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Taste, information, and asset prices: implications for the valuation of CSR

Abstract

Firms often undertake activities that do not necessarily increase cash flows (e.g., costly investments in corporate social responsibility or CSR), and some investors value these non cash activities (i.e., they have a “taste” for these activities). We develop a model to capture this phenomenon and focus on the asset-pricing implications of differences in investors’ tastes for firms’ activities and outputs. Our model shows that, first, investor taste differences provide a basis for investor clientele effects that are endogenously determined by the shares demanded by different types of investors. Second, because the market must clear at one price, investors’ demands are influenced by all dimensions of firm output even if their preferences are only over some dimensions. Third, information releases cause trading volume, even when all investors have the same information. Fourth, investor taste provides a rationale for corporate spin-offs that help firms better target their shareholder bases. Finally, individual social responsibility can lead to corporate social responsibility when managers care about stock price because price reacts to investments in CSR activities.

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Notes

  1. Note that CSR and public relations (PR) activities are often undertaken to mitigate negative publicity related to production externalities. We classify CSR and PR as externalities broadly because they are peripheral to or indirect consequences of the firm’s production.

  2. Clark and Viehs (2014) provide a review of the literature on CSR, focusing on the potential effects on firms’ financial and market performance and costs of capital. Huang and Watson (2015) review the CSR literature appearing in accounting journals.

  3. The Forum for Sustainable and Responsible Investment reports that, based on research in mid-2012, “$3.31 trillion in US-domiciled assets was held by 443 institutional investors, 272 money managers and 1,000-plus community investing institutions that select or analyze their portfolios using various ESG [environmental, community, or other societal or corporate governance] criteria.” (URL: http://www.ussif.org/blog_home.asp?Display=6, accessed April 30, 2014).

  4. While type-1 and type-2 investors may benefit from the firm’s pro-social activities even in the absence of share ownership (e.g., lower pollution), we abstract from such welfare externalities to focus on the implications of investor tastes over investments.

  5. More generally, Lintner (1969) and Rubinstein (1974) discuss conditions under which prices can be written as a weighted average of investors’ beliefs and preference parameters. Our setting satisfies these conditions.

  6. Kondor (2012) and Kim and Verrecchia (1994) present exceptions in which learning about other traders’ beliefs and heterogeneous processing skills, respectively, cause traders’ valuations to diverge even when they receive the same information.

  7. We can think of the firm’s shares as claims to bundled outcomes. There may be scope for an intermediary or the firm to unbundle the firm’s cash flows and CSR activities and sell shares of \(\tilde{x}\) and shares of \(\tilde{y}\) separately. If this unbundling is costly, we expect it to be imperfect and for bundling to persist in equilibrium. For example, it is nearly impossible to perfectly unbundle a firm’s treatment of its employees from the firm’s cash flows. For simplicity, we do not explore the possibility of unbundling here but address it in Sect. 4 on spin-offs.

  8. Empirically, the relation between CSR and financial performance seems ambiguous (see the discussion by Hirigoyen and Poulain-Rehm (2014)). Our assumption simply implies that one-period CSR performance and financial performance are stochastically independent.

  9. Type-2 investors’ valuation of \(\tilde{y}\) could be due to a “warm glow” related to being an owner of a firm with a positive externality (Andreoni 1989).

  10. Furthermore, Lam et al. (2015, abstract) find that firms with unclear overall CSR performance (positive performance in some dimensions and negative performance in others) are “mispriced by the market compared to their ‘neutral’ peers, plausibly due to the ambiguity in their social performance.”

  11. Our expression for price in Lemma 1 is equivalent to the price that would prevail in an agree-to-disagree exchange economy with heterogeneous beliefs and could be derived using the consensus beliefs methodology of Lintner (1969) and Rubinstein (1975) and as discussed by He and Shi (2012).

  12. Altria Group Inc. press release dated March 30, 2007, and accessed on March 16, 2015, at http://investor.altria.com/phoenix.zhtml?c=80855&p=irol-newsArticle&ID=956368. Note that the spin-off was well-anticipated and motivated by additional purposes (e.g., management focus and corporate debt capacity) that are outside of our model. Furthermore, we make no attempt to examine price reactions around specific dates or attribute abnormal returns or volume to shareholder base effects. Instead, we focus on the market valuation of the firm either as a single unit or as two spun-off components.

