chapter 10: understanding interest rates Flashcards
yield to maturity
the most accurate measure of interest rates
what economists mean when they use the term interest rate
streams of cash payments to the holder
cash flows
present value or present discounted value
based on the commonsense notion that a dollar paid to you one year from now is less valuable to you than a dollar paid to you today
In this loan, the lender provides the principal that must be repaid to the lender at the maturity date along with an additional payment for the interest
a simple loan
simple interest rate
the interest payment divided by the amount of the loan
The process of calculating today’s value of dollars received in the future
discounting the future
using PV
FV
forumla to calculate PV
PV = FV / (1 + i)^n
four basic types of credit market instruments
A simple loan
fixed-payment loan (fully amortized loan)
a coupon bond
A discount bond
fixed-payment loan (fully amortized loan)
the lender provides the borrower with an amount of funds, which must be repaid by making the same payment every period (such as a month)
must pay the debt service you already know
a coupon bond
pays the owner of the bond a fixed interest payment (coupon payment) every year until the maturity date
at the maturity date, a specified final amount is repaid
face value or par value of a bond
amount you have to repay at the maturity date
three pieces of information that define a bond
- the corporation or government agency that issues the bond
- the maturity date of the bond
- the bond’s coupon rate
the bond’s coupon rate
the dollar amount of the yearly coupon payment expressed as a percentage of the face value of the bond
A discount bond (also called a zero-coupon bond)
bought at a price below its face value (at discount)
the face value is repaid at the maturity date
bond bought at discount
bought at a price below its face value
most important way of calculating interest rates
the yield to maturity
the yield to maturity
the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today
the internal rate of return required for the present value of all the future cash flows of the bond (face value and coupon payments) to equal the current bond price
for which loan does the simple interest rate equals the yield to maturity?
for the simple loan
formula of loan with payment to give (present value)?
LV = PMT * (1 - (1 + r)^(-n))/r
LV = loan value
formula of coupon bond
P = C / (1 + i)^n + F / (1 + i)^n
C = yearly coupon payment
F = face value of bond
P = price of bond
when the the yield to maturity equals the coupon rate of a coupon bond, whats its price?
coupon bond priced at its face value
when the the yield to maturity is greater than the coupon rate of a coupon bond, whats its price?
the bond price is below its face value
when the the yield to maturity is below than the coupon rate of a coupon bond, whats its price?
the bond price is above its face value
what do we mean when we say that he price of a coupon bond and the yield to maturity are negatively related?
as the yield to maturity rises, the price of the bond falls
As the yield to maturity falls, the price of the bond rises
consol or a perpetuity
a perpetual bond with no maturity date and no repayment of principal that makes fixed coupon payments of $C forever
formula of perpetuity
Pc = C / ic
Pc = price of perpetuity
C = yearly payment
ic = yield to maturity
current yield
the yearly coupon payment divided by the price of the security
ic = C / Pc
Pc = price of perpetuity
C = yearly payment
ic = yield to maturity
The yield-to-maturity calculation for a discount bond
similar to that for the simple loan
PV = FV / (1 + i)^n
rate of return
For any security, the rate of return is defined as the payments to the owner plus the change in its value
expressed as a fraction of its purchase price
will the return on a bond necessarily equal the yield to maturity on that bond?
nah bruuuv
the distinction between interest rate and return can be important
formula for rate of return on a coupon bond
RET = (C + Pt+1 - P1) / (Pt)
RET + return from holding the bond from time t to time t + 1
Pt = price of the bond at time t Pt+1 = price of the bond at time t + 1 C = coupon payment
RET = (C / P) + ((P+1 - P) / P)
first term C/P is the current yield ic (the coupon payment over the purchase price)
The second term is the rate of capital gain
RET= ic + g
g = he rate of capital gain
what does a rise in interest mean for someone holding a bond?
the price of the bond has fallen
if he sells it then, it will result in a capital loss
what does the finding that the prices of longer-maturity bonds respond more dramatically to changes in interest rates explain?
prices and returns for long-term bonds are more volatile than those for shorter-term bonds
long term bonds are riskier
interest-rate risk
the riskiness of an asset s return that results from interest-rate changes
which have a more important interest-rate risk, long term or short term bonds?
long term bonds
which types of bonds have no interest-rate risk? why?
any bond whose time to maturity matches the holding period
the price at the end of the holding period is already fixed at the face value
he change in interest rates can then have no effect on the price at the end of the holding period for these bonds
he return will therefore be equal to the yield to maturity known at the time the bond is purchased
nominal interest rate
interest rate disregarding inflation rate
real interest rate
the interest rate that is adjusted by subtracting inflation
it more accurately reflects the true cost of borrowing
ex post real interest rate
The interest rate that is adjusted for actual changes in the price level
Nominal interest rate - inflation rate
describes how well a lender has done in real terms after the fact
real interest rate equation (Fisher equation)
i = ir + pi^e
i = nominal interest rate
ir = real interest rate
pi^e = expected rate of inflation
ir = i - pi^e
indexed bonds
interest and principal payments are adjusted for changes in the price level
Ex ante real interest rate
Nominal Interest rate - expected inflation rate
