Valuation

Introduction• Up to now, we have taken alphas as given. We must now

confront the harder task—forecasting alphas.• Active management is a competitive game. By its very

nature, alpha insights do not last forever. Competition eventually arbitrages them away. We can’t provide recipes for this. Only examples that once worked, and a framework for building new alphas.

• We will present two approaches:– Modeling mispricings, which lead to alphas.– Modeling alphas directly.

• We will start with the theoretically pure, and move to the ad hoc.

Dividend Discount Model

• A stock’s price should be the present value of its future dividends.

• Financial theory is very clear on this. Less clear are the values of those future dividends, and the appropriate discount rate.

• If dividends and discount rate remain constant, the passage of time leads to:

1

01

tt

d tp

y

1 1 0

0

p d py total return

p

Constant Growth DDM

• The simplest possible model:

• This model is very sensitive to growth assumptions—not surprising given that we assume this growth rate to apply forever.

• In the case of zero growth, the expected return is just the dividend yield.

11 1

10

td t d g

dp

y g

Example

• Let’s assume:

• Then:

1 $1

7.5%F B

d

y i f

DDM Price

$0

$50

$100

$150

$200

$250

0% 1% 2% 3% 4% 5% 6% 7% 8%

Growth Rate

Modeling Growth

• Simple model to provide insight.

• What if earnings grow because we can achieve the same ROE on the retained earnings:

• Hence:

1

e t d t I t

d t e t

I t e t

1

1 1

e t e t I t

e t

1g

More on growth

• According to the DDM:

• We also know that:

• Hence:

10

dp

y g

F By i f

B F

dg f i

P

imp B F

dg f i

P

S&P 500: 12/31/99

-50

0

50

100

150

200

0 10 20 30 40 50 60

Median % LTG Estimate

Realize

d 5

Year

% G

row

th R

ate

Rate

realized = 5.31% + 0.14 * forecast

R-squared = 0.00245

Dealing with Unrealistic Growth

• Improve inputs.– Compare average growth rates to implied rates.– One possibility: match mean and standard deviation of

growth rates by sector.

• Three-stage DDM– More realistic growth pattern:– Short-term growth g1 for time T1.– Implied growth rate for T>T2.– Interpolate growth between T1 and T2.– This lowers the sensitivity of prices and alphas to input

growth rates, but doesn’t eliminate the problem.

Using DDM’s for Active Management

• Approach 1: Internal Rate of Return– Given market prices, solve for internal rates of

return, y.– Relate y to :

– Fundamental assumption: mispricing will remain forever. The alpha exists because the mispricing of each dividend disappears as the dividend is paid out.

F By i f

Approach 2: Net Present Value

• Use consensus expected return to estimate DDM price.

• Compare this to market price to estimate alpha:

• Problem: what is T?– Does it vary by sector or by stock?

1 DDM mkt

mkt

p p

T p

Returns to Value Investing

• We observe a market price, Pmkt(t), and estimate true value as:

• We can also think in terms of multiples:

• The relative mispricing is:

1,true F B

e tP t y i f

y g

,mktmkt true

Pm m

e y g

1 1true true

mkt mkt

P mrmp

P m

Example

• For a given stock, we have:e(1)=$1 y=8% g=5% =0.45

Pmkt(0)=$10

Ptrue(0)=$15

mmkt=10

mtrue=15 rmp=50%

• Hint for solving problems concerning returns or multiples: in the absence of explicit information on earnings, you can often just assume e(1)=$1.

Returns after One Year

• Case 1: Repricing– The market fairly prices the stock at t=1.

• Case 2: Continuing Mispricing– The same mispricing remains at t=1.

• We expect to experience a combination of these.

1 11

0mkt

mkt

d Preturn

P

*Note on the time convention: At t=0, our estimate of d(1) determines the initial price, P(0).

Case 1: Repricing

• Example:e(2)=$1.05

d(1)=$0.45

mmkt=15

Pmkt (1) =$15.75

return=62%

2 1 11 1mkt true

e e gP P

y g y g

1 11

11mkt

e ge

y greturn y rmp y rmp

m e

Case 2: Continuing mispricing

• Example:e(2)=$1.05

d(1)=$0.45

mmkt=10

Pmkt (1) =$10.50

return=9.5%

• Return still exceeds 8%.

1 2mkt mktP m e

1 1 11

1

1

0

mkt

mkt

true

e m e greturn y y rmp g rmp

m e

dy rmp

P

General Case

• Using Ptrue(0), Pmkt(0), Pmkt(1), and g*:

• If multiple doesn’t change, and realized growth matches expected growth, mispriced assets can still generate alpha (i.e. return distinct from y).

* *1

0multtrue

dreturn y r g g g rmp

P

An Empirical View

Comparative Valuation

• A more general approach than DDM. Also more ad hoc.

