2 The Predictive Ability of Variation in
3.7 Empirical Evidence
This section describes our empirical methodology in detail and al so provides an overview of our data sources and main results. The essence of our strategy is to investigate the effect of investment uncertainty on expected stock returns through means of investment policy and financing issue. This channel is critical to realize why the investment uncertainty needs to be priced because this uncertainty relates to systematic risks. As we have stated in the previous section, we attempt to examine that there is a positive relation between investment uncertainty and expected stock returns because financing constraint force firms to choose suboptimal investment timing. If investment is irreversible, then increasing suboptimal investment will increase its systematic risks. In our analysis investment uncertainty and financing constraint are both from uncertainty about future revenue.
We use stock price data from the Center for Research on Securities Prices (CRSP) and financial statement data from COMPUSTAT from 1980 to 2001 to detect relationships between investment uncertainty and firms’ characteristics. Only nonfinancial firms (SIC other than in the 6000) and firms with ordinary common equity (security type 10 or 11 in CRSP) are discussed in our study. In addition, we also require each firm to have a strictly positive book value prior to portfolio formation year.
We focus on expected stock returns of portfolios formed by the widely accepted Fama-French method of classifying stocks based on their market size and investment uncertainty. We apply the expected earning volatility as our proxy of investment
uncertainty. We do not observe the true value of the volatility of future cash flow, but we can use the realized earning volatility between year t+ and 1 t+ as our proxy 5 for future earning volatility in our analysis. When expectations are rational, future earning volatility should be captured reasonably well by the ex post realized value.
Because this variable is likely to include aspects of both revenue and financing uncertainty, we use market size to control financing constraints. The precise definition of variables used below is shown in the appendix. Below we show some properties among portfolios to confirm our inferences.
We follow the methods of Fama and French (1992, 1993) in sorting stocks into portfolios and investigating the influence of firm-specific characteristics on stock returns. Monthly portfolio returns are computed from July of each year t to June of year t+1. According to Myers (1998), we apply growth rate in capital expenditures to proxy for the exercise of growth options.
Table 6 reports some summary statistics of various characteristics computed across firms in the same expected earning volatility portfolio. Median capital expenditure growth rate first increases with the expected earning volatility from 8.44%
in the lowest group to 19.01% in the eighth high quintile. Higher expected earning volatility seems to have large market size. According to Fama and French (1992), we apply two leverage variables, including the ratio of book assets to market equity, A/ME, and the ratio of book assets to book equity, A/BE. A/ME is interpreted as a measure of market leverage while A/BE is a measure of book leverage. The book-to-market ratio, BM, and the market leverage, AME, are rather flat across expected earning volatility.
Monthly stock returns slowly increases with the expected earning volatility while stock return volatility declines with this proxy.
Table 6 Summary Statistics
The table summarizes various statistics for groups of firms of the same expected earning volatility, where expected earning volatility is measured by the variance of earning from year t+1 to year t+5. Year t is the portfolio formation year. This table reports the medians across firms of the characteristics listed in the row label. Return volatility (sigma) and stock return are monthly data and express in percentages. The market size reports by millions. The capital expenditure growth rate, CEGR, is defined during year t to year t+1 and reported in percentage.
Volatility 1 2 3 4 5 6 7 8 9 10
ME 9 16 27 43 68 102 176 321 765 2960
BM 0.90 0.93 0.85 1.10 1.07 1.18 1.23 1.39 1.40 1.37 AME 1.16 1.16 1.13 1.11 1.18 1.12 1.12 1.14 1.24 1.38 ABE 1.63 1.70 1.73 1.74 1.79 1.83 1.88 1.96 2.04 2.17 CEGR 8.44 6.27 11.12 17.59 12.57 13.86 18.88 19.01 16.78 12.38 Return 0.90 0.93 0.85 1.10 1.07 1.18 1.23 1.39 1.40 1.37 sigma -2.86 -0.22 2.48 2.88 5.56 5.70 7.01 8.99 7.35 6.55
Table 7 shows that the expected earning volatility, our proxy for the investment uncertainty, varies positively with realized monthly stock returns. We have stated in previous section that if investment is constrained, higher uncertainty has two opposite effects on investment. On the one hand, based on real options framework, higher uncertainty increases the investment threshold and the value of waiting. On the other hand, the risks of future funding shortfall lower the optimal investment threshold and encourage firms to accelerate investment. This provides a possible explanation to the finding of Whited (2002) that small firms (and presumably more financially constrained) firms invest more than big, safer, and less financially constrained firms.
Intuitively, uncertainty should have a larger impact on the risk and investment characteristics of small rather than large firms. That is what we find in Table 7, where we examine the association between the expected earning volatility and stock returns, controlling for market value of equity. Stocks are first classified into five groups based on market size each June, and then into five quintile portfolios based on the expected earning volatility.
