FIN320 Midterm Study Guide （need to complete within 5 hours）
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FIN320_3_Interest-Rates.pdf
Interest Rates and How They Are Determined
Professor Lamont Black FIN320 Week 3
Interest Rates and Rates of Return
• Are Treasury bonds a risky investment?
• The default risk is effecGvely zero.
• 2.5% was a historically low interest rate for 30-year Treasury bonds in 2016…
Why are interest rates important?
• The cost of borrowing
• Credit cards • Auto loans • Student loan refinancing – Federal student loan interest rates are set by the EducaGon Dept. each year on July 1 and pegged to the 10-year Treasury rate
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The Interest Rate, Present Value, and Future Value
Money today is worth more than money tomorrow. There is a money-Gme conGnuum. Interest rates are the measure of movement along this conGnuum.
Charging Interest and the Future
• Why charge interest?? CompensaGon for – inflaGon – default risk – the opportunity cost of waiGng to spend your money
• Finance is about future payments. – Interest rates provide a link between the financial present and the financial future.
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Use interest rate to find PV and FV
• Compounding
• DiscounGng and the prices of financial assets
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Compounding: )1( n nPV i FV× + =
Discounting: (1 )
n n
FV PV
i =
+
Debt Instruments and Their Prices
• Loans, bonds, and the Gming of payments – Simple loans – Discount bonds – Coupon bonds – Fixed-payment loans
Simple Loan and Discount Bond
• Simple loan
• Discount bond
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Fixed-Payment Loan and Coupon Bond
• Fixed-Payment Loan
• Coupon Bond
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Coupon Bond Terminology • Face value (or par value): the amount to be repaid by the bond issuer (the borrower) at maturity
• Coupon: the annual fixed dollar amount of interest paid by the issuer of the bond to the buyer
• Coupon rate: the value of the coupon expressed as a percentage of the par value of the bond
• Current yield: the value of the coupon expressed as a percentage of the current price
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Bond Prices and Yield to Maturity
• Bond prices • Yield to maturity • Yields to maturity on other debt instrument
Bond Price Example • Consider a coupon bond with i = 6%, FV = $1,000, n = 5 years.
• The price of the bond (P) is the sum of the present values of 6 payments:
• For a bond that makes coupon payments (C) and matures in n years:
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2 3 4 5 5
$60 $60 $60 $60 $60 $1,000 (1 ) (1 ) (1 ) (1 ) (1 ) (1 )
P i i i i i i
= + + + + + + + + + + +
2 3(1 ) (1 ) (1 ) (1 ) (1 )n n C C C C FV
P i i i i i
= + + + + + + + + + +
L
Yield to Maturity Yield to maturity is the interest rate that makes the present value of the payments from an asset equal to the asset’s price today.
– the interest rate on a financial asset for financial markets par8cipants.
• Yield to maturity is a market interest rate.
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YTM Examples • A discount bond with a price of $9,000, which has a face value of
$10,000 and matures in 1 year.
• A corporate bond with a face value of $1,000, a price of $975, a
coupon rate of 10%, and a maturity of 5 years. .
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$10,000 $10,000 $9,000 $9,000 ,or,
(1 ) $9,000 i
i −
= = +
2 3 4 5 5
$100 $100 $100 $100 $100 $1,000 $975 .
(1 ) (1 ) (1 ) (1 ) (1 ) (1 )i i i i i i = + + + + +
+ + + + + +
The Inverse RelaGonship Between Bond Prices and Bond Yields
• What happens to bond prices when interest rates change?
• Bond prices and yields to maturity move in opposite direcGons
• Prices adjust so that investors receive the same yields on comparable securiGes. – Secondary markets, arbitrage, and the law of one price
Bull vs. Bear in Bond Market
• Bonds are currently in a bear market
• For many years, it was a bull market
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A Bond Table
• Bond A matures on May 15, 2019, and has a coupon rate of 3.125%, so it pays
$31.25 each year on its $1,000 face value.
• For Bond A, 106.3906 means a price of $1,063.906 for this $1,000 face value bond.
• The bid price is the sell price; the asked price is the price to buy the bond.
• For Bond A, the bid price rose by $2.891 from the previous day.
