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**Interest Rates and Bond Valuation**

Chapter 6

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**Key Concepts and Skills**

Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields

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**Chapter Outline Bonds and Bond Valuation More on Bond Features**

Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields

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**Issuer (Seller) of Bonds (Borrower) = “Bond Issuer”**

Bonds = Debt = Liability = Long-term debt 1 Bond usually means the corporation borrows $1000 (face value) Corporations usually issue many Bonds Bond Issue: The total number of bonds that a corporation issues at the same time, in denominations of $1,000 or $5,000 each Like any contractual debt: Bond issuer pays periodic interest to the bondholder Bond issuer pays the face value back at the end of the bond term

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**Issuer (Seller) of Bonds (Borrower) = “Bond Issuer”**

When you issue a bond, you borrow the money, then use the money to buy assets that earn more cash than the cash you have to pay out to the bondholder Leverage Example: Borrow money at 8% interest and buy a machine that earns the corporation 13% The difference between 13% and 8%, or 5%, is left for the stockholders

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**Buyer of Bonds (Lender) = “Bondholder”**

Bonds = Asset 1 Bond usually means the borrow lends money to the corporation or government Like any contractual debt: Bondholders are paid periodic interest for loaning money to the corporation and are paid back the face value at the end of the bond term When you buy a bond you are paying for a future steam of cash flow

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Bond Vocabulary: Face value = par value = loan repayment at maturity = FV Annual interest payments = “annual coupon” Coupon is from the days when you presented coupon to get paid interest Annual interest rate (not discount rate) = coupon rate = annual interest rate for calculating interest payments = annual coupon/face value Number of interest payments per year = n Periodic rate (not discount rate) = periodic coupon rate = (annual coupon rate)/n The book is inconsistent with the use of “coupon” (sometimes annual, sometimes semi-annual) Periodic interest payment = periodic rate*face = PMT Years until maturity = term of bond = years until paying back face value and last periodic interest payment = x Maturity = specified date on which principal is repaid

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Bond Vocabulary: Yield To Maturity (YTM) = discount rate used to value bond = i = YTM YTM = Bond Yield = Required Return = Market Rate = Rate required in the market on a bond YTMs are quoted like APRs YTM = (Period Discount Rate) * n Example: YTM = 10% and bond pays semiannual interest payments, then period discount rate = YTM/n = .10/2 =.05 Effective Annual Yield on the Bond = (1+.10/2)2 = .1025

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**Bonds Bonds are interest only loans**

Corporations/Governments borrow money, pay interest each period, then pay back face amount at end of bond term Corporations/Governments plan to issue bonds and then set the coupon rate, but by the time they actually issue the bond the financial markets have already calculated a discount rate for the future values that is often different than the coupon rate Corporations/Governments issue bonds and get the “cash in” (Bonds sold in primary market) Many Bonds from Corporations/Governments can be traded in the financial markets (Bonds sold in the secondary market)

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Bonds Each bond has a price expressed as a percentage of the face value: For example, 103 means 1.03 times the face value of the bond When the corporation issues the $1,000 face-value bond, it receives $1,030 At maturity, the corporation pays back only the face value of $1,000 103 and 103% and 1.03 all convey the same meaning The bond is selling for 3% above the face value

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Example 1 On January 1, Cox Construction Corp. issues year bonds with a face of $1000 with a coupon rate of 9% at 103, with interest payable semiannually, on June 30 and December 31

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**This Bond with its 9% coupon, is priced to yield 8.74% at $1,030**

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**But If The Loan Has A Face Value Of $750,000, Why Did The Bondholder Pay $772,500?**

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If a corporation offers a rate of interest that is higher than the market rate for similar securities, investors may be willing to pay a premium for the bond If a corporation offers a rate of interest that is lower than the market rate for similar securities, investors will demand a discount on the bond

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**What Are Similar Securities?**

Similar securities are bonds or other investment vehicles issue by other corporations (different than the one being considered) that have similar business and financial risks The similarities could be: Similar credit ratings Similar business activities Similar capital structure

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Bond Prices YTM > Coupon Rate YTM < Coupon Rate

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**Definitions Premium Discount**

The excess of the price received over the face value of a bond YTM < Coupon Rate “Bond sold at a premium” Discount The amount by which the issue price is less than the face value of a bond YTM > Coupon Rate “Bond sold at a discount”

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**The Issuance of Bonds at a Discount: Example 2**

