Lecture 4
BEEM119 Economics of Banking
Jan Auerbach
Department of Economics University of Exeter
Contents
1 Financial Institutions and Key Concepts
1 Institutions and Concepts.
2 Understanding Interest Rates.
3 The Risk and Term Structure of Interest Rates.
4 The Efficient Markets Hypothesis.
2 Money
1 What is Money?
2 The Money Supply Process.
3 Quantitative Theory, Inflation, and the Demand for Money.
3 Banking and Financial Intermediation
1 An Economic Analysis of Financial Structure.
2 Banking Industry: Structure and Competition.
4 Banking and Policy
1 Economic Analysis of Financial Regulation.
2 Financial Crises.
Rate of Return
Is the interest rate (yield) an appropriate measure of whether or not an investment is profitable?
The interest rate is negatively related to the price of the security. Suppose you want or need to sell the security before maturity. An accurate measure is the return or rate of return.
It takes into account the payments accruing to the owner of the security as well as the changes in the security’s value.
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Rate of Return
The rate of return from holding a security from time t to time t + 1 equals the sum of the capital gain on the security, plus any cash payments divided by the initial purchase price of the security.
R = C + Pt+1 − Pt , Pt
where
R = the rate of return on the security;
Pt+1 = price at time t + 1, the end of the holding period; Pt = price at time t, the beginning of the holding period; C = cash flow payment made during the holding period.
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Rate of Return
Example: A coupon bond with face value 100, coupon rate 10%, bought at 100, sold at 110 has a return
R= Pt+1 −Pt +C = 110−100+10 = 20 =0.20=20%. Pt 100 100
(Think: The return is all the payments extracted from the asset,
minus all expenses incurred for holding it, as a fraction of the purchase price.)
The return does not equal the yield to maturity, 10%. Why?
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Rate of Return
Rewrite the expression of the return as
R = C + Pt+1 − Pt = ic + g.
Pt Pt The return equals the current yield,
ic = C , Pt
g = Pt+1 − Pt . Pt
plus the rate of capital gain
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Rate of Return
Consider a 10%-coupon bond with face value 100 maturing in 2 years.
The prices are given; we calculate the yields to maturity and returns for holding the bond for one period.
pt pt+1 pt+2 it it+1 110 102 100 4.65 7.84 100 100 100 10.00 10.00
90 98 100 16.25 12.24
Rt+1 Rt+2 1.82 7.84 10.00 10.00 20.00 12.24
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Rate of Return
In general, returns don’t equal yields to maturity.
The rate of return and the yield to maturity are equal only if the holding period equals the time to maturity.
Higher interest rates lead to capital losses if the holding period is shorter than the term to maturity.
The more distant the a bond’s maturity,
• the greater the % change in prices due to interest rate changes; • the lower the rate of return when interest rates rise.
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The Stock Market, rational expectations, and the Efficient Markets Hypothesis
(Mishkin, chapter 7)
Common Stock
Common stock is the main source of equity capital.
Stockholders have a bundle of rights, most importantly: • the right to vote and
• the right to be the residual claimant of cash flows.
Residual claimant: stockholders receive whatever remains after all other claims against the firm’s assets have been satisfied.
An individual stockholder’s claims are proportional to the percentage of the outstanding stock they own.
E.g., periodical payments (dividends) from the firm’s net earnings.
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Computing the Price of Common Stock
The One-Period Valuation Model
P0= D1 + P1 1+ke 1+ke
where
P0 = the current price of the stock;
D1 = the dividend paid at the end of year 1;
ke = the required return on investment in equity;
P1 = the sale price of the stock at the end of the first period.
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Computing the Price of Common Stock
The One-Period Valuation Model
Example: A share of interest sells at $20 today, pays $0.1 of dividends per year and is predicted to sell at $25 next year. Your are aiming for a 10% return on the investment.
P0 = 0.1 + 25 = 251 = 22.82 > 20. 1.1 1.1 11
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Computing the Price of Common Stock
The Generalized Dividend Valuation Model
The value of stock today is the present value of all future cash flows: P0= D1 + D2 + D3 +···+ Dn + Pn .
1+ke (1+ke)2 (1+ke)3 (1+ke)n (1+ke)n
If n is far in the future, then (approximately) Pn doesn’t affect P0 and
P0=∞ Dt . t=1 (1+ke)t
That is, the price of the stock is determined only by the present value of the stream of future dividends.
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Computing the Price of Common Stock
The Gordon Growth Model
P0 = D0(1+g) = D1 ke − g ke − g
where
P0 = the current price of the stock; D0 = the most recent dividend paid;
g = the expected constant growth rate of dividends; D1 = the expected dividend paid next period;
ke = the required return on investment in equity, and dividends grow at g < ke “forever.”
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Gordon model example: Tesco
What return should we require from holding a Tesco share?
The closing share price on 10/11/2014 was 185.25p (google finance). A share paid 14.76p of dividends per year for 2012-2014 (Stockopedia). If we expect next year’s dividends to be 14.76p, we require a return of
or 7.97%.
ke = 14.76p = 0.0797, 185.25p
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Application: Tesco
Let’s take into account the growth of dividends over the last 10 years.
