OUT OF ORDER Bolton and Scharfstein Borrowers are disciplined by the threat of losing access to further credit. Generates Investment cash flow correlation Suppose there is a one period model where an entrepreneur can generate a project with X {X l, X h }. Cash flows are non verifiable and contractible. Entrepreneur will always report X l and if cost of project is sufficiently high = no funding
Two Projects Suppose that self financing for the second period is impossible Projects are contractible = veto power Ownership of key asset is contractible Assume that the investor has full bargaining power. Assume x l = 0 for simplicity Optimal contract: Financing is possible if I + θ(θx h I) > 0. Project 2 is financed if and only if the entrepreneur repays R h = θx H after project 1.
What is R h? Investor has full bargaining power Price == entrepreneurs valuation for running project 2 Valuation? After Project 2, he won t repay... Valuation for running the project is θx h = repayment is R h = θx h. So, the investor extracts all he can from the project i.e., the NPV Entrepreneur s profit (from project 1) : θx h Investors profit: I + θ(θx h I) This can be interpreted as debt: Entrepreneur borrows I against promised repayment R h. If he defaults, the investor shuts down further operations.
Making things more Complicated If X l > 0, then possibility that the the entrepreneur can self finance in the second period. Or raise money from the outside. Rule out self financing, by assuming that X < I. Rule out outside (new) investors, by assuming that (for example) payments to new investors are contractible i.e., the initial investor s claims have priority. Also works with a continuum of outcomes, (Model of VC). Extend to multiple contacts Extend to non independent projects.
Returning to order: What Optimal Investment means for market Returns One strand of the literature tries to explain capital structure... Another: Cross section of returns Starting Point: Asset pricing anomalies.
Market efficiency: joint test with asset pricing model 1. Size effect: small caps on NYSE have higher returns than predicted by CAPM 2. Turn of the year effect: small cap return attributable to first two weeks in JAN 3. Weekend effect: Av Return to S&P negative over weekends. 4. The value effect: firms with high E P abnormal returns relative to CAPM 5. Also, high dividend yields D P 6. High book to market: B M Lead to Fama French, Factors: HML, SMB have positive
Using three factor models: low B M ( growth stocks) small cap have low returns and large cap have high returns. Contrarian effect: past losers (stocks with low returns in the past 3 5 years) have higher average returns than past winners. Momentum effect: past winners outperform past losers. Time series predictability of returns: 1. Negative relation between aggregate stock returns and short term interest rates. (S.t interest rates predict stock returns) 2. Dividend yields predict stock returns
Persistence of IPO returns: Cycles IPO stocks have below normal returns 3 yrs after the IPO. Underperformance in IPOs concentrated in small firms with low B M. Suppose Fama French factors are priced risk: B M indicates value versus growth stocks, and HM L reflects distress risk. High B M reflects assets in place while lose B M have growth options. High B M, high Q, agency problems.
What Does Q way about this? Important result by Restoy and Rockinger (1994). In a world with no arbitrage opportunities, the return on investing in a firm with linear homogenous production and adjustment cost function (Hayashi conditions) is equal state by state to the market return of a claim on the stock of the firm. Intuition: if a no arbitrage condition holds, then it must hold for the investment of the firm. In particular, find a portfolio that replicates state by state, the payoff of the investment asset. Relate the investment return with returns on claims issued by the firm. = returns must be the same.
Consider the simplest neoclassical problem with constant returns to scale. max {I t } E t s.t. K t+1 = A(K t, I t ) I t + j=t+1 [F (K j )λ j I j ] λ is a shock (Markov) and A( ) is the capital accumulation rule FOC implies E t F K(K t+1 )λ t+1 + A K(K t+1, I t+1 A I (K t+1, I t+1 ) A I(K t, I t ) = 1 1 A I (K t+1,i t+1 ) is the value in terms of investment at period t of a unit of capital installed during the next production period. This marginal unit of capital produces F K (K t+1 )λ t+1 of investment good, but depreciates into A K (K t+1, I t+1 ) units of capital
Define terms inside the bracket as investment return ( Euler equation holds)! Now, stock market return is D t+1+v t+1 V t. Take investment return, multiply top and bottom by K t+1, add and subtract I t+1 to numerator and observe that if linearly homogenous, marginal == average. get asset returns. = if variables in the cross section explain optimal investment = explains asset returns. For example, investment rate q, which is proportional to Book/Market. Marginal product of capital is related to profitability, and therefore positive relationship between expected profitability and expected return.
Berk, Green and Naik Uses the relationship between assets in place and growth options to explain changes in the firm s systematic risk. Firm s investment policy involves exercising real options. Partial equilibrium model. Infinite Horizon, discrete time. One project per period; costs I Date t cashflows of the project started at j < t are C j (t) = Ie C 1 2 σ2 j +σ jɛ j (t) Projects may become obsolete: define indicator variables {χ j (t), t j} j=0. Posit a pricing kernel: χ j (t + 1) = χ t (t)y j (t + 1) z(t + 1) = z(t)e [ r(t) 1 2 σ2 z σ z ν(t+1)] One period,riskless continuous interest rate: r(t + 1) = κr(t) + (1 κ) r + σ r ζ(t + 1)
Systematic risk of a project: β j = σ j σ z cov(ɛ j (t), ν(t)) higher beta means more negative correlation with pricing kernel. This is different from the CAPM β. Absence of arbitrage, there is a process so that E t (R t+1 ) = e r(t) [1 cov t (m t+1, R t+1 ] CAPM = m t+1 is decreasing, linear in market return,so cov t (m t+1, R t+1 ) is proportional to the market beta. Here, m t+1 = z(t+1) z(t) = nonlinear. Each β j is drawn from F β at the time it arrives.
Calculate: V j (t) = E t V (t) = E t s=t+1 s=t+1 z(s) z(t) C j(s)χ j (s) z(s) z(t) max[v s(s) I, 0] P (t) = t j=0 V j (t)χ j (t) + V (t)
Hence...Returns... Hence, conditional expected return on a proportional claim on the firm: E t [1 + R t+1 ] = πn(t)[d t[r(t)]e β(t) + 1] + J e [r(t)] n(t)d[r(t)]e β(t) + J [r(t)] Here, n(t) = b(t) I is the number of ongoing projects. So, returns depend on πn(t)[d t [r(t)]e β(t) which are the gross return on assets in place. Where J e [r(t)] is per unit present value of future growth options Valuation of growth options: E t z(s) z(t) max[v s(s) I, 0] Decision at s depends on NPV which depends on r(s) and β s. Value of each of these components have different sensitivity to the state variables: β(t) average systematic risk of existing assets r(t) the current interest rate n(t) the number of active projects
Notice, if only growth options: E t [1 + R t+1 ] = J e [r(t)] J [r(t)] Whereas, if only ongoing projects... E t [1 + R t+1 ] = π[eβ(t) + D e (r(t))] D(t(t)) This is increasing in β. Calibrate and Simulate!