1 Copyright K.Cuthbertson, D.Nitzsche Lecture Equity Investments 11/9/2001.

Copyright K.Cuthbertson, D.Nitzsche 1

Lecture

Equity Investments

11/9/2001


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


Equity Finance and Stock ValuationEquity Finance and Stock Valuation


- excluding ‘Volatility Tests’ p.414-420- excluding ‘Volatility Tests’ p.414-420

READING


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


.

Anomalies:

“Stock-Picking” Strategies:


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.


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


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


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!



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.



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)


Momentum and

Value Stocks


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’)


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’).


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


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


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


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


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.


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


RESULTS (Fama-French 1996 table IV, Cochrane 1999)


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



Stock Picking: Other Methods


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’


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)



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)



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.


The CAPM/ SML

and

Investment Appraisal


CAPM -Required return

-Asset’s “beta” ,portfolio beta and risk-CAPM: Theory and Evidence -Security Market Line

CAPM and Investment Appraisal

Topics:CAPM/SML


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


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


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?


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.



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



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


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


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


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


CAPM and Investment Appraisal


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 )


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)


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)


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


END OF LECTURE

Self Study Slides Follow


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


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.


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 ?


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


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 !



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



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


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


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


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 !).



‘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( ) ( )...


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


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 )


END OF SLIDES

1 Copyright K.Cuthbertson, D.Nitzsche Lecture Equity Investments 11/9/2001.

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Transcript of 1 Copyright K.Cuthbertson, D.Nitzsche Lecture Equity Investments 11/9/2001.