  13. The uncertainty in \(\tilde{y}\) could be related to the realized health impact of Philip Morris cigarettes and the unknown extent of cigarette marketing directed at teenagers and children.

  14. We derive prices in a two-firm economy in the proof to Proposition 1 in the appendix.

  15. In discussing expected returns, we assume the parameters are such that \(p_{1}>0\) so a positive expected return implies \(E[ p_{2}] >p_{1}\).

  16. The cost of capital in Corollary 2 is increased by type-2 investors and is increasing in \(\lambda\). This is similar in spirit to the result of Bloomfield and Fischer (2011, p. 53) that “cost of capital is increased by the extent to which each type believes the other is responding to data that are not value relevant.”

  17. While this is unlikely to describe national stock markets like the NYSE, it may describe novel online markets like Kiva, which connects lenders and borrowers online with the explicit goal of reducing poverty and has facilitated over $600 million in loans from 2005 through mid-2014.

  18. For a more detailed analysis of a firm’s investment decision when some investors value CSR, see Gollier and Pouget (2012). They assume that the CSR outcome is certain, conditional on the firm’s investment choice, and their results would also hold in our model if we assumed no CSR risk.

  19. As a measure for investor sentiment, Naughton et al. (2014) compare the market value of firms with high and low CSR performance. They assume that, when this difference is high, investor sentiment for CSR is strong. In the context of our model, the sentiment measure could measure the fraction of investors who have a taste for CSR or how much utility type-2 investors receive from CSR output.

  20. Taste differences in our model are closely related to the effects of tax clienteles (e.g., Allen et al. 2000) but differ for a substantive reason. In our model, \(\tilde{y}\) could represent the extra after-tax payout to investors facing lower marginal tax rates. In a model that captures tax-based clienteles, \(\tilde{x}\) and \(\tilde{y}\) would have to be perfectly correlated, because differential income tax treatment of equity distributions implies that payouts to one group are proportional to (i.e., perfectly correlated with) payouts to the other groups. We assume that \(\tilde{x}\) and \(\tilde{y}\) are orthogonal to ensure that type-1 investors cannot use \(\tilde{y}\) to learn about \(\tilde{x}\) so that only type-2 investors incorporate information about \(\tilde{y}\) into their valuations.

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Acknowledgments

We thank Stefan Wielenberg (discussant), Steven Huddart (discussant), Raffi Indjejikian (discussant), Russel Lundholm (editor), an anonymous referee, and Paul Fischer as well as workshop participants at UCLA, Wharton, Chicago (Booth), Carnegie Mellon, Minnesota, Utah, Ohio State, Maastricht, Tilburg, the Utah Winter Accounting Conference, the Zurich Accounting Research Workshop, and the Review of Accounting Studies Conference for helpful comments and suggestions.

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Correspondence to Henry L. Friedman.

Appendices

Appendix 1: Proofs

Lemma 1 The first-order condition to ( 1) with respect to demand in shares of the risky asset for an investor of type-i is given by

$$\begin{aligned} E\left[ \tilde{v}_{i}\right] -p-rq_{i}Var\left[ \tilde{v}_{i}\right] =0. \end{aligned}$$
(22)

Solving this for \(q_{i}\) yields the demands in (2). Substituting \(q_{i}\) into the market clearing condition and solving for p proves the claim.

Corollary 1 The expressions for the comparative statics are

$$\begin{aligned} \frac{dp}{d\bar{y}}= & {} \frac{\lambda \sigma _{x}^{2}}{\sigma _{x}^{2}+\left( 1-\lambda \right) \sigma _{y}^{2}}>0, \end{aligned}$$
(23)
$$\begin{aligned} \frac{dp}{d\sigma _{y}^{2}}= & {} \frac{-\left( \bar{y}\left( 1-\lambda \right) +r\sigma _{x}^{2}\right) \lambda \sigma _{x}^{2}}{\left( \sigma _{x}^{2}+\sigma _{y}^{2}\left( 1-\lambda \right) \right) ^{2}}\gtrless 0, \end{aligned}$$
(24)
$$\begin{aligned} \frac{dp}{d\lambda }= & {} \frac{\left( \bar{y}-r\sigma _{y}^{2}\right) \left( \sigma _{x}^{2}+\sigma _{y}^{2}\right) \sigma _{x}^{2}}{\left( \sigma _{x}^{2}+\sigma _{y}^{2}\left( 1-\lambda \right) \right) ^{2}}\gtrless 0 ,\text { and} \end{aligned}$$
(25)
$$\begin{aligned} \frac{dp}{d\sigma _{x}^{2}}= & {} -\frac{r\left( \sigma _{x}^{4}+\sigma _{y}^{4}\left( 1-\lambda \right) +2\sigma _{y}^{2}\sigma _{x}^{2}\left( 1-\lambda \right) \right) -\sigma _{y}^{2}\lambda \bar{y}\left( 1-\lambda \right) }{\left( \sigma _{y}^{2}\left( 1-\lambda \right) +\sigma _{x}^{2}\right) ^{2}}\gtrless 0. \end{aligned}$$
(26)

