Stephen Penman Columbia University Francesco Reggiani Bocconi University
Observations: Price/Earnings and Price/Book predict returns in the 1. data Earnings and Book Value are accounting numbers; 2. P/E and P/B are, in part, accounting phenomena Questions: Are the predictable returns reward for risk? 1. Does the accounting for Earnings and Book Value 2. explain why P/E and P/B indicate risk and return?
For 1963-2006, all U.S. stocks: . E/P Portfolio . 1 (Low ) 2 3 4 5 (High) 1 4.3% 10.9% 14.2% 17.1% 19.7% B/P 2 8.8% 9.1% 13.0% 16.0% 22.1% Port- 3 14.4% 8.5% 12.1% 17.0% 21.6% folio 4 15.5% 13.4% 14.7% 18.0% 24.3% 5 26.4% 20.1% 20.2% 22.6% 30.0% Am I loading up on risk?
For 1963 – 2006: E/P Portfolio E/P Annual Return 5 (high) 14.1%23.5% 4 9.3% 18.2% 3 6.7% 14.9% 2 3.2% 12.4% 1 (low) -18.4% 13.9% E/P is increasing in the expected return: earnings are at risk � Earnings = + No growth → Price → (E/P = r ) t 1 t r E/P is decreasing in expected earnings growth: a low E/P may not indicate expected return because of growth � Earnings t = → = + + Price 1 r E/P g Adjust for growth → t − r g But growth may be risky, both increasing and decreasing the E/P ratio � How does one infer the expected return from E/P if growth is risky? �
Book-to-Price and Returns (Fama and French 1992,1993, 1996) For 1963-2006: B/P Portfolio B/P Annual Return 5 (high) 1.64 25.0% 4 0.93 19.1% 3 0.68 15.8% 2 0.46 12.9% 1 (low) 0.22 9.7% � The “B/P effect” is a mystery (though conjectures abound) � Low B/P is called “growth” and yields a lower return. Yet growth is usually viewed as risky. Note: Mean rank corr (E/P, B/P) = 0.31 (0.48 for positive E/P)
Book value and price: ∞ d ∑ = + τ P t t τ + ( 1 r ) τ = 1 ∞ − Earnings r . B ∑ = + + τ + τ − B t t 1 t + τ ( 1 r ) τ = 1 Accounting: Book-to-price is a numerator issue Finance: Book-to-price is a denominator issue Can the two views be reconciled?
� B/P depends on how the accounting is done � B/P < 1 involves deferral of earnings to the future Can the accounting explain why B/P indicates risk and return? Clue: accountants defer earnings is response to uncertainty
� B/P cannot indicate risk or expected return (The money market fund vs. hedge fund) � E 1 /P = r The result is by construction of the accounting (mark-to-market accounting)
2010 2011 2012 2013 2014 Income Statement Revenue $110 110 110 110 Cost of goods sold $100 100 100 100 Earnings $10 10 10 10 Balance Sheet Assets = Equity $100 100 100 100 100 Investment $100 100 100 100 100 Book rate-of-return 10% 10% 10% 10% Residual income 0 0 0 0 = $10 – (0.10 × 100) Value of Equity = Book value = $100 Book/price 1.0 Forward E/P 10%
Short-form residual earnings model: − Earnings rB = + + 1 t t P B t t − r g Set g = 0 (no growth) − Earnings rB = + + 1 P B t t t t r Earnings t 1 = + r and E 1 /P = r
2010 2011 2012 2013 2014 Income Statement Revenue $112.5 112.5 112.5 112.5 Cost of goods sold $100.0 100.0 100.0 100.0 Earnings $12.5 12.5 12.5 12.5 Balance Sheet Assets = Equity $100 100 100 100 100 Investment $100 100 100 100 100 Book rate-of-return 12.5% 12.5% 12.5% 12.5% Residual income 2.5 2.5 2.5 2.5 = $12.5 – (0.10 × 100) Value of Equity 2 . 5 = = $125 + $ 100 0 . 10 Book/price 0.8 Forward E/P 10%
2010 2011 2012 2013 2014 Income Statement Revenue $110 110 110 110 Cost of goods sold $ 80 80 80 80 Advertising 20 20 20 20 Earnings $(20) 10 10 10 10 Balance Sheet Assets = Equity $80 80 80 80 80 Investment $100 100 100 100 100 Book rate-of-return ( ROCE ) 12.5% 12.5% 12.5% 12.5% Residual income $ 2 2 2 2 = $10 – (0.10 × 80) Value of Equity $100 Book/price 0.8 Forward E/P 10%
− Earnings rB = + + 1 P B t t t t − r g Thus B B = t + − t r ROCE ( 1 ) g + t 1 P P t t Earnings B + = t 1 + − t r ( 1 ) g P P t t E 1 /P ≠ r � B/P recovers r from the E/P ratio depressed by growth � Can B/P indicate r in this case? � Note : r is increasing in B/P for a given ROCE and g ; but ROCE and � g may affect B/P
