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presentation chapter 6
Admin on Tue Dec 16, 2008 1:21 am
Learning Objectives
To learn how money market interest rates are determined, and how those interest rates are used by dealers when trading money market assets.
To explore the important relationships between the interest rates on bonds and other financial instruments and their market value or price.
To look at the many different ways lending institutions calculate interest rates they charge borrowers for loans.
To determine how interest rates or yields on deposits in banks, credit unions, and other depository institutions are figured.
introduction
Many different interest-rate measures attached to different types of financial assets have been developed, leading to considerable confusion, especially for small borrowers and savers.
We will examine the methods most frequently used to measure interest rates and the prices of financial assets in the money and capital markets.
Units of Measurement For Interest Rates
The Interest rate is the price charged to a borrower for the loan of money
Interest Fee required by the lender for
rate on = the borrower to obtain credit X 100
loanable :Amount of credit made
funds available to the borrower
Interest rates usually expressed as annualized percentages
360-day and 365-day years are common
Compounding terms may also differ
A basis point equals 1/100 of a percentage point.
Example
10.5% = 10% + 50 basis points, or 1050 basis points
Interest Rates in the Wholesale Money Markets
Wholesale money market
Lending for short period of time
Large sums of money
Market details in Chapter 10 and 11
This chapter
How interest rates are computed on these assets
How are interest rates reported in the financial press
Computing Interest Rates on Money Market Assets
Most money market assets have similar characteristics
Rate of return on money market instrument
The formula for the actual annualized rate of return for a single year:
Investment rate(IR)
= Par value – Purchase price 365
_________________________ X____________________
Purchase price Days to maturity
In the money market a different rate is quoted
Bank discount rate (DR)
Not the actual annualized rate of return
Used as trading standard
Easier to estimate than IR
Use face value in denominator instead of price
Use 360 rather than 365 days
Holding-Period Yield on Money Market Assets
Financial assets sold at a discount
The holding period yield (HPY) on assets sold at a discount is:
HPY = DR at purchase +/- Change in DR over holding period
Change in DR over holding period=
(Initial days to maturity-Days held) x Difference in DR
_____________________________
Days Held
Difference in DR is the change in the CR between when the asset is purchased and when it is sold
Interest Rate Quotations on US Treasury Bills
Treasury bills are money market assets
Issued by the U.S. government
Various maturities
4 weeks
3 months
6 months
Daily report of information on the bills
Various financial sources
For each maturity
Security dealers who act as “market makers” usually quote two prices
The higher ask price is the dealer’s selling price
The lower bid price is the dealer’s buying price
The difference between the bid and ask prices is the spread – the dealer’s return for creating a market
Interest Rates on Bonds and Other Long-Term Debt Securities
Yield to maturity (YTM) of a financial asset
The rate of interest that the market is currently prepared to pay for the financial asset
It is the rate that equates the purchase price (P) with the present value the stream of coupon payments (C) by the asset
Coupon = Coupon rate * Par value
Adjustments for non-annual rates
Include a parameter k, the number of times during the year that the interest income is paid to the investor
Measures of the Rate of Return (Yield) On a Financial Asset
The holding-period yield is an investment rate of return
Over its actual or planned holding period
It is the discount rate (h) equalizing the purchase price (P) of a financial asset with all the discounted annual payments (C) received until the asset is sold at time m for price Pm
Understanding Yield to Maturity
Example
A 5-year corporate bond has a face value of $1,000. Its promised a annual coupon rate is 10% and it pays $50 in interest every 6 months. The bond is currently selling for $900
Price Quotations on U.S. Treasury Notes and Bonds
U.S. Treasury notes (T-notes) and U.S. Treasury bond (T-bonds)
Original maturities of 2 years to 30 years
Most are fixed payments
Typically semi-annually
Need to know
Price and maturity
Date coupons paid
Amount of coupon payments
Current yield to maturity
The current yield of a financial asset is the ratio of the annual income (dividends or interest) generated by the asset to its market value.