• Relates to many market conventions:– Prevalence of P/E ratios.– Investment banking rules of thumb

1 2 3 4

11DDM

CV

dp c d

y g

p c d c e c b c s

Examples• Certainly, the price Chevron paid for the assets was not cheap. Given total

consideration of about $18 billion, Chevron paid about $10.20 per barrel of oil equivalent for Unocal's reserves, or about $1.71 per thousand cubic feet on a gas equivalent basis. While that is not at the top of the range for recent acquisitions, it is by no means cheap.

– Christopher Edmonds, TheStreet.com, 4/4/05

Company Report date Broker Comment

AOL 7/1/2005 Merrill

Our BUY recommendation is based on the company's compelling valuation, trading at 8.5x EV/EBITDA on 2005E, and only 7.4x on

2006E.

American Express 8/4/2005 LehmanWe rate shares of American Express 1-Overweight and have a 12

month price target of $64. Our target is based on a multiple of 18.0x

Chubb 7/27/2005 Deutsche Bank

Our $98 price target is based on 1.6 times projected book value (x-FAS 115), compared with its historical average multiple of 1.8, which we

believe is reasonable on a projected ROE of 16%.

Exxon 7/28/2005 Citi

Over the past five years XOM shares have traded at an average 12-month [PE relative multiple] of about 93%. With the S&P 500 currently

trading at 16.1x of estimated consensus forward 2006 earnings, this would imply that XOM would trade at a PE of 15.0x a

Dell 8/10/2005 Lehman

We reiterate our 1-OW rating…on Dell. Over the last 4 years, Dell has traded at a relative P/E of 1.1x to 1.7x the S&P 500, vs. its current

multiple of 1.3x, based on CY06 EPS of $1.94.

Implementing Comparative Valuation

• Choose appropriate fundamentals.• Regress observed prices against model to

estimate parameters.– By sector or industry.– Think carefully about appropriate weighting.– What about missing factors, persistent

mispricings?

• Mispricing, plus horizon, lead to alpha estimates.

Jarrod Wilcox P/B-ROE Model*

*Jarrod Wilcox, “The P/B-ROE Valuation Model,” Financial Analysts Journal, Jan-Feb 1984.

Wilcox Model by Industry

Forecasting Alpha Directly

• Version 1: Arbitrage Pricing Theory (APT)

• This approach backed up by academic theory.

• Start with a factor model

• APT says that:

r X b u

B

E

f

f r X m

α X m e

APT Theory

• This looks somewhat like CAPM– E{}=0 versus E{u}=0.

• But there are significant differences:– CAPM based on equilibrium argument versus APT

arbitrage argument.• Since {u} are uncorrelated, unless E{u}=0, you could build an

almost risk free portfolio with expected return.

• Remember that the CAPM does not require uncorrelated {}.– Of more practical importance, the CAPM identifies the market

as the optimal portfolio. The APT supplies neither the identity of the model factors nor the expected factor returns.

Anomalies versus Risk Factors

• The APT framework arises in many academic arguments about market efficiency.

• Believers in market efficiency will try to interpret evident anomalies (e.g. value investing) as risk factors.

• From the standpoint of an active manager, this is a purely academic argument.

Implementing APT

• Requirement 1: The factor model– There is an easily satisfied technical

requirement • The model must be “qualified,” i.e. it must explain

the risk of diversified portfolios. The CAPM wouldn’t qualify, but most of our factor risk models would.

• Requirement 2: Factor forecasts– There are many approaches here, though they

depend somewhat on the factor model.

Factor Forecasts

• Statistical factor models– Without factors explicitly tied to fundamentals,

forecasting techniques here are mainly statistical: moving averages or mean reversion based on historical factor returns.

• Fundamental factor models– Beyond the same statistical approaches, there

may be additional approaches based on fundamental and/or economic intuition.

Returns-based Analysis• This is the most general (and ad hoc) approach. Within the

context of linear models, we can use signals (fundamental ratios, past returns, various market indicators…) to forecast active returns:

• Here A contains the J signals for N stocks, and we estimate the coefficients {g}.

• This differs from (and is more general than) APT because these signals may be forecasting specific returns. That is, in this framework, we do not require E{u}=0. Stated another way, we don’t require our alphas to arise from risk factors.

δ A g ε

Forecasting Excess Returns Directly

• We can forecast excess returns directly, while controlling for risk factors X in the analysis:

• So, for example, the coefficient g1 captures the return to the minimum variance portfolio with unit exposure to A1, and zero exposure to all other risk factors and signals.

r X b A g ε

Typical Equity Return-forecasting Signals*

• Value Signals– P/E, P/B, P/CF, P/S, DDM, D/P, Low Price

• Growth/ROE Signals– Projected Growth, ROE

• Revision/Surprise/Momentum– Estimate revision, Rating revision, Relative Strength,

EPS Surprise, EPS Momentum, EPS Torpedo

• Risk Premia– Beta, Size, EPS Variability, Debt/Equity, Neglect,

Duration, Estimate Dispersion, Foreign Exposure

*Richard Bernstein, Merrill Lynch Institutional Factor Survey, 1998