11/9/2001
Lecture
Equity Investments
Copyright K.Cuthbertson, D.Nitzsche
1
READING
Investments:Spot and Derivative Markets,
K.Cuthbertson and D.Nitzsche
CHAPTER 10:
Section 10.3: CAPM
Section 10.4: Performance Measures
CHAPTER 12:
Equity Finance and Stock Valuation
CHAPTER 13:
- excluding ‘Volatility Tests’ p.414-420
Copyright K.Cuthbertson, D.Nitzsche
2
TOPICS
Anomalies/Stock Picking
Momentum and Value Stocks
Other methods
The CAPM/ SMLand Investment Appraisal
-Required return
-Asset’s “beta” ,portfolio beta and risk
-CAPM: Theory and Evidence
-Security Market Line
- CAPM and Investment Appraisal
Self Study Slides
Valuation Of Stocks Using DPV/CAPM and IRR
Note:
We will concentrate on the ‘Anomalies/stock picking strategies and CAPM/ Investment Appraisal
We will quickly cover the CAPM as this is adequately covered in Cutbertson/Nitzsche. We have
already covered most of the ‘self study’ concepts in the lecture dealing with ‘Valuing Firms’
Copyright K.Cuthbertson, D.Nitzsche
3
Anomalies:
.
“Stock-Picking” Strategies:
Copyright K.Cuthbertson, D.Nitzsche
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Anomalies / “Stock-Picking” Strategies
Beware ! There is a lot of confusing drivel in this area (but not below,
of course !)
Now let’s start to remove some of the mystique and ‘bullshit’ in this
area
Or
Warren Buffet, Jack Schwager, Merrill Lynch Asset Management and
LTCM are not as good as they say they are, over a run of months/
years.
Copyright K.Cuthbertson, D.Nitzsche
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Efficient Markets Hypothesis (EMH)
EMH: (1)
(Excess) stock returns are unpredictable - v. weak condition, and
incorrect definition !
(Note: this implies you cannot make or lose (!) money on
average !)
EHM (2)
It is impossible on average, to outperform the return on the
‘passive’ ‘market portfolio’ by using ‘active’ stock picking
~ once we have accounted for the riskiness of the ‘active
strategy’ and the transactions costs incurred.
This definition does not rule out the possibility that there is some
predictability in stock returns
Copyright K.Cuthbertson, D.Nitzsche
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A Waste of Your Money ?
~ usually h/b, big print, wide margins, and ‘v. pricey’
Big Bucks
Millionaire Mind
Guru Guide
Wizards of Wall St
Day Trade Part Time: Don’t Give up Your Day Job!
‘Net’ Profit
Passport to Profit
Elizabeth I: CEO
Powerplays: Shakespeare’s Lessons in Investing and
Leadership
Technopreneurial
New Market Wizards (J. Schwager)
Heros.com
e-investing
Copyright K.Cuthbertson, D.Nitzsche
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Anomalies : “Stock-Picking” Strategies
It is not that difficult to ‘beat the market (return)’
~ just buy a portfolio of ‘small-cap stocks’ which we
know (empirically) earn high returns (but are also
highly risky).
Also ‘small-cap’ stocks tend to have low prices ~ that’s
why they are ‘low cap’ - consistent with ‘rule 1’ above.
But all this does not necessarily refute the EMH(2). It
merely confirms ‘the first (and only!) law of finance you only get more ‘return’ if you take on more risk!
Copyright K.Cuthbertson, D.Nitzsche
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Anomalies : “Stock-Picking” Strategies
Key issue is whether you earn an average return which
more than compensates for the riskiness of these stock
(portfolios).
This raises the question of how we measure risk.
If our stock portfolio is reasonably well diversified we
may compare ‘performance’ using the Sharp ratio.
Copyright K.Cuthbertson, D.Nitzsche
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Anomalies : “Stock-Picking” Strategies
Assume a series of monthly holding periods.