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Blank Maturity Coupon Bid Asked CHG Asked YLD
Bond A May 15, 2019 3.125 106.3906 106.4063 0.2891 0.912 Blank February 15, 2020 8.500 127.0156 127.0313 0.4063 1.021
Blank May 15, 2020 3.500 109.1719 109.1875 0.4688 1.110
Blank February 15, 2025 7.625 148.8672 148.8828 1.1406 1.583
Blank August 15, 2029 6.125 149.7969 149.8954 1.5000 1.848
A Bond Table
• Observe the relaGonship between coupon, price, and yield
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Blank Maturity Coupon Bid Asked CHG Asked YLD
Bond A May 15, 2019 3.125 106.3906 106.4063 0.2891 0.912 Blank February 15, 2020 8.500 127.0156 127.0313 0.4063 1.021
Blank May 15, 2020 3.500 109.1719 109.1875 0.4688 1.110
Blank February 15, 2025 7.625 148.8672 148.8828 1.1406 1.583
Blank August 15, 2029 6.125 149.7969 149.8954 1.5000 1.848
Interest Rates and Rates of Return
• A general equaGon for the rate of return on a bond – Capital gains maker!
• Interest-rate risk and maturity • How much interest-rate risk do investors in treasury bonds face?
Bond Example Example: A bond with a $1,000 face value and a coupon rate of 5%.
If the end-of-year price is $1,169.84, then the rate of return for the year is:
If the end-of-year price is $864.09, then the rate of return for the year is:
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Coupon Capital gain $50 $169.84 0.220, or 22.0%.
Purchase price $1,000 R
+ + = = =
$50 $135.91 0.086, or 8.6%.
$1,000 R
− = = − −
Maturity and Interest Rate Risk
• Interest rate rises from 5% to 7%
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Years to maturity
Current yield
IniAal price
Price at the end of the year
Rate of capital gain or loss
Rate of return during the year
1 5% $1,000 $1,000.00 0% 5.0% 2 5 1,000 981.31 −1.87 3.1
10 5 1,000 869.70 −13.0 −8.0
20 5 1,000 793.29 −20.7 −25.7
30 5 1,000 754.45 −24.6 −19.6
50 5 1,000 724.66 −27.5 −22.5
Nominal Interest Rates Versus Real Interest Rates
Nominal interest rates are interest rates that are not adjusted for changes in purchasing power. Real interest rate are interest rates that are adjusted for changes in purchasing power.
• The expected real interest rate (r) equals the nominal interest rate (i) minus the expected rate of inflaGon (πe).
• InflaGon surprises are good issuers, not good for bond investors. • Use TIPS to protect against inflaGon.
πei r= +
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Determining Interest Rates
• Why are interest rates so low?
• Chapter 4
How to Build an Investment Pornolio
• The determinants of pornolio choice – Wealth – Expected rate of return – Risk – Liquidity – The cost of acquiring informaGon
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An increase in …
causes the quanAty demanded of the asset in the porNolio to … because …
wealth rise investors have a greater stock of savings to allocate.
expected return on an asset relaGve to expected returns on other assets
rise investors gain more from holding the asset.
risk (that is, the variability of returns)
fall most investors are risk averse.
liquidity (that is, the ease with which an asset can be converted to cash)
rise investors can easily convert the asset into cash to finance consumpGon.
informaGon costs fall investors must spend more Gme and money acquiring and analyzing informaGon on the asset and its returns.
How to Build an Investment Pornolio
• Market (or systemaGc) risk • IdiosyncraGc risk
• DiversificaGon
Risk AppeGte
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Market Interest Rates and the Demand and Supply for Bonds
• A demand and supply graph on the bond market
• Explaining changes in equilibrium interest rates – What determines a bond’s price?
• Factors that shio the demand curve for bonds • Factors that shio the supply curve for bonds
Bond Market
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Shio in Demand
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Factors that Shio Demand
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Factors that Shio Demand
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Factors that Shio Demand
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Bond Supply
• Factors that shio bond supply 1. Expected pretax profitability of physical capital
investment 2. Business taxes 3. Expected inflaGon 4. Government borrowing
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Factors that Shio Supply
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Factors that Shio Supply
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Explaining Changes in Interest Rates
• Why do interest rates fall during recessions? • How do changes in expected inflaGon affect interest rates? The Fisher effect
Why do interest rates fall in a recession?
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What happens when expected inflaGon rises?
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• We are skipping secGon 4.4
