Stephen Penman
Columbia University
Francesco Reggiani
Bocconi University
Observations:
1. Price/Earnings and Price/Book predict returns in the
data
2. Earnings and Book Value are accounting numbers;
P/E and P/B are, in part, accounting phenomena
Questions:
1. Are the predictable returns reward for risk?
2. Does the accounting for Earnings and Book Value
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
Price t =
No growth →
`
(E/P = r)
E/P is decreasing in expected earnings growth: a low E/P may not indicate expected return because of growth
Adjust for growth
`
Earnings t +1
→
r
→
Price t =
Earnings t +1
→ r = E/P + g
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
5 (high)
B/P
1.64
4
3
2
1 (low)
Annual Return
25.0%
0.93
0.68
0.46
0.22
19.1%
15.8%
12.9%
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:
∞
Pt = ∑
τ =1
d t +τ
(1 + r )τ
Earningst +τ − r.Bt +τ −1
(1 + r )τ
τ =1
∞
= Bt + ∑
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)
`
E1/P = r
The result is by construction of the accounting (mark-to-market
accounting)
2010
2011
2012
2013
2014
$110
$100
$10
110
100
10
110
100
10
110
100
10
Income Statement
Revenue
Cost of goods sold
Earnings
Balance Sheet
Assets = Equity
$100
100
100
100
100
Investment
$100
100
100
100
100
10%
0
10%
0
10%
0
10%
0
Book rate-of-return
Residual income
= $10 – (0.10 × 100)
Value of Equity
= Book value =
Book/price
Forward E/P
$100
1.0
10%
Short-form residual earnings model:
Pt = Bt +
Earningst +1 − rBt
r−g
Pt = Bt +
Earnings t +1 − rBt
r
Set g = 0 (no growth)
=
Earnings t +1
r
and
E1/P = r
2010
2011
2012
2013
2014
$112.5
$100.0
$12.5
112.5
100.0
12.5
112.5
100.0
12.5
112.5
100.0
12.5
Income Statement
Revenue
Cost of goods sold
Earnings
Balance Sheet
Assets = Equity
$100
100
100
100
100
Investment
$100
100
100
100
100
12.5%
2.5
12.5%
2.5
12.5%
2.5
12.5%
2.5
Book rate-of-return
Residual income
= $12.5 – (0.10 × 100)
Value of Equity
= = $100 + 2.5
0.10
Book/price
Forward E/P
$125
0.8
10%
Income Statement
Revenue
Cost of goods sold
Advertising
Earnings
Balance Sheet
Assets = Equity
Investment
2010
2011
2012
2013
2014
$(20)
$110
$ 80
20
10
110
80
20
10
110
80
20
10
110
80
20
10
$80
80
80
80
80
$100
100
100
100
100
12.5%
$2
12.5%
2
12.5%
2
12.5%
2
Book rate-of-return (ROCE)
Residual income
= $10 – (0.10 × 80)
Value of Equity
$100
Book/price
Forward E/P
0.8
10%
Pt = Bt +
Thus
`
`
`
`
E1/P ≠r
Earningst +1 − rBt
r−g
r =
Bt
B
ROCE t +1 + (1 − t ) g
Pt
Pt
r=
Earnings t +1
B
+ (1 − t ) g
Pt
Pt
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
r=
Earnings t +1
B
+ (1 − t ) g
Pt
Pt
2010
Income Statement
Revenue
Cost of goods sold
Earnings
2011
2012
2013
2014
$112.5
$ 100.0
12.5
$118.13
105.00
13.13
$ 124.03
110.25
13.78
$ 130.23
115.76
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
12.5%
2.5
12.5%
2.625
12.5%
2.756
12.5%
2.90
5%
5%
5%
Book rate-of-return
Residual operating income
(10% charge)
Residual income growth rate
Value of equity
= 100 +
Book/price
Forward E/P
2.5
=
0.10 − 0.05
$150
0.67
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
r=
Earningst +1
B
+ (1 − t ) g
Pt
Pt
Income Statement
Revenue
Cost of goods sold
Advertising
Earnings
Balance Sheet
Assets = Equity
Investment
2010
2011
2012
2013
2014
$(20)
$(20)
$110.00
$ 80.00
21.00
9.00
$ 115.50
84.00
22.05
9.45
$ 121.28
88.20
23.15
9.92
$ 127.34
92.61
24.31
10.42
$80
84.00
88.20
92.61
97.24
$100
105.00
110.25
115.76
121.55
11.25%
1.00
11.25%
1.05
11.25%
1.1025
11.25%
1.1576
5%
5%
5%
Book rate-of-return
Residual operating income
(10% charge)
Residual income growth rate
Value of equity
$100
Book/price
Forward E/P
0.8
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?
1.
P - B is expected earnings not yet added to book value.
2.
Accounting defers earnings under uncertainty …... and
deferred earnings creates earnings growth
3.
To defer earnings to the future (and create growth), the
accounting must depress earnings (and E/P).
4.
If price is unaffected, the deferral means a higher B/P: the
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
Earningst +1
= rf
Pt
`
But, this ignores growth:
Price t =
Earnings t +1
r−g
Earnings t +1
=r−g
P
`
What is the Fed Model saying?
r = r f + risk premium
r − g = rf
g = risk premium
$21.00
Current Market Price
Price
Per
Share
$13.58
$7.42
$3.58
$3.84
Book Value
(1)
Book Value
(2)
(3)
Value from
Value from
short-term
earnings
long-term
earnings
`
Components (1) and (2) amount to the earnings yield:
Pt = Bt +
`
REt +1 Earningst +1
=
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 t +1
= $ 21
Pt = B t +
r−g
If g = risk premium, r – g = rf+ risk premium – g = rf
Pt = Bt +
REt +1
rf
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