Panel A of Table 7 shows that for the year after portfolio formation, average monthly stock returns are increasing with the expected earning volatility. In the smallest market size quintile, average monthly returns are 1.92% for the lowest earning volatility portfolio versus 3.96% for the highest volatility portfolio. Moreover, the return difference (t-statistics) between the highest and lowest volatility groups is 2.04%
(7.15) for smallest stocks, 1.62% (2.45) for midsize stocks, and 1.00% (0.06) for the larger size stocks. Hence, higher expected earning volatility has higher average stock returns especially among small size firms.
Panel B of Table 7 shows results when returns are value weighted within
portfolios on a monthly basis. Similar results are found in such analysis. Evidence shows that higher volatility follows higher stock returns. In particular, returns increase monotonically with expected earning volatility among smallest size firms. The return difference (t-statistics) between the extreme volatility groups are 2.53% (9.45) in the smallest size group, 1.96% (3.03) in the midsize group, and 1.29% (3.09) in the second to largest group. These evidences confirm our argument that small size firms have liquidity constraint so that they bear more risks from volatile cash flow and have higher return difference.
Finally, Panel C of Table 7 reports the investment activities among different volatility groups, controlling market equity size. Evidence confirms our prediction that more volatility in the firm’s future cash flow raises the risk of future funding shortfall and increases current investment. This property is critical to explain why higher expected earning volatility is associated with higher stock returns. In particular, we suggest that potential future financing restrictions encourage acceleration of investment beyond the first-best level such that forces firms to face higher risks. Because of irreversibility, suboptimal investment decision makes firms have higher systematic risks.
Table 7
Monthly Stock Returns and Investment for Quintile Portfolios Based on Expected Earning Volatility
At the end of June of each year t , t=1980to , five portfolios are formed on the basis of ranked values of expected earning volatility, EAsigma. Quintile portfolios are ranked in ascending order. Firm size (ME, market value of equity) is measured in June of year t . Returns are computed over the 12 months following portfolio formation (total of 264 months). The monthly value-weighted returns are based on monthly rebalancing. The last column of Panel A and B presents the average monthly return difference between high and low quintile portfolios (t-statistics in parentheses). In Panel C the reported median of capital expenditure growth rate is from year t to year t+1. The last column of Panel C reports Wilcoxon rank-sum Z-statistics testing the equality of distributions between the two groups, high and low quintile stocks. All entries are reported in percentages. “-” denotes no observations.
2001
Low EAsigma
2 3 4 High
EAsigma
High-Low EAsigma Panel A: Average Equally Weighted Monthly Returns
Small ME 1.92 1.92 2.27 2.80 3.96 2.04 (7.15)
2 0.22 0.61 0.66 0.96 2.11 1.90 (6.03)
3 -0.22 0.14 0.37 0.39 1.44 1.62 (2.45)
4 -0.68 2.25 -0.81 0.15 1.21 1.30 (0.06)
Large ME - -1.90 -1.22 -1.22 1.22 -
Panel B: Average Value-Weighted Monthly Returns
Small ME 0.54 0.91 1.25 1.98 3.08 2.53 (9.45)
2 -0.30 0.34 0.38 0.79 2.13 2.43 (6.80)
3 -0.47 -0.04 0.13 0.26 1.49 1.96 (3.03)
4 -0.08 1.15 -0.70 -0.07 1.21 1.29 (3.09)
Large ME - -0.26 -0.11 -0.45 1.16 -
Panel C: Capital Expenditure Growth rate
Small ME -4.99 0.39 -2.62 0 4.14 2.973
2 0 -5.54 -0.26 2.52 2.80 2.008
3 -12.09 7.18 2.11 6.10 5.34 1.984 4 -49.80 1.08 11.67 7.48 7.81 2.242
Large ME - 51.00 -1.62 2.01 6.97 -
Next, we investigate association between firm-level book-to-market, size, earning volatility, and average stock returns using regression analysis of monthly returns. Table 8 reports inference based on the style of Fama and MacBeth (1973). The reported slope coefficients are time-series average of the estimated cross-sectional slope coefficients.
The reported t-statistics in the parentheses are adjusted for autocorrelation and conditional heteroskedasticity. Table 8 confirms the previous prediction that higher expected earning volatility has higher stock returns. The coefficient of EAsigma is significantly positive in all specifications. When controlling market size and book-to-market, the EAsigma coefficient is 0.83 with t-statistics 8.10. In particular, we find the value effect disappears when we include EAsigma in the regression analysis.
On the contrary, the size effect becomes apparent. Our evidence suggests that even controlled proxy of financial distress variable, market size and book-to-market, the coefficient of EAsigma is still positively significant. Similar results are found when we replace book-to-market with market and book leverage and when we divide two sample periods.
Table 8
Average Parameter Values from Cross-Sectional Regressions of Monthly Returns on Market Size, Book-to-market, and Expected Earning Volatility
Monthly returns are regressed on ME, BE/ME, proxy of leverage (A/ME and A/BE), and the expected earning volatility. BE is the book value of equity at the end of fiscal year . A is total book assets from the latest fiscal year ending in calendar year . The accounting ratios are measured using market value of equity ME at the end of December of calendar year . Firm size (ME) is measured as the market value of equity (price times share outstanding) at the end of June of each year ,
to . Year is the formation year. Expected earning volatility, EAsigma, is measured by the variance of earning from year t+1 to year t+5. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for heteroskedasticity and one-year lag autocorrelation, are in the parentheses. Ln denotes natural logarithm. To avoid spurious inferences from extreme values, the smallest and largest 1% of the observations for each explanatory variable are replaced by the 1%
and 99% values.