Proposition 1 To prove the claim, we first derive Eqs. (9) and (10). Investors’ utility can be expressed as \(u_{i}=-\exp \{ r( \mathbf {q}_{i}^{T} \mathbf {v}_{i}+l_{i})\}\), \(i\in \{ 1,2\}\), where r is their level of risk aversion, \(q_{i}=( q_{i,k},q_{i,a}) ^{T}\) represents the \(2\times 1\) vector of investor is demand for shares in the 2 firms, \(\tilde{v}_{1}=\tilde{x}=( \tilde{x}_{k},\tilde{x} _{a}) ^{T}\), and \(\tilde{v}_{2}=\tilde{x}+\tilde{y}=( \tilde{x} _{k},\tilde{x}_{a}+\tilde{y}) ^{T}\). Each investor maximizes her expected terminal utility subject to the budget constraint

$$\begin{aligned} w_{i}=\mathbf {q}_{i}^{T}\mathbf {P}+l_{i}, \end{aligned}$$

where \(w_{i}\) is the initial wealth endowment and \(P=( p_{k},p_{a}) ^{T}\) is the price vector. Note that the price per share of the risk-free asset, like its return, has been normalized to one. Substituting the budget constraint, it is straightforward to show that maximizing expected utility is equivalent to maximizing the following certainty equivalent

$$\begin{aligned} CE_{i}=\mathbf {q}_{i}^{T}\left( E\left[ \mathbf {v}_{i}\right] -\mathbf {P} \right) -\frac{1}{2}r\mathbf {q}_{i}^{T}Cov\left[ \mathbf {v}_{i}\right] \mathbf {q}_{i}, \end{aligned}$$

where \(Cov[ \mathbf {v}_{1}] =\Sigma _{x}\) and \(Cov[ \mathbf { v}_{1}] =\Sigma _{x}+\Sigma _{y}\), with

$$\begin{aligned} \mathbf {\Sigma }_{x}=Cov\left[ \left( \tilde{x}_{k},\tilde{x}_{a}\right) \right] = \begin{bmatrix} \sigma _{x_{k}}^{2}&0 \\ 0&\sigma _{x_{a}}^{2} \end{bmatrix} \text { and }\,\mathbf {\Sigma }_{y}= \begin{bmatrix} 0&0 \\ 0&\sigma _{y}^{2} \end{bmatrix}. \end{aligned}$$

Note that Eq. (27) below holds with non-zero covariance terms in \(\Sigma _{x}\) and \(\Sigma _{y}\) and non-zero variance for firm ks CSR performance as long as the covariance matrices remain positive-definite. The first-order condition for an investor of type-i choosing share quantities to maximize wealth is given by

$$\begin{aligned} E\left[ \mathbf {v}_{i}\right] -\mathbf {P}-rCov\left[ \mathbf {v}_{i}\right] \mathbf {q}_{i}=0, \end{aligned}$$

such that the optimal demand for a type-i investor is given by

$$\begin{aligned} \mathbf {q}_{i}=\frac{1}{r}Cov\left[ \mathbf {v}_{i}\right] ^{-1}\left( E\left[ \mathbf {v}_{i}\right] -\mathbf {P}\right) . \end{aligned}$$

Prices are set such that aggregate demand equals aggregate supply. We assume that there is one share of each firm per investor and denote \(1=( 1,1) ^{T}\) the supply vector in the two-firm case. Therefore it has to be the case that, on average, \(( 1-\lambda ) q_{1}+\lambda q_{2}=1\). Substituting the optimal demands yields

$$\begin{aligned} \frac{1-\lambda }{r}Cov\left[ \mathbf {v}_{1}\right] ^{-1}\left( E\left[ \mathbf {v}_{1}\right] -\mathbf {P}\right) +\frac{\lambda }{r}Cov\left[ \mathbf {v}_{2}\right] ^{-1}\left( E\left[ \mathbf {v}_{2}\right] -\mathbf {P} \right) =\varvec{1}. \end{aligned}$$

