finance HW
muteb11
week-3_intro_to_interest_rates_new.pptxWeek-3 Into to Interest Rates
Money and Banking Econ 311
Tuesdays 7 - 9:45
Instructor: Thomas L. Thomas
Measuring Interest Rates
Present Value:
A dollar paid to you one year from now is less valuable than a dollar paid to you today
Why?
A dollar deposited today can earn interest and become $1 x (1+i) one year from today.
2
Discounting the Future
3
Simple Present Value
4
Time Line
$100
$100
Year
0
1
PV
100
2
$100
$100
n
100/(1+i)
100/(1+i)2
100/(1+i)n
Cannot directly compare payments scheduled in different points in the time line
Four Types of Credit Market Instruments
Simple Loan
Fixed Payment Loan
Coupon Bond
Discount Bond
6
Yield to Maturity
The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today
7
Simple Loan
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Fixed Payment Loan
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Coupon Bond
10
Table 1 Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years (Face Value = $1,000)
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
11
Microsoft Excel Example
Consol or Perpetuity
A bond with no maturity date that does not repay principal but pays fixed coupon payments forever
For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturity
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Discount Bond
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The Distinction Between Interest Rates and Returns
Rate of Return:
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The Distinction Between Interest Rates and Returns (cont’d)
The return equals the yield to maturity only if the holding period equals the time to maturity
A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change (also referred to as duration)
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Table 2 One-Year Returns on Different-Maturity 10%-Coupon-Rate Bonds When Interest Rates Rise from 10% to 20%
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Interest-Rate Risk
Prices and returns for long-term bonds are more volatile than those for shorter-term bonds
There is no interest-rate risk for any bond whose time to maturity matches the holding period
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Interest Risk - Duration
Duration - is the weighted average time over which he cash flows form an investment are expected, where the weights are the relative present values of the cash flows.
Focusing on maturity ignore the fact that some cash benefits are received before maturity (can be reinvested) and the benefits may be substantial.
Interest Risk - Duration
Higher yields lead to lower durations. As the yield increases the present value of the distant cash flows gets exponentially smaller thus the weight given to distant time periods in the numerator get smaller lowering the duration.
Interest Risk - Duration
The duration of any instrument is positively related to maturity, except for maturities in excess of 50 years. The duration of a bond increases as yield (coupon) increases.
Interest Risk - Duration
Why is this important? The answer: for a given change in market yields, the percentage change in an asset’s price (PV) are proportional to the asset’s duration.
Hence longer duration instruments are subject to greater price changes (exhibit greater price elasticity).
This is expressed by the following formula:
-Duration × [Di ÷(1+i)]
Examples:
The Distinction Between Real and Nominal Interest Rates
Nominal interest rate makes no allowance for inflation
Real interest rate is adjusted for changes in price level so it 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
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Fisher Equation
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Figure 1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2011
Sources: Nominal rates from www.federalreserve.gov/releases/H15 and inflation from ftp:// ftp.bis.gov/special.requests/cpi/cpia.txt. The real rate is constructed using the procedure outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation,” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends and then subtracting the expected inflation measure from the nominal interest rate.
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Determinants of Asset Demand
Wealth: the total resources owned by the individual, including all assets
Expected Return: the return expected over the next period on one asset relative to alternative assets
Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets
Liquidity: the ease and speed with which an asset can be turned into cash relative to alternative assets
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Theory of Portfolio Choice
Holding all other factors constant:
The quantity demanded of an asset is positively related to wealth
The quantity demanded of an asset is positively related to its expected return relative to alternative assets
The quantity demanded of an asset is negatively related to the risk of its returns relative to alternative assets
The quantity demanded of an asset is positively related to its liquidity relative to alternative assets
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Supply and Demand in the Bond Market
At lower prices (higher interest rates), ceteris paribus, the quantity demanded of bonds is higher: an inverse relationship
At lower prices (higher interest rates), ceteris paribus, the quantity supplied of bonds is lower: a positive relationship
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Supply and Demand for Bonds
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Changes in Equilibrium Interest Rates
Shifts in the demand for bonds:
Wealth: in an expansion with growing wealth, the demand curve for bonds shifts to the right
Expected Returns: higher expected interest rates in the future lower the expected return for long-term bonds, shifting the demand curve to the left
Expected Inflation: an increase in the expected rate of inflations lowers the expected return for bonds, causing the demand curve to shift to the left
Risk: an increase in the riskiness of bonds causes the demand curve to shift to the left
Liquidity: increased liquidity of bonds results in the demand curve shifting right
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Factors That Shift the Demand Curve for Bonds
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Shifts in the Supply of Bonds
Expected profitability of investment opportunities: in an expansion, the supply curve shifts to the right
Expected inflation: an increase in expected inflation shifts the supply curve for bonds to the right
Government budget: increased budget deficits shift the supply curve to the right
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Factors That Shift the Supply of Bonds
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2
3
Let = .10
In one year $100 X (1+ 0.10) = $110
In two years $110 X (1 + 0.10) = $121
or 100 X (1 + 0.10)
In three years $121 X (1 + 0.10) = $133
or 100 X (1 + 0.10)
In years
$100 X (1 + )
n
i
n
i
n
PV = today's (present) value
CF = future cash flow (payment)
= the interest rate
CF
PV =
(1 + )
i
i
1
PV = amount borrowed = $100
CF = cash flow in one year = $110
= number of years = 1
$110
$100 =
(1 + )
(1 + ) $100 = $110
$110
(1 + ) =
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= 0.10 = 10%
For simple loans, the simple interest ra
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yield to maturity
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The same cash flow payment every period
throughout
the life of the loan
LV = loan value
FP = fixed yearly payment
= number of years until maturity
FPFPFPFP
LV = . . . +
1 + (1 + )(1 + )(1 + )
n
n
iiii
+++
23
Using the same strategy used for the fix
ed-payment loan:
P = price of coupon bond
C = yearly coupon payment
F = face value of the bond
= years to maturity date
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1+(1+)(1+)(1+)(1
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