2005 2006 2007 2008 2009 7.56 8.63 9.64 10.9 11.96
The average growth is
9 14.761
g = 7.56 − 1 = 0.0772. Then, we would require a return of
2010 2011 2012 13.05 14.46 14.76
2013 2014 14.76 14.76
ke = (1 + g)D0 + g = (1.0772) 14.76p + 0.0772 = 0.1630, P0 185.25p
or 16.30%.
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How the Market Sets Prices
The price is set by the buyer willing to pay the highest price. That is, the buyer who can take best advantage of the asset.
Better information about an asset may reduce its perceived risk and increase its value.
Information is important for individuals to value each asset. New information about a firm changes expectations and prices.
Market participants constantly receive information and revise their expectations, so stock prices change frequently.
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How the Market Sets Prices
Example (Mishkin, page 187): A stock is expected to pay dividends $2 next year which are expected to then be growing at 3% forever.
Investor 1 has doubts about accuracy and constancy of those numbers. Investor 2 is friends with analysts. Investor 3 knows the CEO.
Investor 1
2
3
Discount rate Calculation 15% $2
0.15−0.03 12% $2
0.12−0.03 10% $2
0.10−0.03
Price $16.67 $22.22 $28.57
The price will be between $22.22 and $28.57.
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Application: The Global Financial Crisis and the Stock Market
In the recent financial crisis, stock market prices slumped. Growth prospects were revised downwards: g ↓. Uncertainty increased: ke ↑.
The Gordon model predicts a drop in stock prices.
P0= D1 . ke − g
What about Monetary Policy?
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The Theory of Rational Expectations
Due to John Muth (Carnegie Mellon), popularized by Robert Lucas (U of Chicago), Nobel Prize 1995
Denote a variable of interest at time t + 1 by xt+1.
Let xt+1 also be the (realized) value of that variable at time t + 1.
Denote by xe the expected value of x formed at time t. t+1 t+1
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The Theory of Rational Expectations
Adaptive expectations:
Expectations are formed from past experience only.
It’s sort of a process of systematic trial and error.
Changes in expectations will occur slowly over time as data changes.
∞
xe −xe =α(x −xe) or xe =α(1−α)ix , 0<α<1.
t+1 t
t t t+1
= xe. Agents assume that nothing changes.
Static: xe t+1
t
Myopic: xe t+1
= x . Agents expect last period’s realization. t
i=0
t−i
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The Theory of Rational Expectations
Extrapolative expectations:
The future is expected to be a continuation of the past.
xe =x +β(x −x ). t+1 t t t−1
β captures the extent to which agents expect trends to continue.
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The Theory of Rational Expectations
Rational expectations:
The difference between the expected value of a variable and its realization is unpredictable.
xe −x =ε . t+1 t+1 t+1
εt+1 is a random error term with mean 0.
If εt = 0 for all t, then perfect foresight.
Expectations equal optimal forecasts using all available information.
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The Theory of Rational Expectations
Rational expectations are identical to optimal forecasts using all available information.
A prediction based on it may not always be perfectly accurate.
• There is some randomness involved that cannot be predicted.
• The predictor may be unaware of some unavailable but relevant information.
What makes an expectation irrational?
• It is (too) costly to make the expectation the best guess possible. • The predictor may ignore some available relevant information.
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The Theory of Rational Expectations
Implications of rational expectations:
If the way a variable moves changes, then the way in which expectations over that variable are formed will change as well.
Changes in the conduct of monetary policy (e.g., target the federal funds rate).
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The Theory of Rational Expectations
Rational:
Why should expectations be rational (why should firms and people incorporate all available information into their decisions)?
Answer: Because it is costly not to do so.
The incentives for equating expectations with optimal forecasts are especially strong in financial markets. Why?
Here, people with better forecasts of the future get rich.
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The Theory of Rational Expectations
The application of the theory of rational expectations to financial markets is thus particularly useful. It is called the efficient market hypothesis or the theory of efficient capital markets.
Due to Eugene Fama (U of Chicago), first formulated in a 1970 paper.
Nobel Prize 2013 “for their empirical analysis of asset prices” shared with Lars Hansen (University of Chicago) and Robert Shiller (Yale).
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The Efficient Market Hypothesis
Recall:
The rate of return from holding a security equals the sum of the capital gain on the security, plus any cash payments divided by the initial purchase price of the security.
R = Pt+1 − Pt + C , Pt
where
R = the rate of return on the security;
Pt+1 = price at time t + 1, the end of the holding period; Pt = price at time t, the beginning of the holding period; C = cash flow payment made during the holding period.
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The Efficient Market Hypothesis
At the beginning of the period, we know Pt and C.
Pt+1 is unknown and we must form an expectation Pte+1 of it. The expected return Re is
Pe −P+C Re=t+1 t .
Pt
Expectations of future prices equal optimal forecasts using all
available information. So, the expected return is an optimal forecast. By the supply and demand analysis, Re equals equilibrium return R∗.
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The Efficient Market Hypothesis
Current prices in a financial market will be set so that
• the optimal forecast of a security’s return, • using all available information,
• equals the security’s equilibrium return.
In an efficient market, the price of a security fully reflects all available information.
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The Efficient Market Hypothesis
The rational:
IfRe >R∗ thenPt ↑andthusRe ↓. IfRe