Example
The current yield of a share of common stock selling for $30 in the market and paying an annual dividend of $3 to the shareholder is $3/$30 = 0.10, or 10%
Characteristics
Price quotes are on $100 of par value
Quoted in 32nd of a dollar
Annualized rate
Price quotations provided in financial press
Including daily trading activity
Often including bid and asked prices
Price Quotations on Corporate Bonds
Price quotes on corporate bonds are similar
Same basic information required
However the need to consider risk
Unlike what is assumed for the US government, some borrowers may default on all or a portion of their promised payments
The market value of the risky asset may rise or fall
Investors require greater returns to compensate them for this risk
Yield-Asset Price Relationships
The price of a financial asset (especially debt securities) and its rate of return are inversely related
A rise in yield implies a decline in price, and vice versa
Investing funds in financial assets can be viewed from two different perspectives
The borrowing and lending of money
The buying and selling of financial assets
Rates of Return on Perpetual Financial Instruments
Some financial instruments never mature
Perpetuity financial instruments
May be fixed-income
Equal payments to its holder every year
Ad infinitum
May be variable-return
Corporate stock
Future payments may change over time
Perpetuity rate
Annual rate of return on a perpetual financial instrument =
Annual cash flow promised
_______________________________--
current price or present value
Or
Current Price =Annual cash flow promised
_______________________
Annual rate of return
Key points to consider
An infinite stream of cash flows has a finite value
There is an inverse relationship between the current price and the rate of return
This can be weaker than for bonds
It does not always hold for common stock
Stock pricing formula
D0 is current dividend
EDi is expected future dividend at time I
R is the minimum rate of return required by a company’s shareholders
SP is the company’s sTOCK PRICE
Price Quotation in Corporate Stocks
There are many professional analysts examining stocks. They can provide information by trading stocks
Interest Rates Charged or Paid by Institutional Lenders
Simple interest method
Assesses interest charges on a loan only for the period of time that the borrower has actual use of the borrowed funds
Interest = principal x rate x term
The more frequently a borrower makes repayments on a loan, the less the total interest
Add-on interest method
Discount loan method
Determines the total interest charged to the customer on the basis of the amount to be repaid
Loan proceeds are only the difference between the total amount owed and the interest bill
Hence, the effective interest rate is
Interest paid
__________________ x 100
Net loan proceeds
Monthly payments of a home mortgage loan
First covers in full the monthly interest on the outstanding principal
The remainder is then applied to the principal of the loan
Annual Percentage Rate
The U.S. Consumer Credit Protection Act of 1968 (Truth in Lending)
Requires lending institutions to calculate and tell the borrower the annual percentage rate (APR)
Rate borrower actually pays
APR measures the yearly cost of credit
Interest costs
Transaction fees or service charges imposed by the lender
Compound Interest
The compounding of interest means that the lender or depositor earns interest income on both the principal and accumulated interest
The formula for calculating the future value of a financial asset earning compound interest is:
APY on Deposits
The U.S. Truth in Savings Act of 1991
Chapter Review
Introduction
Units of measurement for interest rates and asset prices
Calculating and quoting interest rates
Basis points
Prices of stocks and bonds
Measures of the rate of return, or yield, on a loan, security, or other financial asset
Rate of return on a perpetual financial instrument
Coupon rate
Current yield
Yield to maturity
Holding-period yield
Bank discount rate
Yield-asset price relationships
Interest rates and the prices of debt securities
Interest rates and stock prices
Interest rates charged by institutional lenders
To learn how money market interest rates are determined, and how those interest rates are used by dealers when trading money market assets.
To explore the important relationships between the interest rates on bonds and other financial instruments and their market value or price.
To look at the many different ways lending institutions calculate interest rates they charge borrowers for loans.
To determine how interest rates or yields on deposits in banks, credit unions, and other depository institutions are figured.
introduction
Many different interest-rate measures attached to different types of financial assets have been developed, leading to considerable confusion, especially for small borrowers and savers.
We will examine the methods most frequently used to measure interest rates and the prices of financial assets in the money and capital markets.