On January 1, Muller, Inc., issues 700 6%, 20-year bonds with a face value of $1,000, at 96, with interest to be paid semiannually, on June 30 and December 31

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**This Bond with its 6% coupon, is priced to yield 6.25% at $960**

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**Bond Price (Valuation) from Cash Flow Perspective**

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**Excel Bond Valuation from Bondholder’s Point of View:**

=PV(rate,nper,pmt,fv,type) =PV(YTM/n,n*x,PMT,FV,0) Bond Valuation from Bond Issuer’s Point of View: =PV(YTM/n,n*x,-PMT,-FV,0) Finding YTM rate from Bondholder’s Point of View: =RATE(nper,pmt,pv,fv,type,guess) =RATE(n*x,PMT,-PV,FV,0)

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Example 3

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Example 3

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**CF Is From Point Of View Of Issuer**

Example 3 CF Is From Point Of View Of Issuer

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**Bond Values And Why They Fluctuate**

Bond Valuation: As time passes, interest rates change in the market place As new information about the company, the industry, the economy comes out, interest rates change As time passes the amount of cash paid out to the bondholder does not change Because of this the value of the bond will fluctuate Rates , Bond Value Rates , Bond Value

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**Graphical Relationship Between Price and YTM**

Bond characteristics: Coupon rate = 8% with annual coupons; Par value = $1000; Maturity = 10 years

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**Valuing a Discount Bond with Annual Coupons Payments (Example 4)**

Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years left until maturity. The yield to maturity is 11%. What is the value of the bond What is the price to you, buying in the secondary market? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.11)5] / / (1.11)5 B = = Answer: “You would be willing to pay $ cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 11% at $ ” Remember the sign convention on the calculator. The easy way to remember it with bonds is we pay the PV (-) so that we can receive the PMT (+) and the FV(+). Slide 6.8 discusses why this bond sells at less than par

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**Valuing a Premium Bond with Annual Coupons Payments (Example 5)**

Suppose you are looking at a bond that has a 10% annual coupon rate and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the value of the bond what is the price to you? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.08)20] / / (1.08)20 B = = Answer: “You would be willing to pay $ cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 8% at $ ”

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Interest Rate Risk The risk that arises for bond owners from fluctuating interest rates How much interest rate risk a bond has depends on: How sensitive its price is to interest rate change The sensitivity depends on two things: All things being equal, the longer the time to maturity, the greater the interest rate risk All things being equal, the lower the coupon rate, the greater the interest rate risk

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**Interest Rate Risk And Time To Maturity**

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**Interest Rate Risk To Loss Of Principal (current price)**

Longer time to maturity Small changes in market rate have substantial affect on bond value Face value is discounted over many periods and thus compounding magnifies small interest rate changes Lower Coupon rate Bond with lower coupon rate is proportionally more dependent on the face value (Bond with larger coupon rate has a larger cash flow early in life, so value less sensitive to discount rate)

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**Interest Rate Risk Increases At A Decreasing Rate**

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Computing YTM Yield-to-maturity is the rate implied by the current bond price Finding the YTM requires trial and error (iteration) if you do not have a financial calculator and is similar to the process for finding i with an annuity If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

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**YTM with Annual Coupons (Example 6)**

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09 Will the yield be more or less than 10%? The students should be able to recognize that the YTM is more than the coupon since the price is less than par.

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**YTM with Semiannual Coupons (Example 7)**

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $ Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?

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**Use One Bond YTM To Find Price Of Another Bond: Example 8**

Below Market rate = discount Above = premium

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Bonds and Stocks: Like stock, bonds bring capital (money) into the corporation so that it can invest in profitable projects Bondholders are creditors They have a fixed claim to cash flow Stockholders are owners They have a residual claim to cash flow

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**Bonds and Stocks Debt is not an ownership interest in the firm**

Creditors do not have voting rights Interest is tax deductible Dividends are not tax deductible Unpaid debt is a liability Legal claim against assets If debt is not paid creditors have the legal claim to assets before shareholders One of the costs of issuing debt is the possibility that you will not be able to make interest payments creditors force firm into bankruptcy firm is terminated This does not arise when equity is issued Corporations try to create hybrid financial instruments that are Debt/Equity in order to have: Tax benefits of debt Bankruptcy benefits of equity

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**Differences Between Debt and Equity**

Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt

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**Bond Terms and Types Bonds = Long-term debt Finance jargon”**

