1. The Role of Growth Options in Explaining Stock Returns
Lenos Trigeorgis, University of Cyprus

2. Overview Background/ Motivation Theoretical Rationale
Data and Methodology
Empirical Findings
Conclusion 2

3. Question(s) Are growth stocks more or less risky than value stocks?
Do growth firms earn higher or lower average return than value firms?

4. Background/Motivation
Inability of CAPM beta (Sharpe 1964, Lintner 1965) to explain stock returns - an unsettling gap in both the theoretical and empirical asset pricing literatures
Fama and French (1992, 1993) - a deadly blow to rational asset pricing theory (well-diversified investors care only about systematic risk)
beta has little power in explaining stock returns (after controlling for size and book-to-market)
book-to-market found highly significant (but no explanation)
(small) value stocks outperform (large) growth stocks (the value-size puzzle) independent of beta
Possible explanation: size and value (measured by B/M) may proxy for missing priced systematic risk factors not captured by CAPM beta

5. Alternative Explanations
Behavioral - investor preferences for large size and growth drive up their prices and lead to lower subsequent returns
Overoptimism about stocks that have shown good prospects in recent past and excessive pessimism about stocks that exhibited poor recent performance (Doukas et al, 2002; DeBondt and Thaler, 1990; Lakonishok et al, 1994; La Porta, 1996)
Cooper, Gulen, and Schill (2008)
asset growth anomaly exists because investors are too slow to incorporate the information from firm investment into stock prices, which causes mispricing

6. Alternative Explanations
q-theory - firms invest more when expected return (cost of capital) is lower, inducing a negative relation between realized investment and subsequent returns (Lam and Wei, 2011; Li and Zhang, 2010; Liu, Whited, and Zhang, 2009)
Garleanu, Panageas and Yu (2011) - distinct role of two growth option variables, but argue (as Berk et al, 1999) that unexercised growth options are more risky and require a higher return

7. Other Issues/Explanations
Evidence sensitive to treatment of extreme observations (Knez and Ready, 1997), period under study (Hawawini and Keim, 1995), influence of young growth stocks (Loughran, 1997)
When betas estimated using annual (not monthly) returns, B/M less significant and inconsistent across different samples (Kothari et al,1995); empirical support for book-to-market may be exaggerated
Biases from omitted variables (Ball, 1978; Fama and French, 1993, 1996), mispricing (Lakonishok et al., 1994; Daniel and Titman, 1997), biases from data snooping or data sources (Black, 1993; Lo and Mackinlay, 1990; Kothari et al., 1995; Conrad et al., 2003), theoretical inverse relation between expected return and size when proxied by market value (Berk, 1995)

8. Main Idea
Provide a novel explanation based on influence of growth options and active management on reshaping the higher moments of the return distribution, rather than focusing on systematic risk and its impact on average returns
Investors may rationally accept a lower required or average return (first moment) from growth stocks in exchange for the growth option (GO) value and the favorable risk-return characteristics (e.g., skewness) that it offers through active management
The growth option value should be reflected in the current price and lead to lower average subsequent returns 8

9. Main Goals
Provide evidence for a comprehensive asset pricing model incorporating growth option as well as distress/leverage variables
Determine the drivers of growth option value
Re-examine the incremental role of B/M in explaining returns once distress/leverage and growth option variables are included
Shed light on the conditionality of stock returns on firm-specific characteristics

10. Why Beta is Less Relevant?
Skilled active managers increase beta under favorable developments and reduce it under unfavorable
Staging decisions facilitates dynamic adjustment of betas; betas of growth firms more dynamic and less stable than for established large firms
Volatility is more relevant than beta for valuing growth options due to the discretionary nature and asymmetric position of the firm
Staging of decisions enhances favorable asymmetric position by expanding in case of favorable developments and cutting losses in case of unfavorable

11. Why Beta is Less Relevant?
An actively managed firm with options to expand on the upside and truncate losses (e.g., contract or abandon) on the downside creates a convex payoff and (“buys”) more skewness in the firm asset return distribution
The asymmetric impact on equity returns is even more amplified (compared to firm asset returns) through leverage, as equityholders have a valuable default option
Technological innovation and competitive dynamics (e.g., preemption) create further discontinuities (affecting tails). The downside to stockholders is lower the more staged and levered the investment process is