Compare the Sharp ratio for our chosen portfolio Sp
Sp = (Av Monthly Portfolio Return - rmonth ) / month
with Sharp ratio for the market (passive) portfolio:
Sm(annual) = (12-4)/20 = 0.4 annual
Hence:
Sm(monthly) = [8/12] / [20/sqrt(12)]
= 0.67 / 5.77 = 0.115 (monthly)
Copyright K.Cuthbertson, D.Nitzsche
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Momentum
and
Value Stocks
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Basic Empirics: Momentum Strategy
First , note that we cannot predict individual stock
returns (at all) ~ there is just too much ‘specific risk’
(or ‘noise’ ).
The best we can hope to do is to find some predictability
in portfolio returns (e.g. for the manufacturing sector)
SHORT HORIZON
Many stock (portfolios) experience a run of positive
(negative) returns (e.g. monthly returns)
~ basis of ‘momentum strategies’ (or ‘growth stocks’)
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Basic Empirics: Value Stocks
From ‘Momentum’ to ‘Value Stocks’
Stocks that do well (badly) for some time, must have high
(low) prices.
LONG HORIZON
It is found that stocks with ‘high’ (low) prices, subsequently
do badly (well) over the ‘longer term’ (e.g. 1- 3 years)
~ probably due to ‘fundamentals’ of the business cycle and
financial distress.
~ basis of ‘reversal strategies’ (or ‘value stocks’).
Copyright K.Cuthbertson, D.Nitzsche
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Basic Empirics: Value Stocks
Many‘stock picking’ strategies can be viewed as buying
‘low priced stocks’ (or strictly, portfolios of low priced
stocks)
since empirically, it appears that ‘low price’ stocks
subsequently earn ‘high’ returns (over horizons of 1-3
years - ‘long horizon’).
That is, stock returns ARE predictable (though not 100%
predicable !)
Copyright K.Cuthbertson, D.Nitzsche
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Value Stocks
Value Stocks can be defined in a number of different ways
but essentially it involves buying (relatively) ‘low price’
stocks (and selling currently ‘high’ priced stocks)
A typical ‘value stock’ is one whose price has been driven
down by financial distress
- ie. its current low price = ‘good value’ (viz. price of
apples)
Copyright K.Cuthbertson, D.Nitzsche
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Value Stocks
1) ‘Value/Contrarian/Reversal/ Buying “losers”
ASSUME MINIMUM holding period of 1-YEAR (1000 stocks in S&P500
say).
A)Buy 10% of stocks that have fallen the most over the last 4-years
(lowest decile).
B)Short sell 10% of stocks that have risen the most over last 4
years.(these funds are used in “a”)
C) Wait for 1-month (and then repeat and create a new ‘active’
portfolio)
D) Close out each of these active portfolios, after about 1 year
Then it is found that you beat the return on the ‘passive strategy’ (ie.
always holding the S&P index) and may beat it “corrected for risk” ,
that is a higher Sharpe ratio than if you held stocks in same
proportion as in the S&P500.
Copyright K.Cuthbertson, D.Nitzsche
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Value Stocks
RESULTS (Fama-French 1996 table IV, Cochrane 1999)
Here, ‘Value Stocks’ = ‘losers’ = ‘Reversal strategy’
Data period
Reversal Stratg 6307-9312
3101-6302
Portf. Formation
Months
prev 4yrs
prev 4 yrs
Average Return
Monthly %,
(hold for 1 year)
0.74% pm
1.63% pm
Each month allocate all NYSE stocks into deciles (ie. 10 groups)
based on size of ‘price fall’ over previous 4 years
Buy lowest decile stocks and sell highest decile stocks, then hold this
position for a further year, and then close out the positions.
i.e you are buying ‘loosers’ and selling ‘winners’
Reason you ‘win’ is technically known as ‘long horizon mean
reversion in stock prices’ .
Note: Returns only - no corrections
for risk here !
