Copyright K.Cuthbertson, D.Nitzsche 1
Lecture
Equity Investments
11/9/2001
Copyright K.Cuthbertson, D.Nitzsche 2
Investments:Spot and Derivative Markets,
K.Cuthbertson and D.Nitzsche
CHAPTER 10:CHAPTER 10:
Section 10.3: CAPMSection 10.3: CAPM
Section 10.4: Performance MeasuresSection 10.4: Performance Measures
CHAPTER 12:CHAPTER 12:
Equity Finance and Stock ValuationEquity Finance and Stock Valuation
CHAPTER 13:CHAPTER 13:
- excluding ‘Volatility Tests’ p.414-420- excluding ‘Volatility Tests’ p.414-420
READING
Copyright K.Cuthbertson, D.Nitzsche 3
Anomalies/Stock PickingMomentum and Value StocksOther 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 IRRNote: We will concentrate on the ‘Anomalies/stock picking strategies and CAPM/ Investment AppraisalWe 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’
TOPICS
Copyright K.Cuthbertson, D.Nitzsche 4
.
Anomalies:
“Stock-Picking” Strategies:
Copyright K.Cuthbertson, D.Nitzsche 5
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 6
Efficient Markets Hypothesis (EMH)
EMH: (1) (Excess) stock returns are unpredictable - v. weak condition, andincorrect 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 ‘activestrategy’ 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 7
A Waste of Your Money ?~ usually h/b, big print, wide margins, and ‘v. pricey’
Big BucksMillionaire MindGuru GuideWizards of Wall StDay Trade Part Time: Don’t Give up Your Day Job!‘Net’ ProfitPassport to Profit
Elizabeth I: CEOPowerplays: Shakespeare’s Lessons in Investing and
LeadershipTechnopreneurialNew Market Wizards (J. Schwager)Heros.come-investing
Copyright K.Cuthbertson, D.Nitzsche 8
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 9
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 10
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 annualHence:
Sm(monthly) = [8/12] / [20/sqrt(12)] = 0.67 / 5.77 = 0.115 (monthly)
Copyright K.Cuthbertson, D.Nitzsche 11
Momentum and
Value Stocks
Copyright K.Cuthbertson, D.Nitzsche 12
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 HORIZONMany stock (portfolios) experience a run of positive(negative) returns (e.g. monthly returns)
~ basis of ‘momentum strategies’ (or ‘growth stocks’)
Copyright K.Cuthbertson, D.Nitzsche 13
Basic Empirics: Value Stocks
From ‘Momentum’ to ‘Value Stocks’
Stocks that do well (badly) for some time, must have high (low) prices.
LONG HORIZONIt 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 14
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 !)
Basic Empirics: Value Stocks
Copyright K.Cuthbertson, D.Nitzsche 15
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)
Value Stocks
Copyright K.Cuthbertson, D.Nitzsche 16
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.
Value Stocks
Copyright K.Cuthbertson, D.Nitzsche 17
RESULTS (Fama-French 1996 table IV, Cochrane 1999)
Here, ‘Value Stocks’ = ‘losers’ = ‘Reversal strategy’
Data period Portf. Formation Average Return
Months Monthly %, (hold for 1 year)
Reversal Stratg 6307-9312 prev 4yrs 0.74% pm
3101-6302 prev 4 yrs 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 !
Value Stocks
Copyright K.Cuthbertson, D.Nitzsche 18
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 19
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 1- year.
After 1-year and CLOSE OUT EACH POSITION.
Note: You take a new ‘position’ each month.
Momentum/Growth Stocks
Copyright K.Cuthbertson, D.Nitzsche 20
RESULTS (Fama-French 1996 table IV, Cochrane 1999)
Momentum/Growth Stocks
Data period Portf. Formation Average Monthly Return %,
Momentum Stgy 6307-9312 prev yr 1.31% pm3101-6302 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
Momentum/Growth Stocks
Copyright K.Cuthbertson, D.Nitzsche 21
Stock Picking: Other Methods
Copyright K.Cuthbertson, D.Nitzsche 22
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 23
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 b s.e R-squared1-year -1.04 0.33 0.172-years -2.04 0.66 0.26 3-years -2.84 0.88 0.385-years -6.22 1.24 0.59
(Note: these results are not as good as they look -overlapping data problem)
Regression Techniques
Copyright K.Cuthbertson, D.Nitzsche 24
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 R-squared)
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)
Regression Techniques
Copyright K.Cuthbertson, D.Nitzsche 25
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 26
The CAPM/ SML
and
Investment Appraisal
Copyright K.Cuthbertson, D.Nitzsche 27
CAPM -Required return
-Asset’s “beta” ,portfolio beta and risk-CAPM: Theory and Evidence -Security Market Line
CAPM and Investment Appraisal
Topics:CAPM/SML
Copyright K.Cuthbertson, D.Nitzsche 28
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 29
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)
Capital Asset Pricing Model,CAPM
Copyright K.Cuthbertson, D.Nitzsche 30
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 AssetsAlthough 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
WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSETWHEN IT IS HELD IN A PORTFOLIO?
