Econ 160: Chapter 4: Meaning of Interest Rate

Fisher Equation

Nominal Interest Rate = Real Interest Rate + Expected Inflation

when real interest rate is low

there are greater incentives to borrow and fewer incentives to lend

distinction between interest rates and returns

returns will differ substantially from interest rate if price of bond experiences sizable fluctuations producing capital gains/losses

principal

the amount of funds the lender provides the borrower that must be repaid at maturity date

internal finance

using company's retained earnings to pay for investment Cost -opportunity cost of your investment (other main use for retained earning is to lend them at the same rate at which you could borrow)

search for yield

when market interest rates low, investment managers try to generate high interest payment to clients by taking greater risks Possible Results 1. bid up prices of risky securities 2. depress market compensation for risk below sustainable level Housing Crisis -plunge of corporate mortgage security prices highlighted how forcefully markets can reprice risk when search for yield goes too far

coupon rate

the dollar amount of the yearly coupon payment expressed as a percentage of the face value of a coupon bond YTM -captures difference in price and money received at maturity date P > FV : YTM < coupon rate P < FV : YTM > coupon rate

If interest rates rise.

the losses on a long term bond will exceed the losses on a short term bond the further in future the promised payment the more the present value falls when interest rates rise

golden rules

the sooner a payment is to be made, the more it is worth

What can prompt underestimation of risk?

1. Misjudging Interest Rate Risk -extrapolating from recent patterns and not paying attention to more distant past when judging rates 2. Misjudging Default Risk -extrapolation from recent experience leads to misjudging default risk ex) during economic expansions, defaults relatively infrequent so investors can become accustomed to unsustainably low corporate default rates 3. Investment Advisor fraud -investors underestimating risk if managers take risks not evident or purposely concealed

Discounting Important Points

1. Present value sometimes called "present discounted value" 2. The further in future payment received, smaller its present value 3. The higher the interest rate to discount future payments, the smaller the present value 4. The higher the future value of payment the higher the present value 5. Present value of series of future payments simply sum of the discounted value of each individual payment

two applications of present value

1. internal rate of return/yield to maturity 2. valuation of bonds

Important Facts about returns

1. return equals YTM only if holding period equals time to maturity 2. rise in interest rates associated with fall in bond prices -leads to capital loss if time to maturity longer than holding period 3. more distant a bond's maturity date, the greater size percentage price change associated with interest rate change (interest rate risk) 4. interest rates do not always have to be positive

4 types of credit market instruments

1. simple loan 2. fixed payment loan 3. coupon bond 4. discount bond

inverse relationship between ytm and bond price reasoning

1. think of YTM as discount rate 2. think of i as return/risk - higher risk = lower bond price 3. i in denominator

fixed-payment loan (fully amortized loan)

Definition -lender provides borrower with amount of funds that borrower must repay making same payment consisting of part of the principle and interest every period Cash flow -same payment containing part of principle and interest payment Timing -periodical Formula LV = FP / (1+i) + .... + FP / (1+i)^n ex) installment loans and mortgages

Simple Loan

Definition -lender provides borrower with funds (principle) that must be repaid at maturity date along with additional payment for interest Cash Flow -principle + interest payment Timing -maturity date ex) money market instruments like short term commercial loans IRR/Yield to Maturity -equal to simple interest rate

Rise in interest rates associated with fall in bond prices if holding period shorter than maturity time

Intuition 1. already purchased the bonds in pervious periods with lower interest rate 2. coupon bond is fixed and selling when interest rate higher you should sell bond at discounted price -similar bonds that have issued in later periods give investors higher interest rates 3. to compensate for fact that you have lower interest rates, you should ask for lower price

Underestimation

investors underestimate risk of particular assets ex) investors lacking sufficient regard for risk seek higher yield bonds even if riskier due to longer maturity date or higher default possibility

current yield

a bond's annual coupon divided by its price i = C / P equal to yield to maturity with longer term to maturity than 20 years (infinite in theory) -good approximation

real interest rate

adjusted for changes in price level so it more accurately reflects the cost of borrowing -better indicator of incentives to borrow and lend

ante vs. post real interest rate

ante real interest rate -adjusted for expected changes in price level post real interest rate -adjusted for actual changes in price level

consol/perpetuity (coupon bond)

bond with no maturity date that does not repay principle buy pays fixed coupon payments forever P = C / i P = price consol C = yearly interest payment i = yield to maturity

Zero Coupon Bond (Discount Bond)

definition -bought at price below face value and face value repaid at the maturity date -does not make any interest payments cash flow -face value Timing -maturity date YTM/IRR formula i = (F - P) / P -YTM negatively related to the bond price ex) US treasury bills and saving bonds

rate of return

definition -how well person does financially by holding a bond or security for particular time period -the amount of each payment to the owner plus the change in the security's value expressed as a fraction of its purchase price -when holding period is different than maturity date formula ROR = (amount of payment + change in security price) / (security purchase price) formula 2 R = I + g I = current yield rate g = capital gain rate

Coupon Bonds

definition -pays the owner of bond a fixed interest payment every year until maturity date when a specified final amount (face value/par value) repaid Cash flow -coupon payments and face value (par value) Identification 1. bond's face value 2. corp/agency that issues bond 3. maturity date 4. coupon rate Formula P = C / (1+i) +....+ C / (1+i)^n + F / (1+i)^n Characteristics 1. when coupon bond priced at face value, YTM equals coupon rate 2. price of bond and YTM negatively related 3. when bond priced below face value, YTM greater than coupon rate Timing -payment paid periodically and face value paid at maturity date

cash flows

different debt instruments have very different steams of cash payments to the holder with different timing -must understand how to compare value of one kind of debt instrument to another -use this with concept of present value

rate of capital gain

g = (P(t+1) - P(t)) / P(t)

external finance

going to capital market and issuing bonds or to the money market and issuing commercial papers or bank loans

change in interest rates

have no effect on the price at the end of the holding period if maturity time matches holding period

nominal interest rate

ignores the effects of inflation on real costs of borrowing

internal rate of return/yield to maturity

interest rate that equates the present value of an investment with its cost -investment will be profitable if its internal rate of return exceeds the cost of borrowing -interest rate that equates present value of cash flow payments with its value today Solving -sum the present value of each yearly revenue and equate it with machine cost -internal rate of return equation virtually identical to loan equation Key to understand 1. equating today's value (price) of debt instrument with present value of all its future cash flow payments

risk free rate

market interest rate embedded into construction of yield to maturities securities interest rate (YTM) = risk free rate + risk premium

long terms bonds are

more sensitive than short term bonds to the risk that interest rates will change

interest rate risk

prices and returns for long term bonds more volatile than those for shorter term bonds -no interest rate risk for bond whose time to maturity matches holding period -price at end of holding period already fixed at face value Reasoning 1. higher the interest rate we use to discount future payments, smaller the present value of payments 2. further in future payment is received, smaller its present value

present value

process of calculating today's value of dollars received in the future -called discounting the future amount that must be invested today to realize specific amount on given future date value today of a payment promised to be made in the future -amount that must be invested today to realize specific amount on given future date additive (the value of whole is the sum of the value of its parts)