Stock Valuation and Learning about Profitability for presentation at UESTC, June 2011

1. Stock Valuation and Learning about Profitabilityfor presentation at UESTC, June 2011

2. Stock Valuation and Learning about Profitabilityby Pastor and Veronesi (2003, JF) • Investors attempting to value the newly listed firms • are confronted with substantial uncertainty • about their future profitability. • This paper argues that this uncertainty contributes • to the high valuations of young firms, and • the resolution of this uncertainty over time tends to be • accompanied by a decline in the valuation ratios.

3. An example to illustrate the convex nature of compounding • Suppose firms A and B differ only in the future growth rates of their book equity, whose current value is $1m. • While A is going to grow by 10 percent per year with certainty, • B will grow either by 5 or 15 percent with equal probabilities. • Over 10 years, for example, • $1m cumulates to $4.05m at the 15 percent rate, • to $2.59m at the 10 percent rate, and • to $1.63m at the 5 percent rate. • Hence, firm B has a higher expected future book value of equity • than firm A (because (4.05+1.63)/2=2.84>2.59).

4. Assumptions for a simple model • Assuming that competition eliminates the firm’s expected abnormal earnings by T, • the firm’s market value at T equals its book value, and • the market value today is the expected book value at T discounted at some known rate r. • If g is unknown and assumed to be normally distributed with mean g and std σ, • then

5. M/B

6. Firm profitability: ROE

7. Learning • Firm profitability, • measured as the accounting rate of return on book equity, • is assumed to revert to an unknown mean • whose value investors learn over time. • Uncertainty declines over a firm’s lifetime due to learning. • As a result, younger firms have higher σ • and hence also higher M/B ratios, • holding other things (such as g and r) constant.

8. The relation between uncertainty and age

10. The effect of dividends • In the presence of external financing constraints, • which are common for young firms and assumed here, • dividend payouts reduce the growth rate of book equity, • thereby weakening the convexity between the growth rate and the future value of book equity. • As a result, the model implies that • the relation between M/B and the uncertainty about average profitability • should be stronger for stocks that pay no dividends. • The effect of the uncertainty on M/B can be quantitatively large, • especially for nodividend-paying stocks.

11. uncertainty about mean profitability • Higher uncertainty about profitability (the growth rate of ROE) • increases the probability that the future growth rate of book equity • will be persistently high or persistently low. • Due to the convex nature of compounding, • a persistently high growth rate has a bigger impact on the future book value • than a persistently low growth rate, and • the expected future book value increases, together with M/B.

13. The effect of age • Uncertainty about mean profitability declines over time due to learning. • Hence, other things being equal, • the M/B ratio of a typical young firm should be high and • it should fall as investors learn about the firm’s prospects.

15. Idiosyncratic volatility

17. Firm age • A crucial variable in our empirical investigation is firm age. • They consider each firm as ‘‘born’’ in the year of its first appearance in the CRSP database. • They define the AGE variable as • minus the reciprocal of one plus the firm age. • This choice is based on equation (19), • which prescribes a particular functional form for the relation between uncertainty and age.

19. Figure 5. M/B ratio in the years after listing

20. Figure 5. Return volatility in the years after listing

23. Empirical model

24. Table II Determinants of Market-to-Book Ratios

26. Empirical results • There is a difference of over 5 percent between the valuations of • a typical two-year-old firm and • an otherwise identical one-year-old firm. • Among firms that pay no dividends, • this valuation difference is over 12 percent, and • the difference is almost 27 percent between the valuations of • a typical five-year-old dividend nonpayer and • an otherwise identical one year-old nonpayer. • In addition, age is shown to predict future changes in M/B. • The decline of M/B over time is significantly steeper • for younger firms, consistent with the model.

27. Conclusion • Uncertainty about a firm’s average profitability increases • the firm’s M/B ratio as well as its idiosyncratic return volatility. • This uncertainty is especially large for the newly listed firms, • but it declines over time due to learning. • Younger firms indeed tend to have higher M/B ratios • than older firms, after controlling for the known determinants of M/B. • Moreover, this effect is stronger for firms that pay no dividends. • M/B declines faster for younger firms.

28. Future work • It seems reasonable to conjecture that uncertainty about market-wide profitability would reduce stock valuations. • Future work can also model the firm creation process. • Since uncertainty increases valuations, • entrepreneurs have an incentive to start new firms with uncertain profitability • even when expected profitability is low.

29. Was there a Nasdaq bubble in the late 1990s?Pastor and Veronesi (2006, JFE) • On March 10, 2000, the Nasdaq Composite Index closed • at its all-time high of 5,048.62. • In comparison, the same index stood • at 1,114 in August 1996 as well as in October 2002. • It was at 2,874 on April 29, 2011 (when I prepared this slide). • The unusual rise and fall in the prices of technology stocks • has led many academics and practitioners to describe the event • as a stock price ‘‘bubble.’’ • Not necessary! • as this paper argues.