Copyright K.Cuthbertson, D.Nitzsche 31
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.
WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSETWHEN IT IS HELD IN A PORTFOLIO?
Copyright K.Cuthbertson, D.Nitzsche 32
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
WHY DOES ‘BETA’ MEASURE ‘RISK’ OF THE ASSETWHEN IT IS HELD IN A PORTFOLIO?
Copyright K.Cuthbertson, D.Nitzsche 33
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 34
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.
CAPM: Theory and Evidence
Copyright K.Cuthbertson, D.Nitzsche 35
SECURITY MARKET LINE AND SPECULATIONCAPM implies all ‘correctly priced’ assets should lie on the SML
ERi
r=5
Beta, i
SML
SML= Larger is i the larger is required return ERi: ERi = 5 + 8 i
i =0.5 1.0 1.2
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)
Hist.Av. Return = 4%
ERm
beta of market portfolio must =1
Copyright K.Cuthbertson, D.Nitzsche 36
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 37
CAPM and Investment Appraisal
Copyright K.Cuthbertson, D.Nitzsche 38
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 39
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
CAPM and Investment Appraisal(Levered Firm)
Copyright K.Cuthbertson, D.Nitzsche 40
B/(B+S) (B/S)new L(new) Leverage effect
0% 0.0% 1.28(=U ) 0.050% 100% 2.1 0.82 70% 233% 3.2 1.9290% 900% 8.7 7.4
Above uses
L = U [ 1 + (1-t) (B/S) ] 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.
CAPM and Investment Appraisal(Levered Firm)
Copyright K.Cuthbertson, D.Nitzsche 41
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 ] t=0.36
Copyright K.Cuthbertson, D.Nitzsche 42
END OF LECTURE
Self Study Slides Follow
Copyright K.Cuthbertson, D.Nitzsche 43
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 44
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 45
Share Valuation of all-equity firm or, ‘Fair Value’ for Equities
0 1 2 3 4
D4
D3
D2
V
D1
. . . .
• V = ‘fair value of one share’ D1, D2, D3,= expected dividends/earnings per share
Earnings E versus Dividends D ?
Copyright K.Cuthbertson, D.Nitzsche 46
Equity Pricing and DPV
Estimate Fair Value V(all equity firm) as DPV of expected dividends
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)BUTIf P < V then buy this “ced stock”
...3)31(3
2)21(2
)11(1
R
D
R
D
R
DV
Copyright K.Cuthbertson, D.Nitzsche 47
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 !
Equity Pricing and DPV
Copyright K.Cuthbertson, D.Nitzsche 48
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
Equity Pricing and DPV
Copyright K.Cuthbertson, D.Nitzsche 49
Special Case :Gordon Growth Model
0 321
P
D1
D1
(1+g) D1(1+g)2
V = D
R
D g
R
D g
R1 1
2
2
31
1
1
1
1( )
( )
( )
( )
( )...
Assumes dividends grow at a constant rate: g = 0.05 pa
Then
Copyright K.Cuthbertson, D.Nitzsche 50
Hence:
V =
R= chosen discount rate (adjusted for “risk”)g = (constant) forecast for growth rate of dividends
Only need to forecast g and measure R
gR
D
1
( )1 0g D
R g
Special Case :Gordon Growth Model
Copyright K.Cuthbertson, D.Nitzsche 51
Forecasting Dividends
Copyright K.Cuthbertson, D.Nitzsche 52
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 53
Forecast earnings per share ECalculate 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 !).
Forecasting Dividends
Copyright K.Cuthbertson, D.Nitzsche 54
‘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
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 )
PD
y
D
y
1 2
21 1( ) ( )...
Copyright K.Cuthbertson, D.Nitzsche 55
Gordon Growth Model and Discount rate for use in investment appraisal
IF Gordon Growth model is true then
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.
gR
DP
1
Copyright K.Cuthbertson, D.Nitzsche 56
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 57
END OF SLIDES
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