Units of Measurement For Interest Rates
The Interest rate is the price charged to a borrower for the loan of money
Interest Fee required by the lender for
rate on = the borrower to obtain credit X 100
loanable :Amount of credit made
funds available to the borrower
Interest rates usually expressed as annualized percentages
360-day and 365-day years are common
Compounding terms may also differ
A basis point equals 1/100 of a percentage point.
Example
10.5% = 10% + 50 basis points, or 1050 basis points
Interest Rates in the Wholesale Money Markets
Wholesale money market
Lending for short period of time
Large sums of money
Market details in Chapter 10 and 11
This chapter
How interest rates are computed on these assets
How are interest rates reported in the financial press
Computing Interest Rates on Money Market Assets
Most money market assets have similar characteristics
- Short-term
Receives no income until asset matures
At maturity receive par value (face value)
Must pay less than par to purchase security
Return is price appreciation
Assets sold at a discount to par value
Rate of return on money market instrument
- Coupon-equivalent (or bond-equivalent of investment rate) rate of return
Need three pieces to estimate
Par value
Number of days to maturity
Purchase price
The formula for the actual annualized rate of return for a single year:
Investment rate(IR)
= Par value – Purchase price 365
_________________________ X____________________
Purchase price Days to maturity
In the money market a different rate is quoted
Bank discount rate (DR)
Not the actual annualized rate of return
Used as trading standard
Easier to estimate than IR
Use face value in denominator instead of price
Use 360 rather than 365 days
Holding-Period Yield on Money Market Assets
Financial assets sold at a discount
- Price tends to rise over time
Price exactly equal to part at maturity
Prices do not rise at a steady, uniform rate
Price changes will be impacted by continuous changes in the market interest rates
If you hold to maturity, you lock in a nominal return
If you sell early, then price fluctuations impact your investment return
The holding period yield (HPY) on assets sold at a discount is:
HPY = DR at purchase +/- Change in DR over holding period
Change in DR over holding period=
(Initial days to maturity-Days held) x Difference in DR
_____________________________
Days Held
Difference in DR is the change in the CR between when the asset is purchased and when it is sold
Interest Rate Quotations on US Treasury Bills
Treasury bills are money market assets
Issued by the U.S. government
Various maturities
4 weeks
3 months
6 months
Daily report of information on the bills
Various financial sources
For each maturity
Security dealers who act as “market makers” usually quote two prices
The higher ask price is the dealer’s selling price
The lower bid price is the dealer’s buying price
The difference between the bid and ask prices is the spread – the dealer’s return for creating a market
Interest Rates on Bonds and Other Long-Term Debt Securities
Yield to maturity (YTM) of a financial asset
The rate of interest that the market is currently prepared to pay for the financial asset
It is the rate that equates the purchase price (P) with the present value the stream of coupon payments (C) by the asset
Coupon = Coupon rate * Par value
Adjustments for non-annual rates
Include a parameter k, the number of times during the year that the interest income is paid to the investor
Measures of the Rate of Return (Yield) On a Financial Asset
The holding-period yield is an investment rate of return
Over its actual or planned holding period
It is the discount rate (h) equalizing the purchase price (P) of a financial asset with all the discounted annual payments (C) received until the asset is sold at time m for price Pm
Understanding Yield to Maturity
Example
A 5-year corporate bond has a face value of $1,000. Its promised a annual coupon rate is 10% and it pays $50 in interest every 6 months. The bond is currently selling for $900
Price Quotations on U.S. Treasury Notes and Bonds
U.S. Treasury notes (T-notes) and U.S. Treasury bond (T-bonds)
Original maturities of 2 years to 30 years
Most are fixed payments
Typically semi-annually
Need to know
Price and maturity
Date coupons paid
Amount of coupon payments
Current yield to maturity
The current yield of a financial asset is the ratio of the annual income (dividends or interest) generated by the asset to its market value.