31. Interpreting “Bubble” • This label seems appropriate • if the term ‘‘bubble’’ is interpreted as an ex post description of • an extended rise in prices followed by a sharp fall. • However, a more common interpretation is that • the prices of technology stocks exceeded their fundamental values in the late 1990s. • This paper analyzes whether technology stocks were indeed overvalued at that time.

32. Pastor and Veronesi (2003) • An important determinant of a firm’s fundamental value is • uncertainty about the firm’s average future profitability, • which can also be thought of as uncertainty about • the average future growth rate of the firm’s book value. • This uncertainty increases fundamental value. • The late 1990s witnessed high uncertainty about • the average growth rates of technology firms, and that • this uncertainty helps us understand • the observed high level and volatility of technology stock prices.

33. To illustrate how uncertainty about a firm’s growth rate raises the firm’s fundamental value, • consider the Gordon growth model, P/D = 1/(r-g). • If g is uncertain, then P/D is equal to the expectation of 1/(r- g). • This expectation increases with uncertainty about g • because 1/(r-g) is convex in g. • Loosely speaking, • a firm with some probability of failing (a very low g) and • some probability of becoming the next Microsoft (a very high g) is very valuable.

34. Ofek and Richardson’s (2002) argument on growth rate • The earnings of Internet firms would have to grow at • implausibly high rates to justify the Internet stock prices of the late 1990s. • When uncertainty about the growth rate is acknowledged, • the observed price can be justified by a significantly lower expected growth rate. • For example, consider a stock with r = 20% and P/D = 50. • To match the observed P/D in the Gordon formula with a known value of g, the required dividend growth rate is g = 18%. • Suppose instead that g is unknown and that it is drawn from a uniform distribution with a standard deviation of 4%. • The expected g required to match the P/D of 50 then drops to 13.06%.

35. not necessarily irrational ex ante • The Nasdaq valuations were not necessarily irrational ex ante • because uncertainty about average profitability, • which increases the fundamental value of a firm, • was unusually high in the late 1990s. • After calibrating a stock valuation model • that takes this uncertainty into account, • we compute the level of uncertainty • that is needed to match the observed Nasdaq valuations at their peak. • The uncertainty we obtain seems plausible because • it matches not only the high level but also the high volatility of Nasdaq stock prices.

37. The effects of equity risk premium • The effect of uncertainty on stock prices is especially strong • when the equity premium is low. • Uncertainty was high not only in the late 1990s • but also during the biotech boom in the early 1980s. • The M/B ratios were higher in the 1990s because • the equity premium declined between the early 1980s and the late 1990s. • A decline in the equity premium boosts prices in two ways: • by reducing the discount rate, and • by amplifying the positive effect of uncertainty on prices.

39. Why did the ‘‘bubble’’ burst? • Although we argue that Nasdaq prices rose in the late 1990s • partly due to an increase in uncertainty, • we do not claim that prices fell in 2000 due to a decline in uncertainty. • Instead, we argue that • Nasdaq’s expected profitability was revised downward • when Nasdaq’s profitability plummeted in 2000 and 2001. • This revision must have been substantial, • given the high uncertainty at that time.

41. Uncertainty about average profitability and the diversification discountHund, Monk, and Tice (2010,JFE) • Traditional explanations for the diversification discount • (multiple segment firm value is less than the imputed value using single segment firm multiples) • rely on agency problems, a lack of transparency, or lackluster future prospects for diversified firms. • Rational learning about future average long-term profitability • provides an alternative explanation for the diversification discount • that does not rely on suboptimal managerial decisions or a poor firm outlook.

42. Predictions_1 • If diversified firms have less uncertainty about future mean profitability, • we predict the following: • (1) In the cross-section, diversified firms will trade at a discount relative to single segment firms • due to convexity of the discounting function. • (2) As firms age, • the sales or assets multiples of single segment firms will drop more than • the sales or assets multiples of diversified firms • as more uncertainty about mean profitability will be resolved • for single segment firms than for diversified firms.

43. Predictions_2 • (3) The difference in the value change across time • for single segment and diversified firms will be • larger during economic booms (when the equity risk premium is low) and • smaller during economic recessions (when the equity risk premium is high). • (4) After controlling for volatility in profitability, • diversified firms will have lower idiosyncratic return volatility than • single segment firms due to the idiosyncratic nature of learning.

44. Discussions • Though • more agency problems, more asymmetric information, and weaker future prospects for diversified firms • generate a predicted diversification discount, • these explanations do not generate the same dynamic or volatility predictions • as the rational learning model. • The empirical findings are consistent with • rational learning and lower uncertainty about mean profitability for diversified firms • as an explanation for the diversification discount.