Copyright K.Cuthbertson, D.Nitzsche
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Value Stocks: ‘Book to Market’ and Small Cap
1) ‘Value Stocks’ = high ‘book-to-market’ (implies ‘low’ price)
Every month, Buy 10% of stocks with highest “book to market
value” etc.
and short sell 10% with low book to market
then wait one year then close out the portfolio.
2)‘Value Stocks’ = small cap stocks (also implies ‘low’ price)
Buy 10% of ‘smallest’ cap stocks , etc.
These are found to be ‘profitable’ strategies ~ but we would have to
correct for risk.
Copyright K.Cuthbertson, D.Nitzsche
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Momentum/Growth Stocks
THIS IS ‘SHORT-TERM’ STRATEGY- chase the trend (chartist?)
- these are ‘growth stocks’ ~ stocks that have recently done well
Each month:
Buy 10% of stocks that have RISEN the most over the last 1-year
(top/highest decile).
Short sell 10% of stocks that have FALLEN the most over last 1year.
After 1-year and CLOSE OUT EACH POSITION.
Note: You take a new ‘position’ each month.
Copyright K.Cuthbertson, D.Nitzsche
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Momentum/Growth Stocks
RESULTS (Fama-French 1996 table IV, Cochrane 1999)
Momentum/Growth Stocks
Data period
Momentum Stgy 6307-9312
3101-6302
Portf. Formation
Average
Monthly Return %,
prev yr
1.31% pm
prev yr
0.38% pm
Buy highest decile stocks and sell lowest decile stocks, based
on their performance over last year, then hold the position
for a further year Portfolios rebalanced every month.
Some evidence 1963-1993 that strategy might work~ but not
corrected for risk
Copyright K.Cuthbertson, D.Nitzsche
20
Stock Picking: Other Methods
Copyright K.Cuthbertson, D.Nitzsche
21
Regression Techniques
Combine individual effects in a regression
Look for regression equation that predicts stock returns over different
horizons (eg.1m, 6m, 1, 3 and 5 years )
eg Return’ today’ depends on
a) returns “yesterday” (autoregressive)
b) ‘low’ PE ratios, or low ‘book-to-market’ value
c) firm size (ie. ‘small cap’ firms)
Variables in (b) and (c) help predict future returns
Again the regression is telling us to “buy stocks with low ‘prices’
Copyright K.Cuthbertson, D.Nitzsche
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Regression Techniques
REGRESSION RESULTS (Cochrane 1996 - NBER 7169)
(“Excess return on NYSE index t to t+k) = a +b (PE ratio)t
[Note: For NYSE: E/P or D/P are about 5%, giving market P/E or
P/D ratio of 20]
HORIZON
1-year
2-years
3-years
5-years
b
-1.04
-2.04
-2.84
-6.22
s.e
0.33
0.66
0.88
1.24
R-squared
0.17
0.26
0.38
0.59
(Note: these results are not as good as they look -overlapping data
problem)
Copyright K.Cuthbertson, D.Nitzsche
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Regression Techniques
Pesaran and Timmermann (1996- JoForc)
Regression equation can predict ‘out-of-sample’, the correct
direction of change for stock returns R in 65% of cases for
quarterly returns and 80% for annual returns (on the
FTSE100)
Note the emphasis on ‘direction of change’ here (not Rsquared)
Hold stocks if predicted R>0, otherwise hold bonds (bank
account)
They ‘beat’ (I.e. using Sharpe ratio) the passive strategy
corrected for risk and transaction costs. (Tudor Asset
Management)
Copyright K.Cuthbertson, D.Nitzsche
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Technical Trading and Neural ‘Nets’
Technical Trading:
Chartism,
Candlesticks
Neural Nets - highly non-linear forecasting equations for returns
usually “tick by tick” data and trading every 10 minutes !
