Chapter 3 What Do Interest Rates Mean and What is Their Role in Valuation?

Chapter Preview 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. Topics include: – Measuring Interest Rates – The Distinction Between Real and Nominal Interest Rates – The Distinction Between Interest Rates and Returns Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-2

The Big Picture 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. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-3

The Big Picture Any description of interest rates will entail understanding certain vernacular and definitions, most of which will not only pertain directly to interest rates but will also be vital to understanding many other foundational concepts presented later in the text. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-4

Present Value Introduction Different debt instruments have very different streams of cash payments to the holder (known as cash flows), with very different timing. All else being equal, debt instruments are evaluated against one another based on the amount of each cash flow and the timing of each cash flow. This evaluation, where the analysis of the amount and timing of a debt instrument’s cash flows lead to its yield to maturity or interest rate, is called present value analysis. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-5

Present Value The concept of present value (or present discounted 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. The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence or group of cash flows. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-6

Present Value Applications There are four basic types of credit instruments which incorporate present value concepts: 1.Simple Loan 2.Fixed Payment Loan 3.Coupon Bond 4.Discount Bond Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-7

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. 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. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-8

Present Value Concept: Simple Loan Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-9

Present Value Concept: Simple Loan (cont.) The previous example reinforces the concept that $100 today is preferable to $100 a year from now since today’s $100 could be lent out (or deposited) at 10% interest to be worth $110 one year from now, or $121 in two years or $133 in three years. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-10

Yield to Maturity: Loans Yield to maturity = interest rate that equates today's value with present value of all future payments 1.Simple Loan Interest Rate (i = 10%) Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-11

Present Value of Cash Flows: Example Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-12

Present Value Concept: Fixed-Payment Loan Terms Simple Loans require payment of one amount which equals the loan principal plus the interest. Fixed-Payment Loans are loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-13

Present Value Concept: Fixed-Payment Loan Terms Installment Loans, such as auto loans and home mortgages are frequently of the fixed- payment type. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-14

Yield to Maturity: Loans 1.Fixed Payment Loan (i = 12%) Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-15

Yield to Maturity: Bonds 1.Coupon Bond (Coupon rate = 10% = C/F) Copyright © 2006 Pearson Addison- Wesley. All rights reserved Consol: Fixed coupon payments of $C forever

Yield to Maturity: Bonds 1.One-Year Discount Bond (P = $900, F = $1000) Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-17

Relationship Between Price and Yield to Maturity Three interesting facts in Table When bond is at par, yield equals coupon rate 2.Price and yield are negatively related 3.Yield greater than coupon rate when bond price is below par value Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-18

Current Yield Two Characteristics 1.Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond 2.Change in current yield always signals change in same direction as yield to maturity Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-19

Yield on a Discount Basis Copyright © 2006 Pearson Addison- Wesley. All rights reserved One-Year Bill (P = $900, F = $1000) Two Characteristics 1.Understates yield to maturity; longer the maturity, greater is understatement 2.Change in discount yield always signals change in same direction as yield to maturity

Bond Page of the Newspaper

Distinction Between Real and Nominal Interest Rates Real interest rate 1.Interest rate that is adjusted for expected changes in the price level Copyright © 2006 Pearson Addison- Wesley. All rights reserved Real interest rate more accurately reflects true cost of borrowing 2.When real rate is low, greater incentives to borrow and less to lend

Distinction Between Real and Nominal Interest Rates (cont.) If i = 5% and π e = 0% then Copyright © 2006 Pearson Addison- Wesley. All rights reserved If i = 10% and πe = 20% then

U.S. Real and Nominal Interest Rates Copyright © 2006 Pearson Addison- Wesley. All rights reserved Figure 3-1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2004 Sample of current rates and indexes

Distinction Between Interest Rates and Returns Rate of Return Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-25

Key Facts about the Relationship Between Rates and Returns Copyright © 2006 Pearson Addison- Wesley. All rights reserved Sample of current coupon rates and yields on government bonds

Maturity and the Volatility of Bond Returns Key findings from Table Only bond whose return = yield is one with maturity = holding period 2.For bonds with maturity > holding period, i  P  implying capital loss 3.Longer is maturity, greater is price change associated with interest rate change Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-27

