Essex EC248-2-SP Lecture 2 Financial Markets: Determinants and Role of Interest Rates Alexander Mihailov, 23/01/06 Plan of Talk 1. 2. 3. 4. Introduction Interest rates: definition and behaviour The risk and term structure of interest rates

Interest rates and the stock market Interest rates and the exchange rate: UIP Wrap-up 2004 Pearson Addison-Wesley. All rights reserved 2-2 Aims and learning outcomes Aims Understand what determines interest rates and their behaviour Discuss how interest rates affect, in turn, other variables Learning outcomes Compute interest rates for the basic types of credit instruments Characterise the risk and term structure of interest rates Discuss their relationship with the stock market and the exchange rate

2004 Pearson Addison-Wesley. All rights reserved 2-3 Present Value Four Types of Credit Instruments 1. Simple loan 2. Fixed-payment loan 3. Coupon bond 4. Discount (zero coupon) bond Concept of Present Value Simple loan of $1 at 10% (constant) interest p.a. Year 1 2 3 n $1.10 $1.21 $1.33 $1x(1 + i)n $1

PV of future $1 = (1 + i)n 2004 Pearson Addison-Wesley. All rights reserved 2-4 Yield to Maturity: Loans Yield to maturity = interest rate that equates todays value with present value of all future payments 1. Simple Loan (i = 10%) $100 = $110/(1 + i) $110 $100 i= = $100 $100 $10 = 0.10 = 10% 2. Fixed Payment Loan (i = 12%)

$1000 = LV = $126 (1+i) FP (1+i) + + $126 (1+i)2 FP (1+i) 2004 Pearson Addison-Wesley. All rights reserved 2

+ + $126 (1+i)3 FP (1+i) 3 + ... + + ... + $126 (1+i)25 FP (1+i)n 2-5 Yield to Maturity: Bonds 3. Coupon Bond (Coupon rate = 10% = C/F)

P= $100 $100 + + (1+i) (1+i)2 $100 $100 $1000 + ... + + (1+i)3 (1+i)10 (1+i)10 P=

C (1+i) C C + ... + (1+i)3 (1+i)n C + + (1+i)2 F + (1+i)n Consol: Fixed coupon payments of $C forever C

C P= i = i P 4. Discount Bond (P = $900, F = $1000), one year $900 = $1000 (1+i) i= $1000 $900 $900 i= FP P

= 0.111 = 11.1% 2004 Pearson Addison-Wesley. All rights reserved 2-6 Relationship Between Price and Yield to Maturity Three Interesting Facts in Table 1 1. 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 2004 Pearson Addison-Wesley. All rights reserved 2-7 Current Yield ic =

C P 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 Yield on a Discount Basis idb = (F P) F x 360 (number of days to maturity) One year bill, P = $900, F = $1000

$1000 $900 360 idb = x = 0.099 = 9.9% $1000 365 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 2004 Pearson Addison-Wesley. All rights reserved 2-8 Distinction Between Interest Rates and Returns Rate of Return R = C + Pt+1 Pt Pt

where: ic = g= C Pt Pt+1 Pt Pt 2004 Pearson Addison-Wesley. All rights reserved = ic + g = current yield = capital gain/loss 2-9 Distinction Between Real and Nominal Interest Rates Real Interest Rate

Interest rate that is adjusted for expected changes in the price level ir = i e 1. Real interest rate more accurately reflects true cost of borrowing 2. When real rate is low, greater incentives to borrow and less to lend if i = 5% and e = 3% then: ir = 5% 3% = 2% if i = 8% and e = 10% then ir = 8% 10% = 2% 2004 Pearson Addison-Wesley. All rights reserved 2-10 U.S. Real and Nominal Interest Rates 2004 Pearson Addison-Wesley. All rights reserved 2-11 Asset Market Approach to Interest Rates: Derivation of Bond Demand Curve i = R =

e FP P Point A: P = $950 $1000 $950 i= = 0.053 = 5.3% $950 Bd = $100 billion 2004 Pearson Addison-Wesley. All rights reserved 2-12 Derivation of Bond Demand Curve (cont.) Point B: P = $900 ($1000 $900)

i= = 0.111 = 11.1% $900 Bd = $200 billion Point C: P = $850, i = 17.6% Bd = $300 billion Point D: P = $800, i = 25.0% Bd = $400 billion Point E: P = $750, i = 33.0% Bd = $500 billion Demand Curve is Bd (in the figure next) which connects points A, B, C, D, E, has usual downward slope 2004 Pearson Addison-Wesley. All rights reserved 2-13 Derivation of Bond Supply Curve Point F: P = $750, i = 33.0%, Bs = $100 billion Point G: P = $800, i = 25.0%, Bs = $200 billion Point C: P = $850, i = 17.6%, Bs = $300 billion Point H: P = $900, i = 11.1%, Bs = $400 billion Point I:

P = $950, i = 5.3%, Bs = $500 billion Supply Curve is Bs that connects points F, G, C, H, I, and has upward slope 2004 Pearson Addison-Wesley. All rights reserved 2-14 Supply and Demand Analysis of the Bond Market Market Equilibrium d s 1. Occurs when B = B , at P* = $850, i* = 17.6%

s 2. When P = $950, i = 5.3%, B > d B (excess supply): P to P*, i to i* d 3. When P = $750, i = 33.0, B > s B (excess demand): P to P*, i to i* 2004 Pearson Addison-Wesley. All rights reserved 2-15 Loanable Funds Terminology 1. Demand for bonds = supply of loanable funds

2. Supply of bonds = demand for loanable funds 2004 Pearson Addison-Wesley. All rights reserved 2-16 Shifts in the Bond Demand Curve 2004 Pearson Addison-Wesley. All rights reserved 2-17 Factors that Shift the Bond Demand Curve 1. Wealth A. Economy grows, wealth , Bd , Bd shifts out to right 2. Expected Return (identical to the interest rate only for a 1-yr discount bond and a 1-yr holding period but not for longer-term bonds!)

A. i in future, Pe => Re for long-term bonds , Bd shifts out to right B. e , relative Re (to that of real assets) , Bd shifts out to right C. Expected return of other assests , Bd , Bd shifts out to right 3. Risk A. Risk of bonds , Bd , Bd shifts out to right B. Risk of other assets , Bd , Bd shifts out to right 4. Liquidity A. Liquidity of bonds , Bd , Bd shifts out to right B. Liquidity of other assets , Bd , Bd shifts out to right 2004 Pearson Addison-Wesley. All rights reserved 2-18 Factors that Shift the Bond Supply Curve 1. Profitability of Investment Opportunities Business cycle

expansion, investment opportunities , Bs , Bs shifts out to right 2. Expected Inflation e , RIR , Bs , Bs shifts out to right 3. Government Activities Deficits , Bs , Bs shifts out to right 2-19 Increase in Default Risk on Corporate Bonds => Risk Premium 2004 Pearson Addison-Wesley. All rights reserved 2-20

Bond Ratings 2004 Pearson Addison-Wesley. All rights reserved 2-21 Risk Structure of Long-Term Bonds in the United States 2004 Pearson Addison-Wesley. All rights reserved 2-22 Term Structure Facts to be Explained 1. Interest rates for different maturities move together over time 2. Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high 3. Yield curve is typically upward sloping Three Theories of Term Structure 1. Expectations Theory 2. Segmented Markets Theory

3. Liquidity Premium (Preferred Habitat) Theory A. Expectations Theory explains 1 and 2, but not 3 B. Segmented Markets explains 3, but not 1 and 2 C. Solution: Combine features of both Expectations Theory and Segmented Markets Theory to get Liquidity Premium (Preferred Habitat) Theory and explain all facts 2-23 Interest Rates on Different Maturity Bonds Move Together 2004 Pearson Addison-Wesley. All rights reserved 2-24 Yield Curves 2004 Pearson Addison-Wesley. All rights reserved 2-25

Expectations Hypothesis Key Assumption: Bonds of different maturities are perfect substitutes Implication: Re on bonds of different maturities are equal For an n-period bond: int it ite1 ite2 ite( n 1) In words: interest rate on long bond = average n short rates expected to occur over life of long bond Numerical example: One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9% Interest rate for one to five year bonds: 5%, 5.5%, 6%, 6.5% and 7% 2004 Pearson Addison-Wesley. All rights reserved 2-26

Segmented Markets Theory Key Assumption: Bonds of different maturities are not substitutes at all Implication: Markets are completely segmented: interest rate at each maturity determined separately Explains Fact 3 that yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bonds Does not explain Fact 1 or Fact 2 because assumes long and short rates determined independently 2004 Pearson Addison-Wesley. All rights reserved 2-27 Liquidity Premium (Preferred Habitat) Theories => Term (Liquidity) Premium Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes

