates & Risk Default risk (Il)liquidity risk “Risk premium” = i - i T-Bill where the T-Bill is the riskless (“safe”) rate. How do you distinguish default from liquidity risk?

 Bond Price will  interest rate Monetary policy: buys  GDP Fed buys bonds - price rises - interest rates fall - spending rises -  GDP sells  Inflation Fed sells bonds - price falls - interest rates rise - spending falls -  Inflation

Some simple bond pricing problems 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 Market i=7.25%. a)What is the price of this bond? Why is it different than what you calculated in #2a?

Quick 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,

Interest Rates I: Money & Banking - ECO Dr. D. Foster The Basics