金融市场学第三章
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2013-11-23 FM 姜程 13
(2) Fixed-Payment Loan
$126 $126 $126 $126 $1000 2 3 ... 25 1 i 1 i 1 i 1 i
FP FP FP FP LV 2 3 ... n 1 i 1 i 1 i 1 i
Principles of Financial Markets
Chapter 3 Understanding Interest Rates
TIANFU COLLEGE OF SWUFE
Chapter Preview
Since interest rates are among the most closely watched variables in the economy, it is imperative that what exactly is meant by the phrase interest rates is understood. In this chapter, we will see that a concept known as yield to maturity (YTM) is the most accurate measure of interest rates.
2013-11-23 FM 姜程 4
1. Measuring Interest Rates
There are four basic types of credit instruments:
Simple Loan
Fixed Payment Loan
Coupon Bond
Commercial loans to businesses Installment loans and mortgages
If a bond’s price is near par and has a long maturity, then CY is a good approximation. A change in the current yield always signals change in same direction as yield to maturity
2013-11-23
FM 姜程
15
(3) Coupon Bond
$100 $100 $100 $100 $1000 P 2 3 ... 10 1 i 1 i 1 i 1 i 1 i 10
C C C C F P 2 3 ... n n 1 i 1 i 1 i 1 i 1 i
2013-11-23 FM 姜程 11
(1) Simple Loan
$100 $110 1 i
$110 $100 $10 i .10 10% $100 $100
For simple loan, the simple interest rate equals the yield to maturity
Fixed coupon payments of $C forever
C P i
2013-11-23
C i P
FM 姜程 16
Relationship Between Price and Yield to Maturity
When bond is at par, yield equals coupon rate Price and yield are negatively related Yield greater than coupon rate when bond price is below par value.
Simple Interest Rate
the interest payment divided by the loan principal; the percentage of principal that must be paid as interest to the lender. Convention is to express on an annual basis, irrespective of the loan term.
2013-11-23 FM 姜程 21
2) Yield on a Discount Basis
(F - P) 360 idb F (number of days to maturity)
2013-11-23 FM 姜程 2
Chapter Preview
In this chapter, we develop a better understanding of interest rates. We examine the terminology and calculation of various rates, and we show the importance of these rates in our lives and the general economy.
2013-11-23
FM 姜程
9
Present Value Concept: Simple Loan
Simple loan of $100 Year: 0 1 $100 $110 2 $121 3 $133 n 100(1+i)
n
FV PV n (1 i )
2013-11-23 FM 姜程 10
2013-11-23 FM 姜程 12
Present Value Concept: Fixed-Payment Loan Terms
Fixed-Payment Loan are loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term. Installment Loans, such as auto loans and home mortgages are frequently of the fixed-payment type.
2013-11-23
FM 姜程
7
Present Value Concept: Simple Loan Terms
Loan Principal
the amount of funds the lender provides to the borrower.
Maturity Date
the date the loan must be repaid; the Loan Term is from initiation to maturity date.
Interest Payment
the cash amount that the borrower must pay the lender for the use of the loan principal.
FM 姜程 8
2013-11-23
Present Value Concept: Simple Loan Terms
Because the yield to maturity is difficult to calculate, less accurate measures of interest rates have come into common use in bond markets.
Current Yield Yield on a discount basis
2013-11-23 FM 姜程 17
Present Value Concept: Discount Bond A discount bond is also called a zerocoupon bond. It is bought at a price below its face value, and the face value should be repaid at the maturity date.
2013-11-23 FM 姜程 6
1) Present Value
The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence of group of cash flows.
2013-11-23 FM 姜程 14
Present Value Concept: Coupon Bond A coupon bond pays the owner of the bond a fixed interest payment every year until the maturity date, when a specified final amount (face value or par value) is repaid.
2) Yield to Maturity
ห้องสมุดไป่ตู้ield to maturity
The interest rate that equates the present value of payments received from a debt instrument with its value today. To understand the yield to maturity better, we look at how it is calculated for the 4 types of debt instruments.
2013-11-23 FM 姜程 20
1) Current
Yield
ic=C/P Current yield (CY) is just an approximation for YTM – easier to calculate. However, we should be aware of its characteristics:
2013-11-23
FM 姜程
18
(4) Discount Bond
$1000 $900 1 i
$1000 $900 i .111 11.1% $900
FP i P
2013-11-23 FM 姜程 19
2.Other Measures of Interest Rates
Discount Bond
Treasury bills
2013-11-23
Treasury bonds, Treasury notes and Corporate bonds
FM 姜程
5
1) Present Value
The concept of present value is based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. This notion is true because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year.