Privately placed Directly placed with the lender Public-issue bonds Offered to the public Finance jargon” Long-term debt = funded debt Short-term debt = unfunded debt Example: “A firm planning to fund its debt requirements may be replacing short-term debt with long-tern debt”

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**Bond Terms and Types Trustee (Investment Bank, other…) Indenture**

Appointed by the corporation to represent bondholders Must make sure terms are obeyed Must manage sinking fund Must represent bondholders in default Indenture “The written agreement between the corporation and the lender detailing the terms of the debt issue”

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**Bond Types Registered Form Bearer Form**

The form of bond issue in which the registrar of the company records ownership of each bond Payment is made directly to the owner of the bond Bearer Form The form of bond issue in which the bond is issued without record of the owner’s name Payment is made to whoever holds the bond Uncommon in the USA

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Bond Types Security: Generic term that means Stocks or Bonds or other investment vehicles that are backed by an asset A document indicating ownership or creditorship; a stock certificate or bond Dictionary definition of Security: Something deposited or given as assurance of the fulfillment of an obligation; a pledge; collateral

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Bond Types Debt securities are classified according to the collateral and mortgages used to protect the bondholder Securities Backed By Collateral Collateral = any asset pledged on the debt (often means assets such as stocks or bonds – financial assets) If the borrower does not pay the interest and principal to the bondholder, the bondholder can take the collateral Mortgage Securities Debt secured by a mortgage on real assets (property, but not cash or inventory) of the borrower Called: Mortgage Trust Indenture, or Trust Deed Most utility and railroad bonds are secured by a pledge of assets

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**Bond Types Subordinate Debt Unsecured Debt**

These creditors have a claim on property not otherwise pledged Debenture Unsecured debt (maturity >= 10 years) Most financial and industrial companies’ public bonds are debentures Note Unsecured debt (maturity < 10 years) Subordinate Debt Must give preference to superior debt Debt is not subordinate to equity

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**Bond Types Sinking Fund Protective Covenant**

An account managed by the trustee for the purposed of repaying the bonds, or early bond redemption Bond Issuer must put away some money each period to save up in order to pay off the bond Protective Covenant A part of the indenture limiting certain actions that might be taken in order to protect the lender Negative (thou shalt not): Example: Limit the amount of dividends paid Positive (thou shalt): Example: CA/CL must be greater than 1.5

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**Bond Types Call Provision Call Premium (Pay for the Option)**

An agreement giving the corporation the option to repurchase the bond at a specific price prior to maturity Call Premium (Pay for the Option) The amount by which the call price > par value Example: Bond face = $1,000, Call Price = $1,100 Call Price goes down over time Deferred Call Provision Can call only after a certain date Call Protected Bond Can’t be redeemed by issuer Make-Whole Call When bond called, bondholder gets PV of future cash flows at a reasonable rate Derivative security jargon: Call = Buy Put = Sell

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**Financial Markets Primary Markets Secondary Markets**

Original sale of equity or debt Corporation issues security Secondary Markets After original sale of equity or debt You sell/buy security Dealer Markets (Over-the-counter markets (OTC)) Dealers buy and sell for themselves Most debt is sold this way Example: NASDAQ Auction Markets (Exchanges) Brokers and agents match buyers and sellers Most of the large firms’ equity is sold this way Example: NYSE

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**Bond Characteristics and Required Returns**

The coupon rate depends on the risk characteristics of the bond when issued Which bonds will have the higher coupon, all else equal? Secured debt versus a debenture Subordinated debenture versus senior debt A bond with a sinking fund versus one without A callable bond versus a non-callable bond Debenture: secured debt is less risky because the income from the security is used to pay it off first Subordinated debenture: will be paid after the senior debt Bond without sinking fund: company has to come up with substantial cash at maturity to retire debt and this is riskier than systematic retirement of debt through time Callable – bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at lower rates.

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**Bond Ratings And What They Mean**

Bond Rating firms: Moody’s Standard and Poor’s (S&P) They rate: The likelihood of default The probability that creditors are protected They ask they question: What is the risk associated with the firm issuing the debt? They do not rate the probability of bond value change due to interest rate risk The Debt Crisis of 2007 shows that Ratings can be less than accurate: How do they take risky loans and repackage them to get a AAA “Super Senior” rating? (That’s what they did!)