Substituting our terms for output moments and solving for the price vector yields

$$\begin{aligned} \mathbf {P}={\bar{x}}+\left( \left( 1-\lambda \right) \mathbf {\Sigma }_{x}^{-1} +\lambda \left( \mathbf {\Sigma }_{x}+\mathbf {\Sigma }_{y}\right) ^{-1}\right) ^{-1}\left( \lambda \left( \mathbf {\Sigma }_{x}+\mathbf {\Sigma } _{y}\right) ^{-1}{\bar{\mathbf {y}}}-r{\varvec{1}}\right) . \end{aligned}$$
(27)

Equations (9) and (10) in the text follow directly from (27). First, substitute (8), (9), and (10) into \(p_{k}+p_{a}\ge p_{u}\). Substituting \(r\sigma _{y}^{2}> \bar{y}\), \(\lambda =0\), \(\lambda =1\), or \(r\sigma _{y}^{2}=\bar{y}\) proves the claim.

Proposition 2 Expected price in period 2 is defined by \(E[ \tilde{m}] =\bar{x}\) and \(E[ \tilde{n}] =\bar{y}\) as

$$\begin{aligned} E\left[ p_{2}\right] =\bar{x}-r\frac{1}{\tau _{x}+\tau _{m}}+\lambda \left( \frac{\bar{y}\left( \tau _{y}+\tau _{n}\right) -r}{\tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) }\right) . \end{aligned}$$

The expected change in price is therefore:

$$\begin{aligned} E\left[ p_{2}-p_{1}\right]&=\,r\frac{\tau _{m}}{\tau _{x}\left( \tau _{m}+\tau _{x}\right) } \end{aligned}$$
(28)
$$\begin{aligned}&\quad +\lambda r\frac{\tau _{n}+\left( 1-\lambda \right) \tau _{m}}{\left( \tau _{y}+\left( 1-\lambda \right) \tau _{x}\right) \left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) } \end{aligned}$$
(29)
$$\begin{aligned}&\quad +\lambda \bar{y}\frac{\left( 1-\lambda \right) \left( \tau _{n}\tau _{x}-\tau _{m}\tau _{y}\right) }{\left( \tau _{y}+\left( 1-\lambda \right) \tau _{x}\right) \left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) }. \end{aligned}$$
(30)

Corollary 2 Substituting (17) and (18) into \(E[ p_{2}-p_{1}]\) proves the claim.

Proposition 3 The respective derivatives are given by

$$\begin{aligned} \frac{d\alpha }{d\tau _{n}}= & {} \lambda \frac{\left( 1-\lambda \right) \left( \tau _{m}+\tau _{x}\right) +\tau _{y}}{\left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) ^{2}}\ge 0, \end{aligned}$$
(31)
$$\begin{aligned} \frac{d\alpha }{d\lambda }= & {} \frac{\tau _{n}\left( \tau _{m}+\tau _{n}+\tau _{x}+\tau _{y}\right) }{\left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) ^{2}}\ge 0, \end{aligned}$$
(32)
$$\begin{aligned} \frac{d\alpha }{d\tau _{m}}= & {} \frac{-\lambda \left( 1-\lambda \right) \tau _{n}}{\left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) ^{2}}\le 0, \end{aligned}$$
(33)
$$\begin{aligned} \frac{d\alpha }{d\tau _{x}}= & {} \frac{-\lambda \left( 1-\lambda \right) \tau _{n}}{\left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) ^{2}}\le 0\text {, and} \end{aligned}$$
(34)
$$\begin{aligned} \frac{d\alpha }{d\tau _{y}}= & {} \frac{-\lambda \tau _{n}}{\left( \tau _{y}+\tau _{n}+\left( 1-\lambda \right) \left( \tau _{x}+\tau _{m}\right) \right) ^{2}}\le 0. \end{aligned}$$
(35)