12. Why Beta is Less Relevant?
For (small) growth stocks the higher moments (skewness, kurtosis) are relevant
Smaller (and likely more distressed) growth stocks may have a different risk-return profile and a different appeal to many investors than large firms on main exchanges
Higher moments found in individual and cross-sectional stock returns may be manifestations of important growth options factor

13. Beyond Mean-Variance Rubinstein (1976), Leland (1999)
If market portfolio returns are iid in perfect markets prices are determined by power utility --skewness is positively valued by investors (+ 3rd derivative)
The true beta is driven not by the covariance of portfolio i’s return with the market return, but with the market return raised to power –b where b is the equity risk premium/(market volatility) i.e.
the market price of risk/quantity of risk (cyclical)
(only when b = 1 the CAPM holds)

14. Misjudging Performance
Can appear to improve mean-var portfolio performance (fooling investors) by reducing (selling) skewness (e.g., buying value stocks)
A dynamic or active strategy that generates a convex payoff (e.g., through fairly priced options) and enhances (“buys”) skewness (e.g. momentum strategies that buy/expand under favorable developments or sell/contract under unfavorable ones or actively managed growth stocks) will appear to “underperform” by mean-var standards (alpha), especially over long horizons

15. The Puzzle that Isn’t
The true beta of an active/flexible (momentum or growth) strategy or growth firm that enhances skewness is less than suggested by the CAPM (SML)
Expected (required) return (and cost of capital) for such a momentum/growth strategy or growth firm (for a given measured beta) is lower
Actively-managed growth stocks, by being more flexible to expand on upside and contract/abandon with lower costs on downside, are less “risky” (and should have a lower required return and cost of capital) than passively-managed value stocks!!!

16. The Puzzle that Isn’t
Investors rationally accept lower required or average return (first moment) from growth stocks in exchange for higher flexibility or growth option value and favorable risk-return profile (+ skewness or 3rd moment)
Value stocks are less flexible, facing higher adjustment costs on downside, and hence more “risky”; have higher required return as they “sell” skewness
Growth option value is reflected in current prices manifesting itself in lower subsequent returns and a more asymmetric risk profile

17. Firm’s Dynamic Asset Mix
Firm’s dynamic asset mix between growth options and assets in place affects required returns and the cost of capital (e.g.,Berk, Green and Naik, 1999)
But growth options and active management reshape the higher moments
Asymmetry/+skewness is enhanced by uncertainty, staged decisions, active management/ managerial flexibility, interaction with financial flexibility via leverage

18. Value vs Growth
A firm´s stock returns incorporate a different mix of two opposing effects, reflecting the tradeoff between value (from assets in place) and growth options
(Small) growth stocks with significant growth options have more asymmetric (positively skewed) returns, better explained by option variables such as volatility, managerial, organizational or financial flexibility, staged R&D investment
(Large) value stocks exhibit more symmetric returns adequately explained by standard factors (beta, size or book-to-market)

19. Asymmetric Growth Stock Returns

20. Proxying for Growth Options
Capex: recent growth in capital expenditures proxying for the near-term exercise of growth options and their immediate conversion to assets-in-place and installed capacity
GO: creation or development of yet-unexercised future growth option value through innovation and systematic long-term development

21. Expected Findings
The two growth option variables, i.e. growth in capital investment (Capex) proxying for exercising growth opportunities and yet-unexercised growth options (GO), should be significantly negatively related to average stock returns
Investors respond rationally to a firm’s growth prospects accepting lower returns in fair exchange for more favorable skewness

22. Size and Growth/Value Effects

23. Empirical Modeling
Returns = f (β, size, B/M, leverage; Capex, GO, interaction)
GO = f (firm-specific volatility, managerial flexibility/asymmetry, organizational flexibility, financial flexibility, cash flow coverage, R&D intensity, cumulative growth, market power; fixed effects, industry effects, interactions)

24. Sample/Methodology
All (16,975) U.S. firms during ( ) with data available in Compustat and CRSP
Regression procedure of Fama-MacBeth (1973)