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**Bond Ratings – Investment Quality**

High Grade Moody’s Aaa and S&P AAA – capacity to pay is extremely strong Moody’s Aa and S&P AA – capacity to pay is very strong Medium Grade Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

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**Bond Ratings - Speculative**

Low Grade Moody’s Ba, B, Caa and Ca S&P BB, B, CCC, CC Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. Very Low Grade Moody’s C and S&P C – income bonds with no interest being paid Moody’s D and S&P D – in default with principal and interest in arrears It is a good exercise to ask students which bonds will have the highest yield-to-maturity (lowest price) all else equal.

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**Some Different Types of Bonds**

Government Bonds Treasury Bill Years < 1 Treasury Note 1< years < 7 Treasury Bonds Other No default risk Treasury issues are exempt from state income tax (must pay Fed IT)

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**U.S. NATIONAL DEBT CLOCK The Outstanding Public Debt as of 13 Nov 2007 at 11:28:01 PM GMT is:**

The estimated population of the United States is 303,525,093 so each citizen's share of this debt is $30, The National Debt has continued to increase an average of $1.49 billion per day since September 29, 2006!

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**Some Different Types of Bonds**

Municipal Bonds “Munis” State and local government debt Example: Bond to build Highway These do have varying degrees of default risk Almost always callable Coupons exempt from federal income taxes (must pay State IT) Attractive to high-income/high-tax bracket investors Because of this the yields are lower Which do you (with 25% Fed tax Bracket) prefer: corporate bond that yields 5%, or a muni (with comparable risk and maturity) that yields 3.90%? .039 > .05(1-.25) = .0375

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**Some Different Types of Bonds**

Zero Coupon Bonds A bond that makes no coupon payments, and thus is initially priced at a deep discount Issuer must deduct interest every year Tax Benefit A deductions for taxes (fewer taxes paid like cash coming in) even though no cash going out (interest expense) Bondholder must accrue interest revenue every year Taxes paid on revenue Cash going out (taxes paid) even though cash is not coming in (interest revenue) Regular amortization table is constructed to track interest accrual

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**Pure Discount Loans (Zero Coupon)**

Borrow an amount today, then pay back principal and all interest at the end of the loan period Example: US Government Treasury Bills, or T-bills (government loans < 1year) Payback Amount Loan amount received today

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**Example 9: Pure Discount Loans (Zero Coupon)**

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**Example 10: Interest Only Bond v. Zero Coupon Bond**

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**Interest Only Bond v. Zero Coupon Bond**

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**Interest Only Bond v. Zero Coupon Bond**

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**Interest Only Bond v. Zero Coupon Bond**

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**Floating-Rate Bonds Coupon Payments are adjustable**

Rated can be tied to an interest rate index such as the Treasury bill interest rate or 30-year Treasury bond rate Rate and payments are adjusted periodically Holder may have the right to redeem the note at par on the coupon payment date after some specified amount of time This is called a “Put” Provision The coupon rate has a floor and ceiling “Capped” or “Collared” means they have an upper and lower barrier

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**Other Bonds: Income Bonds: Convertible Bonds Put Bond**

Coupon payments are dependent on the company income Convertible Bonds Debt that can be converted to a fixed amount of equity anytime before maturity at the holder’s option Half Debt half equity? How do you list it on the Balance Sheet? Put Bond Allows holder to force the issuer to buy the bond back at a stated price (reverse of a call) CoCo and NoNo Bonds These have many features that require complex valuing techniques. Because the features can be valuable to the bondholder, the YTM could be negative!

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Bond Markets Because the bond market is almost entirely OTC, it has little or no transparency (can’t see a great deal of Buy/Sells to gage market value of bonds) US Treasury market is the largest security market in the world Terminology: Bid Price The price a dealer is willing to pay for a security Ask Price The price a dealer is willing to take for a security Bid-ask spread Bid – Ask = Dealers Profit

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**The Impact Of Inflation On Interest Rates**

Increase in price over time Example: Price of milk now = $3.39/gal. Price of milk in 1 year = $3.56/gal.

