Public Information and Effi cient Capital Investments: Implications for the Cost of Capital and Firm Values

Transcription

1 Public Information and Effi cient Capital Investments: Implications for the Cost of Capital and Firm Values Peter O. Christensen Department of Finance, Copenhagen Business School Hans Frimor Department of Accounting and Auditing, Copenhagen Business School February 17, 2015 Chistensen and Frimor February 17, / 21

2 Facts about FASB (fasb.org/facts/) Establishing standards of financial accounting Such standards are important to the effi cient functioning of the economy because decisions about the allocation of resources rely heavily on credible, concise, and understandable financial information. Mission The mission of the FASB is to establish and improve standards of financial accounting and reporting that foster financial reporting by nongovernmental entities that provides decision-useful information to investors and other users of financial reports. Chistensen and Frimor February 17, / 21

3 Equilibrium Prices, Effi cient Resource Allocation and Information The equilibrium price system should ensure Effi cient risk sharing among investors Effi cient allocation of resources over time (i.e., aggregate investments) Effi cient allocation of resources among firms (i.e., allocation of aggregate investments among firms) Better pre-decision information leads to More effi cient action choices in settings with a single decision maker (cf. Blackwell s Theorem) More effi cient resource allocation in a capital market setting if (cf. Kunkel 1982, Hakansson et al. 1982, Feltham and Christensen 1988) Markets are suffi ciently complete Investors have homogeneous beliefs Investors have time-additive utilities The decision-facilitating role of information Single-person decision making: updating of beliefs Capital market setting: updating of beliefs and equilibrium prices Chistensen and Frimor February 17, / 21

4 Information and Effi cient Resource Allocation in Large Economies Feltham and Christensen (CAR 1988) Windfall information (affects beliefs about the level of future payoffs but not the productivity of current investments) not valuable if it pertains to firm-specific events (due to diversifiability of firm-specific risks) valuable if it pertains to economy-wide events (through changes in economy-wide state prices) Productivity information (affects beliefs about both the level of future payoffs and the productivity of current investments) valuable if it pertains to firm-specific events (due to a more effi cient allocation of aggregate investments among firms) valuable if it pertains to economy-wide events (due to both a better allocation of aggregate investments among firms and over time through changes in economy-wide state prices) Chistensen and Frimor February 17, / 21

5 Can we empirically assess the economic consequences of improvements in public information systems? Daske et al. (JAR 2008): The economic consequences of mandatory International Financial Reporting Standards (IFRS) reporting around the world Cost of capital studies: Better information means lower risk and, thus, lower risk premia A lower risk premium means a lower risk-adjusted cost of capital (interest rate plus risk premium) A lower risk-adjusted cost of capital means more investments have positive NPVs Event studies: More effi cient allocation of aggregate capital investments means firms use their resources more effi ciently More effi cient use of resources means higher ex ante firm values All of the above turns out to be false! Chistensen and Frimor February 17, / 21

6 Standard General Equilibrium Asset Pricing Model with Value Maximizing Firms Better decision-facilitating information unambiguously increases the investors ex ante certainty equivalents generally increases the firms ex ante cost of capital is associated with a negative (positive) ex ante stock market reaction if the investors RRA is above (less than) one Chistensen and Frimor February 17, / 21

7 Why is this so? Better quality information may give lower ex post risk premia but is perfectly offset (in an exchange economy) by a higher risk premium for pre-posterior risk: Christensen et al. 2010: The ex ante risk premium depends only on the risks in the underlying cash flows but not on when we get to know more about these cash flows Given aggregate capital investments: better firm-specific productivity information improve the allocation of aggregate investments among firms a higher future payoff on well-diversified portfolios for the same aggregate investment the investors willingness to pay for an additional unit of future payoff decreases, i.e., the interest rate increases higher interest rates reduces ex ante firm values stocks are claims to future payoffs What is the impact on aggregate capital investments? Chistensen and Frimor February 17, / 21