25. TABLE 1. Summary Statistics of Growth Option Variables
Panel A: Descriptive Statistics
Variable
Mean
Median
Std. Dev.
GO (market)
0.5231
0.5040
0.7547
GO (model)
0.4630
0.4526
0.8278
Firm-specific volatility
0.4591
0.3910
0.2650
Asymmetry (Skewness)
2.0558
1.5748
2.9680
R&D intensity
0.2423
0.0034
7.6057
Organizational flex (SGA)
0.3307
0.2220
2.8804
Financial flex (Leverage)
0.3223
0.2950
0.1781
Cumulative sales growth
0.2451
0.1514
0.4250
Market power (HHI)
0.9760
0.1524
2.9230
Cash flow coverage (CFC)
0.1038
0.0116
0.4321

26. TABLE 1. Summary Statistics of Growth Option Variables
Panel B: Correlation Coefficients
GO (market)
GO (model)
Volatility
Skewness
R&D intensity
SGA
Leverage
Cumulat. growth
Market power
Cash flow 1
0.774
Firm-spec volatility
0.312
0.286
0.164
0.170
0.667
0.198
0.175
0.152
0.076
0.058
0.053
0.043
0.026
0.128
-0.191
-0.183
-0.036
0.037
-0.109
-0.032
Cumulative growth
0.118
0.115
0.161
0.083
0.016
0.000
-0.117
0.169
0.168
0.324
0.240
0.040
0.023
-0.064
0.019
Cash flow coverage
0.027
0.088
0.136
0.014
0.010
-0.145
0.011
0.583

27. TABLE 2. Growth Option Model Estimation
Dependent:
GO (market)
Coef.
t-statistic
Firm-specific volatility (σ)
0.0731
2.54
Asymmetry (Skewness)
-2.09
R&D intensity
0.1076
8.25
Organizational flex (SGA)
0.0050
2.63
Financial flex (Leverage)
-9.82
Cumulative sales growth
0.1390
13.38
Market power (HHI)
0.0547
15.37
Cash flow coverage (CFC)
-5.36
Skewness*Leverage
0.0150
2.60
R-square (overall)
7.50% N
55,795

28. TABLE 3. Average (Mean) vs. Median Returns in Growth vs
TABLE 3. Average (Mean) vs. Median Returns in Growth vs. Size Sorts Portfolios
Panel A: Average returns
1 Small 2 3 4
5 Big
Small-Big
t-value
1 Low GO
0.0142
0.0108
0.0093
0.0076
0.0073
0.0069
2.9159
0.0129
0.0064
0.0066
3.2116
0.0118
0.0075
0.0065
0.0060
0.0058
2.6852
0.0132
0.0074
0.0056
0.0061
0.0071
2.8500
5 High GO
0.0134
0.0079
0.0046
0.0039
0.0035
0.0100
3.3853
Whole sample
0.0131
0.0086
0.0067
0.0059
3.5124
Panel B: Median returns
1 Small 2 3 4
5 Big
Small-Big
t-value
1 Low PVGO
0.0005
0.0030
0.0045
0.0049
0.0059
0.0021
0.0031
0.0040
0.0048
0.0003
0.0023
0.0035
0.0002
0.0041
5 High PVGO
0.0009
Whole sample
0.0047
0.0121
0.0206
Panel C: Mean-Median Differences
1 Small 2 3 4
5 Big
1 Low GO (Value)
0.014
0.008
0.005
0.003
0.001
0.013
0.007
0.004
0.002
0.015
0.009
0.006
5 High GO (Growth)
0.021
0.010

29. TABLE 4. Summary Statistics for Main Regression Variables
Panel A: Summary Statistics
Market Risk
(β)
Size
B/M
Neg_d
Leverage
Capex GO
Mean
1.1267
0.6123
0.0334
0.2999
0.0065
0.4987
Median
1.0469
0.5274
0.0000
0.3525
0.0038
0.5068
Stdev
0.7519
2.1997
4.3575
0.1796
2.1728
0.0661
0.2380
Panel B: Correlation Coefficients
Market Risk
(β)
Size
B/M
Neg_d
Leverage
Capex GO
Market Risk (β) 1
0.088
-0.015
-0.040
0.055
-0.080
-0.061
-0.147
-0.194
0.038
0.134
0.004
0.058
-0.006
-0.026
-0.063
 0.040
-0.179
0.079
-0.151
-0.020