Implication: Modifies Expectations Theory with features of Segmented Markets Theory Investors prefer short rather than long bonds must be paid positive liquidity (term) premium, lnt, to hold long-term bonds Results in following modification of Expectations Theory it + iet+1 + iet+2 + ... + iet+(n1) int = + lnt n 2004 Pearson Addison-Wesley. All rights reserved 2-28 Computing the Price of Common Stock Basic Principle of Finance Value of Investment = Present Value of Future Cash Flows One-Period Valuation Model Generalised Dividend Valuation Model D1

P0 1 ke P1 1 ke Since last term of the above equation is small, it can be written as Dn Pn D1 D2 P0 1 2

n (1 ke ) (1 ke ) (1 ke ) (1 ke ) n Dt P0 t (1 k ) t 1 e 2004 Pearson Addison-Wesley. All rights reserved 2-29 Theory of Rational Expectations Rational expectation (RE) = expectation that is optimal forecast

(best prediction of future) using all available information: i.e., RE Xe = Xof 2 reasons expectation may not be rational 1. Not best prediction 2. Not using available information Rational expectation, although optimal prediction, may not be accurate Rational expectations makes sense because is costly not to have optimal forecast Implications: 1. Change in way variable moves, way expectations are formed changes 2. Forecast errors on average = 0 and are not predictable 2004 Pearson Addison-Wesley. All rights reserved 2-30 Efficient Markets Hypothesis Pt+1 Pt + C R= Pt Peet+1 Pt + C R = Pt

Rational Expectations implies: Pet+1 = Poft+1 Re = Rof (1) Market equilibrium Re = R* (2) Put (1) and (2) together: Efficient Markets Hypothesis Rof = R* Why the Efficient Markets Hypothesis makes sense If Rof > R* Pt , Rof If Rof < R* Pt , Rof until Rof = R* 1. All unexploited profit opportunities eliminated 2. Efficient Market holds even if are uninformed, irrational participants in market 2004 Pearson Addison-Wesley. All rights reserved 2-31

Evidence on Efficient Markets Hypothesis Favorable Evidence 1. Investment analysts and mutual funds dont beat the market 2. Stock prices reflect publicly available information: anticipated announcements dont affect stock price 3. Stock prices and exchange rates close to random walk If predictions of P big, Rof > R* predictions of P small 4. Technical analysis does not outperform market Unfavorable Evidence 1. Small-firm effect: small firms have abnormally high returns 2. January effect: high returns in January 3. Market overreaction 4. Excessive volatility 5. Mean reversion 6. New information is not always immediately incorporated into stock prices Overview Reasonable starting point but not whole story 2004 Pearson Addison-Wesley. All rights reserved 2-32

Law of One Price Example: American steel $100 per ton, Japanese steel 10,000 yen per ton If E = 50 yen/$ then prices are: In U.S. In Japan American Steel Japanese Steel $100 5000 yen $200 10,000 yen If E = 100 yen/$ then prices are: In U.S. In Japan American Steel

Japanese Steel $100 10,000 yen $100 10,000 yen Law of one price E = 100 yen/$ 2-33 Purchasing Power Parity (PPP) PPP Domestic price level 10%, domestic currency 10% 1. Application of law of one price to price levels 2. Works in long run, not short run Problems with PPP 1. All goods not identical in both countries: Toyota vs Chevy 2. Many goods and services are not traded: e.g. haircuts

2004 Pearson Addison-Wesley. All rights reserved 2-34 PPP: U.S. and U.K 2004 Pearson Addison-Wesley. All rights reserved 2-35 Expected Returns and Interest Parity $ Deposits Euro Deposits Francois iD + (Eet+1 Et)/Et iF Relative Re

iD iF + (Eet+1 Et)/Et Re for Al iD iF (Eet+1 Et)/Et iD iF + (Eet+1 Et)/Et Interest Parity Condition: $ and Euro deposits perfect substitutes iD = iF (Eet+1 Et)/Et Example: if iD = 10% and expected appreciation of $, (Eet+1 Et)/Et, = 5% iF = 15% 2004 Pearson Addison-Wesley. All rights reserved 2-36

The Dollar and Interest Rates 1. Value of $ and real rates rise and fall together, as theory predicts 2. No association between $ and nominal rates: $ falls in late 70s as nominal rate rises 2004 Pearson Addison-Wesley. All rights reserved 2-37 Concluding Wrap-Up What have we learnt? Why interest rates are so important in the economy

What are their types and how they are related How interest rates interact with other key financial market variables Where we go next: to a closer look at financial intermediaries, with a focus on banking and regulation 2004 Pearson Addison-Wesley. All rights reserved 2-38