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**Inflation and Interest Rates**

Real Rates Base interest rate that does not take inflation into consideration The percentage change in buying power Interest rates or rates of return that have been adjusted downward from the nominal rate for inflation Nominal Rates Interest rates or rates of return that have not been adjusted downward for inflation % change in the number of dollars you have The nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation

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**The Fisher Effect (Irving Fisher)**

The Fisher Effect defines the relationship between real rates, nominal rates and inflation R =r + h + r*h r = (R-h)/(1+h) = (1+R)/(1+h) - 1 (1 + R) = (1 + r)(1 + h) R = nominal rate r = real rate h = expected inflation rate Approximation R = r + h

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Example 11:

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Example 6.6 If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? R = (1.1)(1.08) – 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

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The Fisher Effect Real rate is hard to observe directly, so we observe it indirectly: r = (R-h)/(1+h) = (1+R)/(1+h) - 1 Real Rate is fairly constant Take into consideration taxes: r (R*(1-taxrate)-h)/(1+h)

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**The Term Structure Of Interest Rates And Determinants Of Bond Yields**

The risks associated with loaning money are added into a “base” interest rate known as the real rate

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**Bond Yields represent 6 effects:**

Some Components of Interest Rates: Real Rate Inflation Premium Interest Rate Risk Premium Default Risk Premium Taxability Premium Liquidity Premium

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Real Rate Compensation investors demand for foregoing the use of their money Basic component underlying every interest rate When real rate high, all rates tend to be high Doesn’t really determine shape of term structure (overall effect)

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Inflation Premium The portion of a nominal interest rate that represents compensation for expected future inflation Very strongly influences the shape of term structure Inflation expected increase structure upward Inflation expected decrease structure downward

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**Interest Rate Risk Premium**

Compensation demanded for bearing interest rate risk longer-term bonds have a much greater risk of loss resulting from changes in interest rate than so short-term bonds This premium increases at a decreasing rate

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**Term Structure Of Interest Rates (Based On Pure Discount Bonds)**

This shows the relationship between short and long-term interest rates Tells us what the nominal interest rates are on default-free (Treasury), pure discount securities of all maturities This shows the relationship between nominal interest rates on default-free, pure discount securities and time to maturity These rates are “pure” because they involve no risk of default The term structure tells us the pure time value of money for different lengths of time Upward sloping = long-term rates > short-term rates Downward sloping = long-term rates < short-term rates

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**Upward-Sloping Yield Curve**

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**Downward-Sloping Yield Curve**

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**Term Structure Of Interest Rates**

Assumes: Real Rates remain constant Inflation linear Rates could be “Humped” Rates increase at first, but then decline as we look at longer-termed notes

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Treasury Yield Curve A plot of the yields on Treasury Notes and Bonds relative to Maturity Treasury Yield Curve and the Term Structure Of Interest Rates re almost the same thing The difference is: Treasury Yield Curve Based On Coupon Bond Yields Term Structure Of Interest Rates Based On Pure Discount Bonds

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**Treasury Yield Curve (Coupon Bond Yields)**

www: Click on the web surfer to go to Bloomberg to get the current Treasury yield curve

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Default Risk Premium Bonds other than Treasury: Credit risk/default risk The portion of a nominal interest rate or bond yield that represents compensation for the possibility of default Lower rated bonds have higher yields

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Taxability Premium The portion of a nominal interest rate or bond yield that represents compensation for unfavorable tax status Remember municipal versus taxable Bonds that are taxed at both the state and Federal level are less favorable than a bond that is only taxed at the Fed. level

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Liquidity Premium The portion of a nominal interest rate or bond yield that represents compensation for a lack of liquidity Liquidity: How quickly an asset can be converted to cash Example: Maybe the bond is hard to sell quickly and therefore would require a premium for that lack of liquidity Less liquid bonds have higher yields than more liquid bonds

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**Three Principles in Bond Finance**

Rates are inversely related to price Market rate , Bond Price Par, Discount, Premium Market rate = Coupon Rate Bond sells at Par or Face Value Market rate > Coupon Rate Bond sells at a Discount Market rate < Coupon Rate Bond sells at a Premium The more years there are to maturity, the higher the interest rate risk becomes “Interest rate risk to loss of principal”

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**Bond Vocabulary: Current Yield = Annual Interest Payment/Closing Price**

Not equal to YTM (unless bond sells for par); it does not include the capital gain from discounted face value (principal) Premium Bond CY >YTM Discount Bond CY <YTM In all cases (Current Yield) + (Expected one-period capital gain/loss yield of the bond) must be equal to the YTM

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Securitization Securitization = “The process of Securitization involves the collection or pooling of loans and the sale of securities backed by those loans (Cash flows in loan) Whereas, Banks once made loans and kept them on their books, now they can initiate loans and then sell the loans to someone else. Securitization = packaging a set of cash flows and then selling claims (bonds or other) against them Claims = asset backed securities This means that the cash is the asset that backs it

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