8 Impact on Aggregate Capital Investments Better firm-specific productivity information increases the productivity of aggregate investments: Substitution effect: higher marginal productivity increases the incentive to invest more Income effect: Higher future payoffs for the same investment reduces the incentive to invest and, thus, increases the incentive to invest less and consume more now Chistensen and Frimor February 17, / 21

9 A Simple Model Preferences (representative investor): u t (c t ) = e δt 1 1 γ c1 γ t, c t > 0, γ > 0, γ = 1, where γ = RRA = 1/EIS, with state-price deflator Technology (market portfolio): m t = u t (c t ) = e δt c γ t f (q) = e p q k, q > 0, k (0, 1) where p is a productivity parameter, with marginal rate of transformation MRT (q) = e p kq k 1 Budget constraints: c 0 = ĉ 0, c 1 = ĉ 1 q, c 2 = f (q) Chistensen and Frimor February 17, / 21

10 Equilibrium Aggregate Investments Equilibrium condition MRS(c 1, c 2 ) = MRT (q ) Substituting in the budget constraints u 1 (ĉ 1 q ) u 2 (f (q )) = ep k (q ) k 1 Impact of productivity p on aggregate investments dq dp = 1 γ γ [ f (q)/c2 + 1/c 1 + (1 k)/q ] 0 γ 1 Increased productivity of aggregate investments due to more informative firm-specific productivity information reduces the equilibrium investments for γ > 1 (lowers consumption growth) and, thus, dampens the increase in the interest rate increases the equilibrium investment for γ < 1 (increases consumption growth) and, thus, further increases the interest rate Chistensen and Frimor February 17, / 21

11 Interest rates and implied cost of capital Interest rates and implied cost of capital Impact of Firm-specific Productivity Information on Interest Rates and Implied Cost of Capital Left panel γ = 2; Right panel γ = % 12% 10% 8% 6% 4% 2% 8% 6% 4% 2% 0% % Firm specific productivity informativeness Spot interest rate Zero coupon interest rate Implied cost of capital 2% Firm specific productivity informativeness Spot interest rate Zero coupon interest rate Implied cost of capital Chistensen and Frimor February 17, / 21

12 Ex ante firm value Ex ante firm value Impact of Firm-specific Productivity Information on Firm Values and Certainty Equivalents Left panel γ = 2; Right panel γ = Ex ante certainty equivalent Ex ante certainty equivalent Firm specific productivity informativeness Ex ante firm value Ex ante certainty equivalent Firm specific productivity informativeness Ex ante firm value Ex ante certainty equivalent Chistensen and Frimor February 17, / 21

13 Asset Pricing with Economy-wide Risks No arbitrage: T [ ] T mτ v t = E t d τ = τ=t+1 m t B τt {E t [d τ ] + Cov t [m τt, d τ ]} τ=t+1 where m τt is a normalized state-price deflator, and B τt is the price of a zero-coupon bond at date t paying one unit of account at date τ Effectively complete markets, homogeneous beliefs, and time-additive utility: m τt = u τ(c τ ) E t [u τ(c τ )] ; B τt = E t [u τ(c τ )] u t (c t ) where c τ is equilibrium consumption for a representative investor (i.e., aggregate consumption per capita) Implied cost of capital ρ t solves the equation: v t = T exp [ ρ (τ t)] E t [d τ ] τ=t+1 Chistensen and Frimor February 17, / 21

14 A Simple Model with Economy-wide Risks Power utility and normally distributed productivity parameter f (q) = e p q k, q > 0, k (0, 1), p N(p 0, σ 2 ) Pre-decision information signal y at t = 1 equal to the posterior mean p y N(y, σ 2 1 ); y N(p 0, σ 2 0 ); σ2 0 + σ2 1 = σ2 where the informativeness is measured as the pre-posterior variance of the signal σ 2 0 Expected marginal rate of transformation given y: E[f (q) y] = e y σ2 1kq k 1 Value-maximizing investment q (y): 1 = B 21 {E [ f (q ) y ] [ u + Cov 2 (f ]} (q )) E[u 2 (f (q )) y], f (p, q) u 1 (ĉ 1 q (y)) u 2 (E[f (q ) y]) = ey k (q (y)) k 1 H(σ 2 1, γ), H(σ2 1, γ) > 0 Chistensen and Frimor February 17, / 21