(eg.predicting spot exchange rates : Olsen Associates, Zurich)
Fundamentals/ Bubbles - “MARKET TIMING STRATEGIES’
- Buy after a ‘big crash’ hold for 1-5 years
- different country indices - on basis of business cycles
- currency crises (overshooting/bounce back)
“Irrational over-exuberance” When will the bubble burst ?
Note: If the market is “reasonably efficient” then “old” anomalies will
eventually disappear but new ones might replace them.
Copyright K.Cuthbertson, D.Nitzsche
25
The CAPM/ SML
and
Investment Appraisal
Copyright K.Cuthbertson, D.Nitzsche
26
Topics:CAPM/SML
CAPM
-Required return
-Asset’s “beta” ,portfolio beta and risk
-CAPM: Theory and Evidence
-Security Market Line
CAPM and Investment Appraisal
Copyright K.Cuthbertson, D.Nitzsche
27
Capital Asset Pricing Model,CAPM
Why would you WILLINGLY hold an asset (as part of your portfolio)
if it had a ‘low’ expected return (and low historic return)?
The CAPM gives the
Expected/required return on any asset-I
ERi = risk free rate + ‘risk premium’ = r + i ( ERm - r )
ERm = expected market return - in practice measured by the historic
average return on say the S&P500 index.
If you have two assets with beta’s of A= 0.25 and B= 0.5 then you
would say that B was ‘twice as risky’ as A and CAPM predicts
that ‘average return’ on B equals twice that on A.
(ERB - r) / (ERA - r) = beta-B / beta-A
Copyright K.Cuthbertson, D.Nitzsche
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Capital Asset Pricing Model,CAPM
How do you measure the ‘beta’ of the stock?
Beta can be obtained from a (OLS) regression of (ERi - r) on
( ERm -r ) using say 60 monthly ‘returns’. (Often the
regression is ERi on ERm although this is incorrect)
Technically
i = (Ri ,Rm) / 2 (Rm)
i = cov(Ri ,Rm) / var(Rm)
Hence, individual asset’s “beta” measures the covariance
between Ri and Rm (scaled by the variance of the market
return)
Copyright K.Cuthbertson, D.Nitzsche
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WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSET
WHEN IT IS HELD IN A PORTFOLIO?
Single asset
Holding a single asset with a high variance is very risky and
taken “on its own”, you would require a high expected
return in order that you were willing to hold this single asset
( the high average return would compensate you for the
“high” idiosyncratic risk - I.e. risk specific to the firm (e.g.
lost orders, fire, strikes)
Portfolio of Assets
Although a single share has a high variance, this risk can be
‘diversified away’ if the share is held as part of a portfolio.
So, you DO NOT receive any return/payment for this
‘source’ of risk, WHEN THIS SHARE IS HELD AS PART OF
A PORTFOLIO
Copyright K.Cuthbertson, D.Nitzsche
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WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSET
WHEN IT IS HELD IN A PORTFOLIO?
Holding a PORTFOLIO of risky assets
You only receive a ‘payment’ for this single asset’s contribution to
the overall riskiness of the portfolio
BUT the contribution of asset-i to the overall portfolio variance
depends on this asset’s covariance with all the other assets
already in the portfolio (the latter is the so-called “market
portfolio”).
If the covariance of the return on asset-i with the rest of the assets
in the portfolio is small or negative, then holding this asset may
reduce overall portfolio variance.
Copyright K.Cuthbertson, D.Nitzsche
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WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSET
WHEN IT IS HELD IN A PORTFOLIO?
The expected/required return therefore depends crucially on the
COVARIANCE between asset-i and all the other assets.
Negative covariances implies that a “low” expected return is OK
Positive covariances implies that a “high” expected return is required
The individual asset’s “beta” is proportional to this covariance, and
therefore the ‘beta’ measures ‘asset-I’ riskiness
CAPM implies you will willingly hold a risky asset-i even though it
has a low expected return and an high “own variance”, providing
it has a ‘small’ beta, because the latter implies it helps reduce the
overall risk of your WHOLE portfolio
Copyright K.Cuthbertson, D.Nitzsche
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Uses of CAPM: Desired Beta
Portfolio Beta: P = 0.2 1 + 0.8 2
The ‘weights’ 0.2 and 0.8 = proportions held in asset-1 and asset-2.