Growth adds to price but does not add to risk: � E/P decreases (denominator effect) � B/P decreases (denominator effect) � B/P cancels growth to recover r that would be indicated by E/P with no growth Earnings B + = t 1 + − t r ( 1 ) g P P t t
2010 2011 2012 2013 2014 Income Statement Revenue $112.5 $118.13 $ 124.03 $ 130.23 Cost of goods sold $ 100.0 105.00 110.25 115.76 Earnings 12.5 13.13 13.78 14.47 Balance Sheet Assets = Equity $100 105.00 110.25 115.76 121.55 Investment $100 105.00 110.25 115.76 121.55 Book rate-of-return 12.5% 12.5% 12.5% 12.5% Residual operating income 2.5 2.625 2.756 2.90 (10% charge) Residual income growth rate 5% 5% 5% Value of equity 2 . 5 = + = 100 $150 − 0 . 10 0 . 05 Book/price 0.67 Forward E/P 8.33%
Growth adds to risk but not to price � E/P decreases (numerator effect) � B/P unaffected � E/B decreases (and, for a given E/P, B/P is higher) � Rather than B/P canceling growth, risk cancels growth, to leave price unchanged Earnings B + = t 1 + − t r ( 1 ) g P P t t
2010 2011 2012 2013 2014 Income Statement Revenue $110.00 $ 115.50 $ 121.28 $ 127.34 Cost of goods sold $ 80.00 84.00 88.20 92.61 Advertising $(20) 21.00 22.05 23.15 24.31 Earnings $(20) 9.00 9.45 9.92 10.42 Balance Sheet Assets = Equity $80 84.00 88.20 92.61 97.24 Investment $100 105.00 110.25 115.76 121.55 Book rate-of-return 11.25% 11.25% 11.25% 11.25% Residual operating income 1.00 1.05 1.1025 1.1576 (10% charge) Residual income growth rate 5% 5% 5% Value of equity $100 Book/price 0.8 Forward E/P 9%
What if the accounting that defers earnings to the future is in response to risk? What if the firm investing in advertising is more risky?
P - B is expected earnings not yet added to book value. 1. Accounting defers earnings under uncertainty …... and 2. deferred earnings creates earnings growth To defer earnings to the future (and create growth), the 3. accounting must depress earnings (and E/P). If price is unaffected, the deferral means a higher B/P: the 4. growth is not priced Conservative accounting in response to risk
For 1963-2006: . E/P Portfolio . 1 (Low ) 2 3 4 5 (High) 1 4.3% 10.9% 14.2% 17.1% 19.7% B/P 2 8.8% 9.1% 13.0% 16.0% 22.1% Port- 3 14.4% 8.5% 12.1% 17.0% 21.6% folio 4 15.5% 13.4% 14.7% 18.0% 24.3% 5 26.4% 20.1% 20.2% 22.6% 30.0%
� r and g are not independent in valuation � Fama and French model is doubtful: no earnings! � Price-to-book is not growth � “Growth” versus “Value” redefined � “Cash flow betas” need correction � The Fed Model implies growth and risk cancel
Earnings + 1 = t r f P t � But, this ignores growth: Earnings = + 1 t Price t − r g Earnings t + 1 = − r g P � What is the Fed Model saying? = + r r risk premium f − = r g r f = g risk premium
$ 21.00 Current Market Price Price $13.58 Per Share $7.42 $3.58 $3.84 Book Value (1) (2) (3) Book Value Value from Value from short-term long-term earnings earnings
� Components (1) and (2) amount to the earnings yield: RE E arnings + = = + + t 1 t 1 P B t t r r � For Cisco: forward earnings is $0.89 per share Price = $0.89/0.12 = $7.42 Components (1) + (2) = $7.42 No growth (component 3 = 0) means E/P = r For Cisco, E/P = 0.89/$7.42 = 12%
RE 1 = = + + t P B $ 21 t t − r g If g = risk premium, r – g = r f + risk premium – g = r f RE = + + t 1 P B t t r f − × 0 . 89 ( 0 . 12 3 . 85 ) = + = $ 3 . 85 $ 13 . 36 0 . 045 Now: Do I want to add value for growth?
Stephen Penman, Accounting for Value , Columbia University Press, January 2011
� We do not claim to provide a comprehensive explanation for the B/P effect in stock returns � Observed returns might be due to market inefficiency rather than rational pricing of risk ----- However, we do observe returns to B/P that are consistent with both the rational pricing of risk and the accounting for book value
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