Maturity and the Volatility of Bond Returns (cont.) Key findings from Table 3-2 (continued) 1.Longer is maturity, more return changes with change in interest rate 2.Bond with high initial interest rate can still have negative return if i  Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-28

Maturity and the Volatility of Bond Returns (cont.) Conclusion from Table 3-2 analysis 1.Prices and returns more volatile for long-term bonds because have higher interest-rate risk 2.No interest-rate risk for any bond whose maturity equals holding period Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-29

Reinvestment Risk 1.Occurs if hold series of short bonds over long holding period 2.i at which reinvest uncertain 3.Gain from i , lose when i  Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-30

Calculating Duration i =10%, 10-Year 10% Coupon Bond Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-31

Calculating Duration i = 20%, 10-Year 10% Coupon Bond Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-32

Formula for Duration Key facts about duration 1.All else equal, when the maturity of a bond lengthens, the duration rises as well 2.All else equal, when interest rates rise, the duration of a coupon bond fall Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-33

Formula for Duration 1.The higher is the coupon rate on the bond, the shorter is the duration of the bond 2.Duration is additive: the duration of a portfolio of securities is the weighted- average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-34

Duration and Interest-Rate Risk i  10% to 11%: – Table 3-4,  10% coupon bond Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-35

Duration and Interest-Rate Risk (cont.) i  10% to 11%: – 20% coupon bond, DUR = 5.72 years Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-36

Duration and Interest-Rate Risk (cont.) The greater is the duration of a security, the greater is the percentage change in the market value of the security for a given change in interest rates Therefore, the greater is the duration of a security, the greater is its interest-rate risk Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-37

Chapter Summary Measuring Interest Rates: We examined several techniques for measuring the interest rate required on debt instruments. The Distinction Between Real and Nominal Interest Rates: We examined the meaning of interest in the context of price inflation. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-38

Chapter Summary (cont.) The Distinction Between Interest Rates and Returns: We examined what each means and how they should be viewed for asset valuation. Copyright © 2006 Pearson Addison- Wesley. All rights reserved. 3-39

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Chapter Preview Although interest rates in the U.S. have been relatively stable in recent history, this has not always been the case. We examine the forces the move interest rates and the theories behind those movements. Topics include: – Determining Asset Demand – Supply and Demand in the Bond Market – Changes in Equilibrium Interest Rates

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Determinants of Asset Demand An asset is a piece of property that is a store of value. Facing the question of whether to buy and hold an asset or whether to buy one asset rather than another, an individual must consider the following factors: 1.Wealth, the total resources owned by the individual, including all assets 2.Expected return (the return expected over the next period) on one asset relative to alternative assets 3.Risk (the degree of uncertainty associated with the return) on one asset relative to alternative assets 4.Liquidity (the ease and speed with which an asset can be turned into cash) relative to alternative assets

Copyright © 2006 Pearson Addison-Wesley. All rights reserved EXAMPLE 1: Expected Return What is the expected return on the Mobil Oil bond if the return is 12% two-thirds of the time and 8% one-third of the time? Solution The expected return is 10.68%. R e = p 1 R 1 + p 2 R 2 where p 1 = probability of occurrence of return 1=2/3=.67 R 1 = return in state 1=12%= 0.12 p 2 = probability of occurrence return 2=1/3=.33 R 2 = return in state 2=8%=0.08 Thus R e = (.67)(0.12) + (.33)(0.08) = = 10.68%

Copyright © 2006 Pearson Addison-Wesley. All rights reserved EXAMPLE 2: Standard Deviation (a) What is the standard deviation of the returns on the Fly-by-Night Airlines stock and Feet-on- the Ground Bus Company, with the same return outcomes and probabilities described above? Of these two stocks, which is riskier?