15 Impact of Productivity Information on Aggregate Investments and Risk-adjustments Equilibrium aggregate investments are decreasing in y if γ > 1, i.e., high productivity means lower investments increasing in y if γ < 1, i.e., high productivity means higher investments More informative economy wide productivity information reduces the risks in future payoffs for γ > 1 and, thus, reduces the dollar risk premium amplifies the risks in future payoffs for γ < 1 and, thus, increases the dollar risk premium This suggests that as the informativeness of economy wide productivity information increases, ex ante firm values should increase for γ > 1 decrease for γ < 1 This is not so even though expected payoffs do not change much Chistensen and Frimor February 17, / 21

16 Impact of Productivity Information on Discount Rates Recall the prices of zero-coupon bonds are determined as where the state-price deflator B τt = E t [u τ(c τ )] u t (c t ) m τ = u τ(c τ ) = e δτ c γ τ is a decreasing convex function of aggregate consumption per capita In other words, zero-coupon bond prices (interest rates) are decreasing (increasing) in expected consumption growth zero-coupon bond prices (interest rates) are increasing (decreasing) in mean-preserving spreads of future consumption (i.e., as consumption risk increases) The latter is due to the impact on the incentive for precautionary savings Chistensen and Frimor February 17, / 21

17 Impact of Productivity Information on Discount Rates... Through the impact on equilibrium aggregate investments, more informative economy wide productivity information reduces aggregate consumption risks and, thus, increases discount rates when γ > 1 increases aggregate consumption risks and, thus, decreases discount rates when γ < 1 The impact on discount rates dominates the impact on risk-adjusted expected equilibrium dividends such that more informative economy wide productivity information reduces ex ante firm values when γ > 1 increases ex ante firm values when γ < 1 Chistensen and Frimor February 17, / 21

18 Ex ante firm value Ex ante firm value Impact of Economy-wide Productivity Information on Firm Values and Certainty Equivalents Left panel γ = 2; Right panel γ = Economy wide productivity informativeness Ex ante firm value Ex ante certainty equivalent Ex ante certainty equivalent Economy wide productivity informativeness Ex ante firm value Ex ante certainty equivalent Ex ante certainty equivalent Chistensen and Frimor February 17, / 21

19 Interest rates and implied cost of capital Interest rates and implied cost of capital Impact of Economy-wide Productivity Information on Interest Rates and Implied Cost of Capital Low gamma: Left panel γ = 0.5; Right panel log utility 6% 7% 5% 6% 4% 5% 3% 4% 2% 3% 1% 2% 0% % Economy wide productivity informativeness Spot interest rate Zero coupon interest rate Impiled cost of capital One period ahead exp return 1% 0% Economy wide productivity informativeness Spot interest rate Zero coupon interest rate Impiled cost of capital One period ahead exp return Chistensen and Frimor February 17, / 21

20 Interest rates and implied cost of capital Interest rates and implied cost of capital Impact of Economy-wide Productivity Information on Interest Rates and Implied Cost of Capital High gamma: Left panel γ = 2; Right panel γ = 4 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% Economy wide productivity informativeness Spot interest rate Zero coupon interest rate Impiled cost of capital One period ahead exp return 12% 10% 8% 6% 4% 2% 0% Economy wide productivity informativeness Spot interest rate Zero coupon interest rate Impiled cost of capital One period ahead exp return Chistensen and Frimor February 17, / 21

21 Conclusion Better decision-facilitating public information unambiguously increases the investors ex ante certainty equivalents due to a more effi cient resource allocation generally increases the firms ex ante cost of capital but there are exceptions (γ slightly above one) is associated with a negative (positive) ex ante stock market reaction if the investors RRA is above (less) than one We do not really know whether the investors EIS (or RRA) is above or below one Recursive utility breaks the link between EIS and RRA but introduces other issues like preferences for early versus late resolution of uncertainty Chistensen and Frimor February 17, / 21