Proposition 4 Substituting (16) and ( 15) into \(T=( 1-\lambda ) \left| q_{1,2}-q_{1,1}\right|\) yields

$$\begin{aligned} T&=\,\left( 1-\lambda \right) \left| \frac{E\left[ \tilde{v}_{i}|m,n \right] -p_{2}}{rVar\left[ \tilde{v}_{i}|m,n\right] }-1\right| \nonumber \nonumber \\&=\,\left( 1-\lambda \right) \frac{\tau _{x}^{\prime }}{r}\left| -\frac{ \lambda }{1+\left( 1-\lambda \right) \frac{\tau _{x}^{\prime }}{\tau _{y}^{\prime }}}\left( \frac{\bar{y}\tau _{y}+n\tau _{n}}{\tau _{y}^{\prime } }-r\frac{1}{\tau _{y}^{\prime }}\right) \right| \nonumber \nonumber \\&=\,\frac{\lambda \left( 1-\lambda \right) }{1-\lambda +\frac{\tau _{y}+\tau _{n}}{\tau _{x}+\tau _{m}}}\left| 1-\frac{\bar{y}\tau _{y}+n\tau _{n}}{r} \right| . \end{aligned}$$
(36)

Appendix 2: Non-zero correlation between x and y

This section discusses the baseline model when x and y are correlated, with \(Cov[ \tilde{x},\tilde{y}] =\rho \sigma _{x}\sigma _{y}\) and \(\rho \in [ -1,1]\). While a type-1 investor’s certainty equivalent and therefore demand is not affected, a type-2 investor’s certainty equivalent and demand are now

$$\begin{aligned} CE_{2}&=\,q_{2}\left( \bar{x}+\bar{y}-p\right) -\frac{1}{2}rq_{2}^{2}\left( \sigma _{x}^{2}+\sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) \text { and} \end{aligned}$$
(37)
$$\begin{aligned} q_{2}&=\,\frac{\bar{x}+\bar{y}-p}{r\left( \sigma _{x}^{2}+\sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }. \end{aligned}$$
(38)

The market-clearing condition is then given by

$$\begin{aligned} \left( 1-\lambda \right) \frac{\bar{x}-p}{r\sigma _{x}^{2}}+\lambda \frac{ \bar{x}+\bar{y}-p}{r\left( \sigma _{x}^{2}+\sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }=1. \end{aligned}$$
(39)

This implies that the equilibrium price is

$$\begin{aligned} p&=\,\bar{x}+\frac{\lambda \sigma _{x}^{2}}{\sigma _{x}^{2}+\left( 1-\lambda \right) \left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }\bar{y}-r \frac{\sigma _{x}^{2}\left( \sigma _{x}^{2}+\sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }{\sigma _{x}^{2}+\left( 1-\lambda \right) \left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) } \end{aligned}$$
(40)
$$\begin{aligned}&=\,\bar{x}-r\sigma _{x}^{2}+\frac{\lambda \sigma _{x}^{2}}{\sigma _{x}^{2}+\left( 1-\lambda \right) \left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }\left( \bar{y}-r\left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) \right) \text {.} \end{aligned}$$
(41)

This implies that an increase in the correlation, \(\rho\), decreases the extent to which \(\bar{y}\) is priced. The reason is that an increase in \(\rho\) increases the perceived risk of type-2 investors and therefore decreases their equilibrium holdings. The increase in perceived risk and the decrease in holdings have countervailing effects on the risk premium. However, the first effect dominates such that the risk premium increases when \(\rho\) increases,

$$\begin{aligned} \frac{\partial \left( r\frac{\sigma _{x}^{2}\left( \sigma _{x}^{2}+\sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }{\sigma _{x}^{2}+\left( 1-\lambda \right) \left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) }\right) }{\partial \rho }=2r\frac{\lambda \sigma _{x}^{5}\sigma _{y}}{ \left( \sigma _{x}^{2}+\left( 1-\lambda \right) \left( \sigma _{y}^{2}+2\rho \sigma _{x}\sigma _{y}\right) \right) ^{2}}>0. \end{aligned}$$

This implies that when \(\bar{y}>0\) then \(\frac{dp}{d\rho }<0\).

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Friedman, H.L., Heinle, M.S. Taste, information, and asset prices: implications for the valuation of CSR. Rev Account Stud 21, 740–767 (2016). https://doi.org/10.1007/s11142-016-9359-x

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  • DOI: https://doi.org/10.1007/s11142-016-9359-x

Keywords

  • Asset pricing
  • Taste
  • Reporting
  • Corporate social responsibility

JEL

  • G11
  • G12
  • L30
  • M40