chapter 10: the meaning of interest rates Flashcards
present value meaning?
a dollar paid to you one year from now is less valuable than a dollar paid to you today
simple interest rate example?
the interest rate of a simple loan
Loan $100 today and require $110 repayment in one year
The simple interest rate is 10%
Simple Present Value formula
PV = FV / (1 + i)^n
simple loan
One payment at the maturity date
Fixed Payment Loan
Multiple fixed payments at pre-specified dates
Coupon Bond
A bond that pays fixed amounts (the coupons) at fixed dates
plus a final payment (the face value) at maturity
discount bond
A bond that pays zero coupons, only a final payment at maturity
“Discount” since price typically less than face value.
Four Types of Credit Market Instruments
- Simple Loan
- Fixed Payment Loan
- Coupon Bond
- Discount Bond
the most important way to calculate interest rates?
the yield to maturity
the yield to maturity
the interest rate that equates the present value of all cash flow payments received from a debt instrument with its value today (the current price)
yield to maturity example with simple loan: If today’s value is $100 and the payment due in one year’s time is $110, what is the yield to maturity
then the yield to maturity is 10%
fixed payment loan formula
PV = PMT · (1-(1 + i)^n) / i
coupon bond formula
C / (1 +i)^n + F / (1 +i)^n = P
P = price of coupon bond
C = yearly coupon payment
F = face value of the bond
n = years to maturity
Three Facts About Coupon Bonds
- When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate
- The price of a coupon bond and the yield to maturity are negatively related
- The yield to maturity is greater than the coupon rate when the bond price is below its face value
Consol or Perpetuity formula
Pc = price of the consol
C = yearly interest payment
ic = yield to maturity of the consol
ic = C/Pc
Consol or Perpetuity definition
A bond with no maturity date that does not repay principal but pays fixed coupon payments forever
interest of discount bound formula
i = (F - P) / P
rate of return
How well a person does financially by holding a bond for some period of time
The return (R) depends on coupons received (C) and the price for which the bond is eventually sold
what is the formula for the return that depends on coupons?
R = C/Pt + (Pt+1 - Pt)/Pt
C/Pt = current yield = ic
(Pt+1 - Pt)/Pt = rate of capital gain = g
when does the return equal equals the yield to maturity?
only if the holding period equals the time to maturity
what does a rise in interest rate mean in a bond price? does it lead to capital gain or loss if time to maturity is longer than holding period?
with a fall in bond prices
results in a capital loss
when is the size of the percentage price change increasingly associated with an interest-rate change
The more distant a bond’s maturity
an increase In interest rate will bring a bigger or larger rate of return when the bond’s maturity is most distant?
The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate
can a bond’s return be negative if the interest rate rises?
yes
interest-rate risk
The risk level associated with an asset’s return that results from interest-rate change
what has more interest risk?
long-term bonds
which types of bonds has no interest-risks
any bond whose time to maturity matches the holding period
Nominal interest rates
make no allowance for inflation
real interest rates
adjust for changes in price level
more accurately reflects the cost of borrowing
Ex ante real interest rate
is adjusted for expected changes in the price level
Ex post real interest rate
is adjusted for actual changes in the price level
Fisher Equation
i = r + pi^e
according to the fisher equation, when do you have more I centavos to borrow?
when interest rates are low
when do lenders have less incentive to lend according to fisher’s equation?
when interest rates are low