Copyright © 2006 Pearson Addison-Wesley. All rights reserved EXAMPLE 2: Standard Deviation (b) Solution – Fly-by-Night Airlines has a standard deviation of returns of 5%.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved EXAMPLE 2: Standard Deviation (c) Feet-on-the-Ground Bus Company has a standard deviation of returns of 0%.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved EXAMPLE 2: Standard Deviation (d) Fly-by-Night Airlines has a standard deviation of returns of 5%; Feet-on-the-Ground Bus Company has a standard deviation of returns of 0% Clearly, Fly-by-Night Airlines is a riskier stock because its standard deviation of returns of 5% is higher than the zero standard deviation of returns for Feet-on-the-Ground Bus Company, which has a certain return A risk-averse person prefers stock in the Feet-on-the-Ground (the sure thing) to Fly-by-Night stock (the riskier asset), even though the stocks have the same expected return, 10%. By contrast, a person who prefers risk is a risk preferrer or risk lover. Most people are risk-averse, especially in their financial decisions

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Determinants of Asset Demand (2) The quantity demanded of an asset differs by factor. 1.Wealth: Holding everything else constant, an increase in wealth raises the quantity demanded of an asset 2.Expected return: An increase in an asset’s expected return relative to that of an alternative asset, holding everything else unchanged, raises the quantity demanded of the asset 3.Risk: Holding everything else constant, if an asset’s risk rises relative to that of alternative assets, its quantity demanded will fall 4.Liquidity: The more liquid an asset is relative to alternative assets, holding everything else unchanged, the more desirable it is, and the greater will be the quantity demanded

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Determinants of Asset Demand (3)

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Point B Derivation of Demand Curve Point A

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Derivation of Demand Curve Point C:P = $850i = 17.6%B d = 300 Point D:P = $800i = 25.0%B d = 400 Point E:P = $750i = 33.0%B d = 500 Demand Curve is B d in Figure 1 which connects points A, B, C, D, E. – Has usual downward slope

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Figure 4.1 Supply and Demand for Bonds Supply and Demand Analysis of the Bond Market

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Derivation of Supply Curve Point F:P = $750i = 33.0%B s = 100 Point G:P = $800i = 25.0%B s = 200 Point C:P = $850i = 17.6%B s = 300 Point H:P = $900i = 11.1%B s = 400 Point I:P = $950i = 5.3%B s = 500 Supply Curve is B s that connects points F, G, C, H, I, and has upward slope

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Market Equilibrium 1.Occurs when B d = B s, at P* = 850, i* = 17.6% 2.When P = $950, i = 5.3%, B s > B d (excess supply): P  to P*, i  to i* 3.When P = $750, i = 33.0, B d > B s (excess demand): P  to P*, i  to i*

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Market Demand Conditions Market equilibrium occurs when the amount that people are willing to buy (demand) equals the amount that people are willing to sell (supply) at a given price Excess supply occurs when the amount that people are willing to sell (supply) is greater than the amount people are willing to buy (demand) at a given price Excess demand occurs when the amount that people are willing to buy (demand) is greater than the amount that people are willing to sell (supply) at a given price

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Loanable Funds Terminology 1.Demand for bonds = supply of loanable funds 2.Supply of bonds = demand for loanable funds Figure 4.2 A Comparison of Terminology: Loanable Funds and Supply and Demand for Bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Shifts in the Demand Curve Figure 4.3 Shifts in the Demand Curve for Bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved How Factors Shift the Demand Curve 1.Wealth – Economy , wealth , B d , B d shifts out to right 2.Expected Return – i  in future, R e for long-term bonds , B d shifts out to right – π e , relative R e , B d shifts out to right

Copyright © 2006 Pearson Addison-Wesley. All rights reserved How Factors Shift the Demand Curve 1.Risk – Risk of bonds , B d , B d shifts out to right – Risk of other assets , B d , B d shifts out to right 2.Liquidity – Liquidity of bonds , B d , B d shifts out to right – Liquidity of other assets , B d ,B d shifts out to right

Factors That Shift Demand Curve

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Summary of Shifts in the Demand for Bonds 1.Wealth: in a business cycle expansion with growing wealth, the demand for bonds rises, conversely, in a recession, when income and wealth are falling, the demand for bonds falls 2.Expected returns: higher expected interest rates in the future decrease the demand for long-term bonds, conversely, lower expected interest rates in the future increase the demand for long-term bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Summary of Shifts in the Demand for Bonds (2) 1.Risk: an increase in the riskiness of bonds causes the demand for bonds to fall, conversely, an increase in the riskiness of alternative assets (like stocks) causes the demand for bonds to rise 2.Liquidity: increased liquidity of the bond market results in an increased demand for bonds, conversely, increased liquidity of alternative asset markets (like the stock market) lowers the demand for bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Shifts in the Supply Curve 1.Profitability of Investment Opportunities – Business cycle expansion, investment opportunities , B s , Bs shifts out to right 2.Expected Inflation – π e , B s , B s shifts out to right 3.Government Activities – Deficits , B s , B s shifts out to right Figure 4.4 Shift in the Supply Curve for Bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Factors That Shift Supply Curve