Example
The current yield of a share of common stock selling for $30 in the market and paying an annual dividend of $3 to the shareholder is $3/$30 = 0.10, or 10%
Characteristics
Price quotes are on $100 of par value
Quoted in 32nd of a dollar
Annualized rate
Price quotations provided in financial press
Including daily trading activity
Often including bid and asked prices
Price Quotations on Corporate Bonds
Price quotes on corporate bonds are similar
Same basic information required
However the need to consider risk
Unlike what is assumed for the US government, some borrowers may default on all or a portion of their promised payments
The market value of the risky asset may rise or fall
Investors require greater returns to compensate them for this risk
Yield-Asset Price Relationships
The price of a financial asset (especially debt securities) and its rate of return are inversely related
A rise in yield implies a decline in price, and vice versa
Investing funds in financial assets can be viewed from two different perspectives
The borrowing and lending of money
The buying and selling of financial assets
Rates of Return on Perpetual Financial Instruments
Some financial instruments never mature
Perpetuity financial instruments
May be fixed-income
Equal payments to its holder every year
Ad infinitum
May be variable-return
Corporate stock
Future payments may change over time
Perpetuity rate
Annual rate of return on a perpetual financial instrument =
Annual cash flow promised
_______________________________--
current price or present value
Or
Current Price =Annual cash flow promised
_______________________
Annual rate of return
Key points to consider
An infinite stream of cash flows has a finite value
There is an inverse relationship between the current price and the rate of return
This can be weaker than for bonds
It does not always hold for common stock
Stock pricing formula
D0 is current dividend
EDi is expected future dividend at time I
R is the minimum rate of return required by a company’s shareholders
SP is the company’s sTOCK PRICE
Price Quotation in Corporate Stocks
There are many professional analysts examining stocks. They can provide information by trading stocks
- Closing price is price at end of prior trading day
How much the stock price has changed
Compare to prior year’s high and low
Determine if the stock pays a dividend and how much
Price to earnings ratio
Interest Rates Charged or Paid by Institutional Lenders
Simple interest method
Assesses interest charges on a loan only for the period of time that the borrower has actual use of the borrowed funds
Interest = principal x rate x term
The more frequently a borrower makes repayments on a loan, the less the total interest
Add-on interest method
- Interest is calculated on the full loan principal
The sum of interest and principal payments is divided by the number of payments to determine the dollar amount of each payment
In a single payment loan, the simple interest and add-on methods give the same interest rate
As the number of installment payments increases, the borrower pays a higher effective rate under the add-on method
Discount loan method
Determines the total interest charged to the customer on the basis of the amount to be repaid
Loan proceeds are only the difference between the total amount owed and the interest bill
Hence, the effective interest rate is
Interest paid
__________________ x 100
Net loan proceeds
Monthly payments of a home mortgage loan
First covers in full the monthly interest on the outstanding principal
The remainder is then applied to the principal of the loan
Annual Percentage Rate
The U.S. Consumer Credit Protection Act of 1968 (Truth in Lending)
Requires lending institutions to calculate and tell the borrower the annual percentage rate (APR)
Rate borrower actually pays
APR measures the yearly cost of credit
Interest costs
Transaction fees or service charges imposed by the lender
Compound Interest
The compounding of interest means that the lender or depositor earns interest income on both the principal and accumulated interest
The formula for calculating the future value of a financial asset earning compound interest is:
APY on Deposits
The U.S. Truth in Savings Act of 1991
- Requires depository institutions to use the daily average balance in a customer’s deposit
Over each interest-crediting period
To determine the customer’s annual percentage yield (APY) for that deposit account
Chapter Review
Introduction
Units of measurement for interest rates and asset prices
Calculating and quoting interest rates
Basis points
Prices of stocks and bonds
Measures of the rate of return, or yield, on a loan, security, or other financial asset
Rate of return on a perpetual financial instrument
Coupon rate
Current yield
Yield to maturity
Holding-period yield
Bank discount rate
Yield-asset price relationships
Interest rates and the prices of debt securities
Interest rates and stock prices
Interest rates charged by institutional lenders
- Simple interest rate
Add-on rate of interest
Discount loan method
Home mortgage interest rate
Annual Percentage Rate (APR)
Compound interest
Annual Percentage Yield (APY) on deposits
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