Then required return on the portfolio (= average historic return if
CAPM is true) is:
ERp = r + P ( ER.m - r )
‘Beta Services’ :
Estimation of betas (eg. BARRA for 10,000 companies world-wide)
Is beta constant over time ?
Knowing betas enables you to construct a portfolio with a
“preferred” beta
Copyright K.Cuthbertson, D.Nitzsche
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CAPM: Theory and Evidence
CAPM: Theoretical Model :
CAPM assumes:
~ mean-variance portfolio theory
~‘active traders have identical expectations about future returns,
variances and covariances
~ therefore everyone holds the ‘market portfolio
Does it hold ‘in practice’ - DEBATABLE
- but see Clare et al J. of Banking and Fin. (22) 1998 p 1207 1229
“Report of betas death are premature:..”
they find that I helps to explain Ri.(in a cross-section regression)
that is, higher betas are associated with higher average returns.
Also they find the mkt price of risk is 0.259 - 0.287 % per month (ie.
using monthly data) equiv to about 3.4% per annum.
The APT does not appear to outperform ‘ the beta only’ regression.
Copyright K.Cuthbertson, D.Nitzsche
34
SECURITY MARKET LINE AND SPECULATION
CAPM implies all ‘correctly priced’ assets should lie on the SML
SML= Larger is i the larger is required return ERi:
ERi = 5 + 8 i
ERi
SML
ERm
ERi = 9
Sell asset-i: It’s actual average return of 4%pa is
below its ‘required return’ ERi =9% given its riskiness
(as measured by its beta)
r=5
Hist.Av. Return = 4%
beta of market portfolio must =1
i =0.5
1.0
1.2
Copyright K.Cuthbertson, D.Nitzsche
Beta, i
35
Summary: CAPM/SML
The CAPM/SML gives the risk adjusted/required return on a
stock (or portfolio of stocks), so that investors will willingly
hold it (as part of their diversified portfolio)
A key determinant of the required return is NOT the assets
variance but the correlation between the asset’s return and
the market return – i.e. the assets “beta”
The SML is an alternative and equivalent way of representing
the CAPM and the ‘required return’ on a stock
Copyright K.Cuthbertson, D.Nitzsche
36
CAPM and Investment Appraisal
Copyright K.Cuthbertson, D.Nitzsche
37
CAPM and Investment Appraisal(All Equity Firm)
ERi calculated from the CAPM formula is (often) used as the
discount rate in a DPV calculation to assess a physical
investment project (eg. extend hamburger chain) for an all-equity
financed firm.
We use ERi because it reflects the riskiness of the firm’s ‘new’
investment project ~ provided the “new” investment project has
the same ‘business risk characteristics as the firm’s existing
projects (ie. “scale enhancing”).
This is because ERi reflects the return required by investors to
hold this share as part of their portfolio (of shares), to
compensate them for the (beta) risk of the firm (I.e. due to
covariance with the market return, over the past )
Copyright K.Cuthbertson, D.Nitzsche
38
CAPM and Investment Appraisal(Levered Firm)
What if the project will alter the debt-equity mix, in the future. How
do we measure the ‘equity return’ (and the WACC)?
L = U [ S + (1-t) B ] / S
= U [ 1 + (1-t) (B/S) ]
(see Cuthbertson and Nitzsche, eqn A11.20, p.367 and set ‘debt-beta’=0)
1) Measure L using historic data (monthly regression, 1996-2001)and
calc. the average (B/S)av and tav
2) Calc the average historic unlevered beta using:
U = L/ [ 1 + (1-tav ) (B/S)av ]
3) Measure the ‘new’ or target debt-equity ratio, with ‘new’ project
and calc, the ‘new’ (levered) beta.