30. TABLE 5. Adjusted Fama-French Type Regressions
Model
Market Risk (β)
Size
ln(B/M)
Neg_d (-E Dummy)
E(+)/P
Leverage
Size_Lever 1
0.613
-0.193
0.266
0.044
0.687
0.064
( 1.86)*
(-3.95)***
( 4.46)***
( 0.25)
( 1.81)*
( 0.95) 2
0.598
-0.284
0.195
-0.623
0.807
-0.054
( 1.77)*
(-4.41)***
( 3.55)***
(-2.63)***
( 3.14)***
(-2.66)***

31.     TABLE 6. Extended Analysis: Growth Option Variables and
Marginal Contributions
Panel A. Extended Analysis: Adding Growth Option Variables (Capex and GO)
Model
MrktRisk (β)
Size
B/M
Neg_d
Leverage
Size_Lever
Capex GO 3
0.586
-0.300
-0.006
-0.650
0.855
-0.050
( 1.74)*
(-4.67)***
(-0.11)
(-2.65)***
( 3.33)***
(-2.48)** 4
0.458
-0.308
-0.017
-0.656
1.137
-0.075
-1.792
( 1.37)
(-4.85)***
(-0.3)
(-2.55)**
( 4.18)***
(-3.61)***
(-3.04)*** 5
0.561
-0.338
0.030
-0.497
1.648
-0.106
-1.005
( 1.73)*
(-5.31)***
( 0.56)
(-2.44)**
( 4.77)***
(-4.08)***
(-2.42)** 6
0.521
-0.345
0.021
-0.482
1.798
-0.119
-1.719
-1.212
( 1.6)
(-5.37)***
( 0.38)
(-2.27)**
( 5.18)***
(-4.55)***
(-2.36)**
(-2.97)***
small
0.791
-0.666
0.011
-0.517
1.166
-0.072
-1.282
-1.629
( 2.27)**
(-6.1)***
( 0.18)
(-1.91)*
( 1.76)*
(-1.27)
(-1.78)*
(-3.73)***
large
0.218
-0.107
0.104
-0.320
1.165
-0.614
-1.295
( 0.69)
(-2.02)**
( 0.94)
(-1.39)
( 3.2)***
(-2.75)***
(-0.59)
(-2.85)***
Nasdaq
0.706
-0.635
0.068
-0.458
2.474
-0.191
-2.045
-1.330
(Growth)
( 2.07)**
(-6.72)***
( 0.83)
(-1.58)
( 5.31)***
(-5.23)***
(-2.52)**
(-2.92)***
Main
0.310
-0.288
-0.472
2.005
-0.125
-0.248
-1.779
 (Value)
( 1.01)
(-5.38)***
(-0.26)
(-1.95)*
(-4.25)***
(-0.27)
(-3.39)*** X    X X  X X

32. TABLE 6. Extended Analysis: Growth Option Variables and
Marginal Contributions
Panel B. Marginal Contribution of Key Variables
Model
Mrkt Risk (β)
Size
B/M
Neg_d
Leverage
Capex GO 7
0.554
-0.226
0.123
( 1.58)
(-3.73)***
( 1.75)* 8
0.564
-0.238
0.076
-0.664
( 1.67)*
(-4.09)***
( 1.13)
(-2.97)*** 9
0.595
-0.221
0.077
0.209
( 1.72)*
(-3.68)***
( 1.33)
( 2.6)*** 10
0.465
-0.213
0.128
-2.059
-1.367
( 1.42)
(-4.22)***
( 2.18)**
(-2.84)***
(-3.18)***
Book-to-market may be proxying for omitted distress and leverage variables
B/M is not a good proxy for growth options (consistent with Chen, 2011). Capex and GO add incremental explanatory power beyond what is captured by B/M, leverage or distress

33. Conclusion
Growth option variables help explain cross-sectional stock returns beyond Fama-French (1992) variables (after controlling for distress & leverage)
direct negative relation between creation of future growth options (GO) and stock returns
growth in capital expenditures, representing exercise of maturing growth options, is confirmed to have a negative relation with stock returns
book-to-market appears less significant to explain cross-sectional returns on pooled samples that include firms with negative book equity and when leverage is included