Money & Banking - ECO 473 - Dr. D. Foster Interest Rates I: The Basics Money & Banking - ECO 473 - Dr. D. Foster

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? Savers Borrowers Policymakers Forecasters Time value of money Liquidity Risk

Maturity date (in n years) Interest Rates & Bonds Bond $ $ $ $ $ $ $$$ mm/yyyy Face value (FV) Maturity date (in n years) Coupons & value (C) We will only consider annual coupons

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

Present & Future Values $1 today is worth more than $1 tomorrow PV shows the “discounted” value of future $ $X in “n” years = $X/[(1+i)n] today FV show the “compounded” value of present $ $X today = $X·(1+i)n in n years 6

Problems You have $1000 now; i=5%, n=18. What is FV? You get $1000 in 9 years; i=7%. What is PV? You get $2000 in 4 years and $500 in 2 years; i=8%. What is the PV? 1000*(1.0518) = $2406 1000/(1.079) = $544 2000/(1.084) + 500/(1.082) = $1470 + $429 = $1899 7

On calculator: FV=1000 PMT=60 PV=-950 n=3 (annual) Compute i Problems If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? $950 = $60 (1+𝑖) + $60 1+𝑖 2 + $60 1+𝑖 3 + $1000 1+𝑖 3 Solve for i: On calculator: FV=1000 PMT=60 PV=-950 n=3 (annual) Compute i i = 7.94% 8

Problems $950 = $60 (1+𝑖) + $60 1+𝑖 2 + $60 1+𝑖 3 + $1000 1+𝑖 3 If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? $950 = $60 (1+𝑖) + $60 1+𝑖 2 + $60 1+𝑖 3 + $1000 1+𝑖 3 Confirm by using i = 7.94% $949.95 $950 = $55.58 + $51.50 + $47.71 + $795.16 9

Problems $950 = $60 (1+𝑖) + $60 1+𝑖 2 + $60 1+𝑖 3 + $1000 1+𝑖 3 If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM? $950 = $60 (1+𝑖) + $60 1+𝑖 2 + $60 1+𝑖 3 + $1000 1+𝑖 3 No financial calculator? Trial & error We know that i > 6% because … At i=7%, PV=$973.76 … too high, so i At i=8%, PV=$948.46 … too low, but close, so i At i=7.9, PV=$950.94 … too high, closer, so … At i=7.92%, PV=$950.45 … almost there! 10

Interest Rates & Bond Pricing $ $ $ $ $ $ $$$ mm/yyyy Face value (FV) Maturity date (in n years) Coupons & value (C) Market price of the bond = present value of income stream discounted at the relevant market interest rate: Special case: Perpetuity Price = C/i

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

Interest Rates, Bonds & the Fed $ $ $ $ $ $ $$$ mm/yyyy Face value (FV) Maturity date (in n years) Coupons & value (C) When the Fed buys bonds, their prices will ___ and interest rates will ___. When the Fed sells bonds, their prices will ___ and interest rates will ___.

Quick Hits A wide spectrum of interest rates: Federal Funds rate Prime rate 30 year bond rate Real interest rate (r)= i -  ( = inflation) Note, this can only be calculated for past. Note, i = re + e (e = expected values for r & ) Irving Fisher

Real and Nominal Interest Rates, 1980-2015 Nominal interest rate on 3 month Treasuries and real interest; derived as (3 month rate - CPI). 15

Bond Pricing Worksheet I A bond has a face value (FV) of $1000, will mature in 2023 and has an annual coupon of $74 and the market rate of interest is 8.1%. What is the current market price of this bond? Suppose that interest rates change such that the current yield on this bond is 7.067%. What will be the market price for this bond? From this find the current market interest rate. Suppose that when the bond was first sold, it’s market price was $1000. What must have been the market rate of interest then? Consider a bond with FV=$1000, maturity = 2025, C=$81 and i=7.25% What is the current price of this bond? 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? The bond in #2 was given to you by your kindly aunt. She told you it matures in 2025, but her eyesight isn’t so good. You take a close look at the bond and see that it matures in 2021. Market i=7.25%. What is the price of this bond? Why is it different than what you calculated in #2a?

iRISKLESS = 3 mo. T-bill rate; RP = risk premium Bond Pricing Worksheet II Four years ago today, Koala, Inc. issued a 10 year bond w/coupon=$55. Initially, the bond sold for $1025. Today it is at $955. The riskless rate of interest four years ago was 4.5%; today it is 4% (including expected inflation). Risk premium: For any bond, i = iRISKLESS + RP iRISKLESS = 3 mo. T-bill rate; RP = risk premium

Bond Pricing Worksheet II Four years ago today, Koala, Inc. issued a 10 year bond w/coupon=$55. Initially, the bond sold for $1025. Today it is at $955. The riskless rate of interest four years ago was 4.5%; today it is 4% (including expected inflation). 1. What was the nominal and current yield on this bond at both times? 2. What was the YTM on this bond at both times? 3. What was the risk premium on this bond at both times? 4. Speculate about why the risk premium would have changed. 5. Suppose that suddenly today the riskless rate falls (from 4%) to 2.5%. a. What will be the new selling price of this bond today? b. Identify the income stream and its present value for this bond for the next 6 years. What do you notice about the sum of these PVs?

Money & Banking - ECO 473 - Dr. D. Foster Interest Rates I: The Basics Money & Banking - ECO 473 - Dr. D. Foster