L(new) = U [ 1 + (1-t) (B/S)new ]
4) Use ‘the new’ L , then use CAPM to calc the required return RS
Copyright K.Cuthbertson, D.Nitzsche
39
CAPM and Investment Appraisal(Levered Firm)
B/(B+S)
0%
50%
70%
90%
(B/S)new
L(new)
0.0%
100%
233%
900%
1.28(=U )
2.1
3.2
8.7
Above uses
L = U [ 1 + (1-t) (B/S) ]
Leverage effect
0.0
0.82
1.92
7.4
t=0.36
The levered beta increases with leverage (B/S) and hence so does
the required return RS given by the CAPM. This can then be
used to calculate WACC (if debt and equity finance is used) for
the project.
Copyright K.Cuthbertson, D.Nitzsche
40
CAPM and Investment Appraisal (‘Bottom Up’ approach
Firm is ‘normally’ in the oil business but:
New Project = 25% retail and 75% entertainment sector
Repeat the method on the previous slide ‘(1) to (4)’ using data on
firms in the ‘retail’ and ‘entertainment’ sectors.
Obtain the TWO unlevered betas U(,i) for each sector (in ‘2’), using
each sectors average, historic L(,i) and debt-equity ratio
(B/S)av,i
U(,i) = L(,i) / [ 1 + (1-tav ) (B/S)av,i, ]
Take a weighted average (25%,75%) to get the unlevered beta for
the firm , U
The ‘bottom up’ new levered beta for the project/firm is then
L = U [ 1 + (1-t) (B/S)new ]
Copyright K.Cuthbertson, D.Nitzsche
t=0.36
41
END OF LECTURE
Self Study Slides Follow
Copyright K.Cuthbertson, D.Nitzsche
42
Self Study Slides
Valuation Of Stocks Using
DPV/CAPM and IRR
Note: We have covered these concepts in the lectures on ‘valuing
firms’,so you will be able to cover this material with ease
Copyright K.Cuthbertson, D.Nitzsche
43
Valuation of Stocks using DPV/CAPM
The discount rate is adjusted for “risk” = ERi from the CAPM/SML, etc
Levered firm, calculate WACC
If we use DPV of TOTAL $ Free Cash Flows (FCF) then we are
estimating, value of the whole firm (= Vfirm)
The fair value of ONE share is then
Vone share = Vfirm / N.
BUT we will use ‘earnings/dividends per share’ in PV calculation and get
Vone share directly.
Copyright K.Cuthbertson, D.Nitzsche
44
Share Valuation of all-equity firm or, ‘Fair Value’ for Equities
V
D2
D1
0
1
D4
D3
2
Earnings E versus
Dividends D ?
3
• V = ‘fair value of one share’
dividends/earnings per share
. . . .
4
D1, D2, D3,= expected
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Equity Pricing and DPV
Estimate Fair Value V(all equity firm) as DPV of expected dividends
D3
D1
D2
V 


 ...
(1  R1) (1  R )2 (1  R )3
2
3
where R1, R2 are 1-, 2-, ..., n-period CAPM/SML RISK ADJUSTED
discount rates.
EFFICIENT MARKET = NO (RISKY) PROFIT OPPORTUNITIES
Actual market price P = V (fair value)
BUT
If P < V then buy this “ced stock”
Copyright K.Cuthbertson, D.Nitzsche
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Equity Pricing and DPV
Use the DCF formula to calculate the “fair VALUE” V
INVESTMENT RULE FOR P< V
If the actual quoted price, P is BELOW the “fair value = V” , then
buy the stock ( as it is currently under-priced in the market).
Wait for the actual price to rise towards the “fair value” and
hence make a capital gain (ie. a profit). This is a “risky strategy”
. Why ?
Variant on the above:
Buy immediately after announcement of exceptionally good
dividends (ie. V has just increased and is now greater than P) move fast !
