Week One B Flashcards
What do interest rates do as a mechanism (3)
Link the present to the future
Tell the future reward for lending today
Tell the cost of borrowing now and repaying later
What is future value
the value on some future date of an investment made today.
What is future value equation
FV =PV +PV ×(i)=PV ×(1+i)
The higher the interest rate or the higher the amount invested the higher the future value
What is the equation of future value with compound interest
FV = PV × (1 + i)^n
What is present value
The value today of a payment that is promised to be made in the future
What is the present value equation
PV = FV/ (1+i)^n
When is present value higher
- The higher future value of payment, FV
- the shorter time until payment, n
- the lower the interest rate, i
Doubling the future value of the payment, without changing the time of the payment or the interest rate, doubles the present value.
How are high interest rates and present value connected
Higher interest rates are associated with lower present values no matter the size or timing of the payment
What is a bond
- A bond is a promise to make a series of payments on specific future dates.
- Bonds create obligations, and are therefore thought of as legal contracts that:
Require the borrower to make payments to the lender, and
specify what happens if the borrower fails to do so.
How much should you be willing to pay for a bond?
The price of a bond depends on the bond characteristics.
What is a zero coupon bond
single future payment.
What is a fixed payment loans
Sequence of fixed payments
What are coupon bonds
periodic interest payments + principal repayment at maturity.
What are consol or perpetuity bonds
like coupon bonds whose payments last forever
What is a zero coupon bond
- They represent a pro use to pay a certain amount on a fixed future date
- there price is less than their face value as they sell at discount
- the price is the present value
Price of one year zero coupon bond
Face value / (1+i)
What is the price of s six month zero coupon bond
Face value /(1+)^1/2
What is an example of a fixed payment loan
Conventional home mortgages and car loans are fixed-payment loans.
What is a fixed payment loan equation
Fixed payment / (1+i) …..the sum of the present value of the payments
What is a coupon bond
The issuer of a coupon bond promises to make a series of periodic interest payments (coupon payments), plus a principal payment at maturity.
What is the coupon bond equation
Coupon payment/ (1+i)
What is a consol or perpetuity bonds
The issuer of a perpetuity promises to make a series of periodic interest payments forever.
Consol or Perpetuity equation
Yearly Coupon Payment/ i
How do we determine the return to an investment based on a bonds price
By combining information about the promised payments with the bond’s price to obtain the yield
What does yield represent in the context of investing?
Yield serves as a measure of both the cost of borrowing for the issuer of the bond and the reward for lending for the bondholder.
Can yield and interest rate be used interchangeably?
Yes, in the context of bonds and other fixed-income securities, yield and interest rate are often used interchangeably to refer to the return on investment.
What is the nominal yield of a bond?
The nominal yield is the stated rate of the bond.
Why is yield to maturity considered the most useful measure of the return on holding a bond?
Yield to maturity represents the yield bondholders receive if they hold the bond to its maturity when the final principal payment is made.
Define current yield
Current yield is the interest rate of the bond given its current price, calculated as Yearly Coupon Payment divided by Price Paid. It measures the return from buying the bond that arises solely from the coupon payments.
Current yield equation
Yearly coupon payment / price paid
What is the fundamental property of a bond regarding its price and the required yield?
A fundamental property of a bond is that its price changes in the opposite direction to the change in the required yield.
Why does the price of a bond move inversely to changes in yield?
The price of the bond is the present value of its cash flows. As the required yield increases, the present value of future cash flows decreases, leading to a decrease in bond price. Conversely, as the required yield decreases, the present value of future cash flows increases, leading to an increase in bond price.
The price of a bond moves inversely to changes in yield due to the relationship between bond prices and interest rates. When interest rates rise, newly issued bonds offer higher yields to investors, making existing bonds with lower yields less attractive. As a result, the prices of existing bonds decrease to make their yields more competitive with the new bonds.
Conversely, when interest rates fall, newly issued bonds offer lower yields, making existing bonds with higher yields more attractive. This increased demand for higher-yielding existing bonds causes their prices to rise.
What happens to the yield to maturity when the bond price increases?
When the bond price increases, the yield to maturity decreases
Par bond
Bond Price = Face value (par value): Coupon rate = Current yield = Yield to maturity
Discount Bond
Bond price < Face value (par value): Coupon rate < Current yield< Yield to maturity
Premium bond
Bond price > Face value (par value): Coupon rate > Current yield > Yield to maturity
What is Holding Period Return (HPR)?
Holding Period Return is the return of holding a bond and selling it before maturity.
How does Holding Period Return (HPR) differ from yield to maturity?
HPR can differ from yield to maturity because it accounts for capital gains or losses when selling the bond before maturity, whereas yield to maturity assumes holding the bond until maturity.
What happens whenever the price of a bond changes?
Whenever the price of a bond changes, there is a capital gain or loss associated with the price change.
Why does the importance of Holding Period Return increase with larger price changes?
The greater the price change of a bond, the more significant the impact on the overall return, making Holding Period Return more important to consider.
How does the term of the bond affect price movements and associated risks?
The longer the term of the bond, the greater the potential for price movements and associated risks due to changes in interest rates and market conditions.
Fisher equation
I = r + πe
- The nominal interest rate you agree on (i) must be based on expected inflation (πe) over the term of the loan plus the real interest rate you agree on (r).
The higher expected inflation, the higher the nominal interest rate.
Real interest rate equation
R= i - πe
