1192001 Lecture Equity Investments 1 1 READING Investments

11/9/2001 Lecture Equity Investments 1 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 2 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’ 3 3

Anomalies: . “Stock-Picking” Strategies: 4 4

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. 5 5

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 6 6

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 7 7

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! 8 8

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. 9 9

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) 10 10

Momentum and Value Stocks 11 11

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’) 12 12

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’). 13 13

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 !) 14 14

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) 15 15

Value Stocks 1) ‘Value/Contrarian/Reversal/ Buying “losers” ASSUME MINIMUM holding period of 1 -YEAR (1000 stocks in S&P 500 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&P 500. 16 16

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 4 yrs 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 ! 17 17

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. 18 18

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 1 - year. After 1 -year and CLOSE OUT EACH POSITION. Note: You take a new ‘position’ each month. 19 19

Momentum/Growth Stocks RESULTS (Fama-French 1996 table IV, Cochrane 1999) Momentum/Growth Stocks Data period Momentum Stgy 6307 -9312 3101 -6302 Portf. Formation prev yr Average Monthly Return %, 1. 31% pm 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 20 20

Stock Picking: Other Methods 21 21

Regression Techniques Combine individual effects in a regression Look for regression equation that predicts stock returns over different horizons (eg. 1 m, 6 m, 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’ 22 22

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. 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) 23 23

Regression Techniques Pesaran and Timmermann (1996 - Jo. Forc) 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 FTSE 100) 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) 24 24

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. 25 25

The CAPM/ SML and Investment Appraisal 26 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 27 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&P 500 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 28 28

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) 29 29

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 30 30

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. 31 31

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 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 32 32

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 33 33

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. 34 34

SECURITY MARKET LINE AND SPECULATION CAPM implies all ‘correctly priced’ assets should lie on the 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 35 1. 2 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 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 36 36

CAPM and Investment Appraisal 37 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 ) 38 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 A 11. 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 39 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. 40 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 ] 41 t=0. 36 41

END OF LECTURE Self Study Slides Follow 42 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 43 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. 44 44

Share Valuation of all-equity firm or, ‘Fair Value’ for Equities V D 2 D 1 0 1 D 4 D 3 2 Earnings E versus Dividends D ? 3 • V = ‘fair value of one share’ dividends/earnings per share . . 4 D 1, D 2, D 3, = expected 45 45

Equity Pricing and DPV Estimate Fair Value V(all equity firm) as DPV of expected dividends where R 1, R 2 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” 46 46

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 ! 47 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 48 48

Special Case : Gordon Growth Model Assumes dividends grow at a constant rate: g = 0. 05 pa P D 1 0 1 D 1 (1+g) 2 D 1(1+g)2 3 Then V= 49 49

Special Case : Gordon Growth Model 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 50 50

Forecasting Dividends 51 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 52 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 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 !). 53 53

‘Stock Picking’: Using “Internal Rate of Return IRR” This is an alternative but equivalent to the DPV method of stock-picking. P 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 54 ) 54

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= D 1 / 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. 55 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 56 ) 56

END OF SLIDES 57 57