Copyright K.Cuthbertson, D.Nitzsche
47
Equity Pricing and DPV
INVESTMENT RULE FOR P>V
Short-sell the stock (- wait for price to fall, then buy it back and
return it to the broker)
Ideally you would buy an underpriced stock and short sell an
overpriced stock
~ you are then largely protected against a general fall in the
market as a whole and you use little or no ‘own funds’ to
speculate
Copyright K.Cuthbertson, D.Nitzsche
48
Special Case :Gordon Growth Model
P
Assumes dividends grow at a constant rate: g = 0.05 pa
D1
0
1
D1 (1+g)
2
D1(1+g)2
3
Then
V=
D1
D1 (1  g )
D(1  g ) 2


...
2
3
(1  R)
(1  R)
(1  R)
Copyright K.Cuthbertson, D.Nitzsche
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Special Case :Gordon Growth Model
Hence:
V
=
D1
R  g
(1  g ) D0

R g
R= chosen discount rate (adjusted for “risk”)
g = (constant) forecast for growth rate of dividends
Only need to forecast g and measure R
Copyright K.Cuthbertson, D.Nitzsche
50
Forecasting Dividends
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51
Forecasting Dividends
1) Forecasting dividends
2) internal rate of return (IRR) of a stock (and stock
picking)
3) using the Gordon Growth Model to calculate the ‘cost
of equity capital (ie. the ‘required return on equity)
from the current observed stock price
Copyright K.Cuthbertson, D.Nitzsche
52
Forecasting Dividends
Forecast earnings per share E
Calculate payout ratio, p ( eg. 40% ) to obtain dividend
forecast , D = p . E
Earnings forecast
1) Extrapolative (trends \ EWMA)
2) Regression (eg. autoregression)
3) Industry analysis (look at detailed accounts and
company plans to predict future demand and via income
elasticity and price elasticity of demand, we obtain future
revenues etc.
Check revenue figures in relation to forecasts for other firms
in the industry and change in market share - this is
ECONOMICS !).
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‘Stock Picking’: Using “Internal Rate of Return IRR”
This is an alternative but equivalent to the DPV method of stock-pickingP
P = actual (quoted) market price
Di = Dividend forecast
D1
D2
P 

 .. .
2
( 1 y )
( 1 y )
y = calculated IRR on equity(given the current market rice)
Now suppose you also have a value for Ri = “risk adjusted” required return
(eg from CAPM \ SML)
Investment Rule:
Buy STOCK if : (actual IRR , y) > (CAPM, required return, Ri )
Copyright K.Cuthbertson, D.Nitzsche
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Gordon Growth Model and Discount rate for use in investment appraisal
IF Gordon Growth model is true then
D1
P 
R g
Hence, the required return on equity, ‘reflected in’ the current market
price of the stock (and under constant growth assumption) is:
R=
D1 / P +
g
= Div-price ratio + estimated growth rate of earnings/dividends
This is an alternative method of measuring the required return on
equity of the firm, for use as the discount rate in DCF calculations
- only useful where historic dividend-price ratios and growth rates
are reasonably constant and the debt-equity ratio is expected to
remain unchanged in the future.
Copyright K.Cuthbertson, D.Nitzsche
55
Summary: Valuation of Stocks using CAPM/DPV and IRR
DPV Investment Rule
The fair value V, of a stock (in an all-equity financed firm) is the DPV
future dividends (per share) discounted using the (CAPM/SML)
risk-adjusted return
Buy stock (portfolio) if the market price, P < V, (calculated fair value)
Short sell stock (portfolio) if the market price, P > V
IRR Investment Rule:
Buy STOCK if : (actual IRR , y) > (CAPM, required return, Ri )
Copyright K.Cuthbertson, D.Nitzsche
56
END OF SLIDES
Copyright K.Cuthbertson, D.Nitzsche
57