2013-11-23 FM 姜程 3
Topics include:
Measuring Interest Rates
The Distinction Between Real and Nominal Interest Rates
The Distinction Between Interest Rates and Returns
(2) Fixed-Payment Loan
$126 $126 $126 $126 $1000 2 3 ... 25 1 i 1 i 1 i 1 i
FP FP FP FP LV 2 3 ... n 1 i 1 i 1 i 1 i
Principles of Financial Markets
Chapter 3 Understanding Interest Rates
TIANFU COLLEGE OF SWUFE
Chapter Preview
Since interest rates are among the most closely watched variables in the economy, it is imperative that what exactly is meant by the phrase interest rates is understood. In this chapter, we will see that a concept known as yield to maturity (YTM) is the most accurate measure of interest rates.
2013-11-23 FM 姜程 4
1. Measuring Interest Rates
There are four basic types of credit instruments:
Simple Loan
Fixed Payment Loan
Coupon Bond
Commercial loans to businesses Installment loans and mortgages
If a bond’s price is near par and has a long maturity, then CY is a good approximation. A change in the current yield always signals change in same direction as yield to maturity
2013-11-23
FM 姜程
15
(3) Coupon Bond
$100 $100 $100 $100 $1000 P 2 3 ... 10 1 i 1 i 1 i 1 i 1 i 10
C C C C F P 2 3 ... n n 1 i 1 i 1 i 1 i 1 i
2013-11-23 FM 姜程 11
(1) Simple Loan
$100 $110 1 i
$110 $100 $10 i .10 10% $100 $100
For simple loan, the simple interest rate equals the yield to maturity
Fixed coupon payments of $C forever
C P i
2013-11-23
C i P
FM 姜程 16
Relationship Between Price and Yield to Maturity
When bond is at par, yield equals coupon rate Price and yield are negatively related Yield greater than coupon rate when bond price is below par value.
Simple Interest Rate
the interest payment divided by the loan principal; the percentage of principal that must be paid as interest to the lender. Convention is to express on an annual basis, irrespective of the loan term.
2013-11-23 FM 姜程 21
2) Yield on a Discount Basis
(F - P) 360 idb F (number of days to maturity)
2013-11-23 FM 姜程 2
Chapter Preview
In this chapter, we develop a better understanding of interest rates. We examine the terminology and calculation of various rates, and we show the importance of these rates in our lives and the general economy.
2013-11-23
FM 姜程
9
Present Value Concept: Simple Loan
Simple loan of $100 Year: 0 1 $100 $110 2 $121 3 $133 n 100(1+i)
n
FV PV n (1 i )
2013-11-23 FM 姜程 10
2013-11-23 FM 姜程 12
Present Value Concept: Fixed-Payment Loan Terms
Fixed-Payment Loan are loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term. Installment Loans, such as auto loans and home mortgages are frequently of the fixed-payment type.
2013-11-23
FM 姜程
7
Present Value Concept: Simple Loan Terms
Loan Principal
the amount of funds the lender provides to the borrower.
Maturity Date
the date the loan must be repaid; the Loan Term is from initiation to maturity date.
Interest Payment
the cash amount that the borrower must pay the lender for the use of the loan principal.
FM 姜程 8
2013-11-23
Present Value Concept: Simple Loan Terms
Because the yield to maturity is difficult to calculate, less accurate measures of interest rates have come into common use in bond markets.
Current Yield Yield on a discount basis
2013-11-23 FM 姜程 17
Present Value Concept: Discount Bond A discount bond is also called a zerocoupon bond. It is bought at a price below its face value, and the face value should be repaid at the maturity date.
2013-11-23 FM 姜程 6
1) Present Value
The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence of group of cash flows.
2013-11-23 FM 姜程 14
Present Value Concept: Coupon Bond A coupon bond pays the owner of the bond a fixed interest payment every year until the maturity date, when a specified final amount (face value or par value) is repaid.
2) Yield to Maturity
ห้องสมุดไป่ตู้ield to maturity
The interest rate that equates the present value of payments received from a debt instrument with its value today. To understand the yield to maturity better, we look at how it is calculated for the 4 types of debt instruments.
2013-11-23 FM 姜程 20
1) Current
Yield
ic=C/P Current yield (CY) is just an approximation for YTM – easier to calculate. However, we should be aware of its characteristics:
2013-11-23
FM 姜程
18
(4) Discount Bond
$1000 $900 1 i
$1000 $900 i .111 11.1% $900
FP i P
2013-11-23 FM 姜程 19
2.Other Measures of Interest Rates
Discount Bond
Treasury bills
2013-11-23
Treasury bonds, Treasury notes and Corporate bonds
FM 姜程
5
1) Present Value
The concept of present value is based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. This notion is true because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year.
2013-11-23 FM 姜程 3
Topics include:
Measuring Interest Rates
The Distinction Between Real and Nominal Interest Rates
The Distinction Between Interest Rates and Returns