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Summary of Shifts in the Supply of Bonds 1.Expected Profitability of Investment Opportunities: in a business cycle expansion, the supply of bonds increases, conversely, in a recession, when there are far fewer expected profitable investment opportunities, the supply of bonds falls 2.Expected Inflation: an increase in expected inflation causes the supply of bonds to increase 3.Government Activities: higher government deficits increase the supply of bonds, conversely, government surpluses decrease the supply of bonds

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Changes in π e : The Fisher Effect If π e  1.Relative R e , B d shifts in to left 2.B s , B s shifts out to right 3.P , i  Figure 4.5 Response to a Change in Expected Inflation

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Figure 4.6 Expected Inflation and Interest Rates (Three-Month Treasury Bills), 1953–2004 Evidence on the Fisher Effect in the United States

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Summary of the Fisher Effect 1.If expected inflation rises from 5% to 10%, the expected return on bonds relative to real assets falls and, as a result, the demand for bonds falls 2.The rise in expected inflation also means that the real cost of borrowing has declined, causing the quantity of bonds supplied to increase 3.When the demand for bonds falls and the quantity of bonds supplied increases, the equilibrium bond price falls 4.Since the bond price is negatively related to the interest rate, this means that the interest rate will rise

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Business Cycle Expansion 1.Wealth , B d , B d shifts out to right 2.Investment , B s , B s shifts right 3.If B s shifts more than B d then P , i  Figure 4.7 Response to a Business Cycle Expansion

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Evidence on Business Cycles and Interest Rates Figure 4.8 Business Cycle and Interest Rates (Three-Month Treasury Bills), 1951–2004

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Profiting from Interest-Rate Forecasts Methods for forecasting 1.Supply and demand for bonds: use Flow of Funds Accounts and judgment 2.Econometric Models: large in scale, use interlocking equations that assume past financial relationships will hold in the future

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Profiting from Interest-Rate Forecasts (cont.) Make decisions about assets to hold 1.Forecast i , buy long bonds 2.Forecast i , buy short bonds Make decisions about how to borrow 1.Forecast i , borrow short 2.Forecast i , borrow long

Web Appendix Applying the Asset Market Approach to a Commodity Market: The Case of Gold

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Supply and Demand in Gold Market Deriving Demand Curve – P e t+1 is held constant – P t , g e , R e   G d  – Demand curve is downward sloping Deriving Supply Curve – P t , more production, G s  – Supply curve is upward sloping

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Supply and Demand in Gold Market Market Equilibrium 1.G d = G s 2.If P t > P* = P 1, G s > G d, P t  to P* 3.If P t < P* = P 1, G s < G d, P t  to P*

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Changes in Equilibrium Factors That Shift Demand Curve for Gold 1.Wealth 2.Expected return on gold relative to alternative assets 3.Riskiness of gold relative to alternative assets 4.Liquidity of gold relative to alternative assets Factors That Shift Supply Curve for Gold 1.Technology of mining 2.Government sales of gold

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Response of Gold Market to a Change in π e If π e  1.π e , P e t+1  ; at given P t, g e   G d   G d shifts right 2.Go to point 2; P t  3.Price of gold positively related to π e 4.Gold price is barometer of π- pressure Figure 4.Web A1 A Change in the Equilibrium Price of Gold

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Chapter Summary Determining Asset Demand: We examined the forces that affect the demand and supply of assets. Supply and Demand in the Bond Market: We examine those forces in the context of bonds, and examined the impact on interest rates.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Chapter Summary (cont.) Changes in Equilibrium Interest Rates: We further examined the dynamics of changes in supply and demand in the bond market, and the corresponding effect on bond prices and interest rates.