1
t− t−1
1 t−
t 1980
t= 2001 t
Ln(ME) Ln(BE/ME) Ln(A/ME) Ln(A/BE) Ln(1+EAsigma) Panel A: Full samples
-0.75 0.15 0.83
(-5.52) (0.95) (8.10)
-0.79 0.09 -0.40 0.89
(-5.53) (0.58) (-4.43) (7.22)
Panel B: Sub-sample 1980-1990
-0.46 0.57 0.53
(-3.39) (1.02) (4.77)
-0.51 0.13 -0.45 0.61
(-3.58) (0.74) (-3.37) (4.87)
Panel C: Sub-sample 1991-2001
-1.04 0.11 1.13
(-4.52) (0.46) (6.86)
-1.07 0.06 -0.36 1.18
(-4.19) (0.22) (-2.87) (5.67)
3.8 Conclusion
Considerable research has found corporate investment can explain the conditional dynamics in expected stock returns (Zhang (2005), and Cooper (2006)). In addition, a number of studies state that uncertainty about investment affects the timing and the amount of investment because of irreversibility (McDonald and Siegel (1986)).
Meanwhile, literature shows that the relationship between investment and uncertainty is inclusive if firms also face financing constraint (Minton and Schrand (1999), and Boyle and Guthrie (2003)). Yet, despite the substantial development of these two literatures, it is still unclear how the uncertainty about investment affects stock returns.
This paper develops a real options model to relate the value of growth options and the value of the firm to the uncertainty about investment, in which uncertainty refers to the volatility of growth rates in cash flows. Because investment is irreversible, the uncertainty about investment affects firms’ expansion plans by changing the investment threshold. By introducing the learning-by-doing effect, the value of growth options declines with uncertainty. Our contribution is that we find a positive relationship between investment uncertainty and expected stock returns by means of learning-by-doing.
A related issue of our study can refer to Gomes, Yaron, and Zhang (2006). They incorporate costly external finance into the investment-based asset pricing model and examine whether financing frictions help in explaining the expected stock returns.
Minton and Schrand (1999) also have noted that cash flow volatility is positive related to the costs of accessing external capital. Our analysis differs with these studies in that we not only investigate financing problem but also potential gains from investing. As a
result, we find the higher expected earning volatility induces firms to increase current investment, while they sate that higher cash flow volatility is associated with lower level of investment.
Although our framework links asset prices to learning effect, we need some empirical research to support our theoretical findings. Another limitation of our work is that we only discuss one possible expansion options. An obvious extension of our work would analyze the more general case that the firm has many projects, in which the learning effect could alter with the number of projects. Besides, if the firm is not all-equity, debts may affect its investment decision and average stock returns. In such case, investment would alter the distribution of future cash flows so that a firm’s ability to commit its future payment also changes. Further analysis of this complex problem has the potential to yield additional insights.
Chapter 4 Conclusion
In this thesis we provide two different schemes to investigate the behavior of stock returns. Based on the rational pricing framework of Pástor and Veronesi (2003), we state that the market equity value is from profitability such that the book-to-market ratio and the evolution of stock return are governed by return-on-equity. It is plausible to examine stock return through means of profitability. In particular, Wei and Zhang (2006) state that the variation in return-on-equity is useful to capture the idiosyncratic return volatility. As a result, it is reasonable to apply the variation in return-on-equity as proxy for idiosyncratic volatility risks in predicting stock returns. Evidence shows that higher variation in return-on-equity predicts lower average stock returns. To explain this negative relation, we count on the cash flow perspective and the risk argument of book-to-market.
Next we introduce the learning-by-doing effect in the real options model to examine the investing and liquidity impacts on stock returns. Although literature has noted the financing constraint to investment, it only focuses on the negative impact of cash flow volatility on expansion. Actually, uncertainty about investment has two opposite impacts on investment. On the one hand, more investment uncertainty increases the value of waiting if investment is irreversible. On the other hand, uncertainty raises the possibility of cash flow shortfall and lowers the value of growth options. The logic of this study is as follows: if investment is irreversible, liquidity
systematic risks. Evidence shows that expected earning volatility is positively related to stock returns.
This thesis may attribute to the recent literature that idiosyncratic risks need to be priced. In addition to size and value effect, we find firms’ fundamentals provide some critical information in examining stock returns. Profitability and investment both attribute to idiosyncratic risks of the firm. Even though equity market size and book-to-market ratio are controlled, our evidence is still significant. In particular, we provide the liquidity issue though means of investment. However, this liquidity problem cannot represent the financial distress risk. The problem about debt issue or debt valuation needs further research.
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