Jinqiang Yang

Optimal consumption and savings with stochastic income and recursive utility

We develop a tractable incomplete-markets model with an earnings process Y subject to permanent shocks and borrowing constraints. Financial frictions cause the marginal (certainty equivalent) value of wealth W to be greater than unity and decrease with liquidity w=W/Y. Additionally, financial frictions cause consumption to decrease with this endogenously determined marginal value of liquidity. Risk aversion and the elasticity of inter-temporal substitution play very different roles on consumption and the dispersion of w. Permanent earnings shocks, especially large discrete stochastic jumps, make consumption smoothing quantitatively difficult to achieve. Borrowing constraints and permanent discrete jump shocks can generate empirically plausible values for marginal propensities to consume in the range of 0.2 to 0.6.

Investment under Uncertainty and the Value of Real and Financial Flexibility

This paper considers a model of (irreversible) investment under uncertainty for a firm facing external financing costs. Such a firm prefers to fund its investment through internal funds, so that the firm’s optimal investment policy and value now depend on the size of its retained earnings. We show that the standard real options results are significantly modified when there are external financing costs. Investment and abandonment hurdles are higher in the presence of external financing costs, and most importantly the investment hurdle is highly non-monotonic in the firm’s internal funds: when these are sufficient to cover capital expenditures then the investment hurdle is decreasing in the size of internal funds. But when they fall short then the firm’s investment policy becomes more and more conservative when it accumulates cash, as it has stronger incentives to postpone its investment until the point where it has sufficient internal funds to entirely cover its investment outlays. Our analysis brings out the subtle interactions between sources of funds (external, internal, and prospective retained earnings once the investment is undertaken) and the optimal timing of investment. ∗First draft: December, 2012. We thank Ilona Babenka, Martin Cherkes, Sudipto Dasgupta, Peter DeMarzo, Mark Gertler,Vicky Henderson and seminar participants at Columbia, HKUST 2013 Finance Symposium, 2014 American Finance Association (AFA) meetings in Philadelphia, and Zhejiang University for helpful comments. †Columbia University, NBER and CEPR. Email: pb2208@columbia.edu. Tel. 212-854-9245. ‡Columbia Business School and NBER. Email: neng.wang@columbia.edu. Tel. 212-854-3869. §The School of Finance, Shanghai University of Finance and Economics (SUFE). Email: yang.jinqiang@mail.sufe.edu.cn.We develop a model of investment under uncertainty for a nancially constrained firm. Facing external financing costs, the firm prefers to fund its investment through internal funds, so that the firms optimal investment policy and value now depend on both its earnings fundamentals and liquidity holdings. We show that financial constraints significantly alter the standard real options results, with the financial flexibility conferred by internal funds acting as a complement, and at times as a substitute, to the real flexibility given by the optimal timing of investment. We show that: 1) the investment hurdle (whose deviation from the first-best Modigliani-Miller benchmark measures investment distortions) is highly nonlinear and non-monotonic in the firms internal funds, as the firm may prefer accumulating internal funds rather than accessing external capital markets to finance investment when internal funds are sufficiently high; 2) with multiple rounds of growth options, a value-maximizing financially constrained firm may choose to over-invest via accelerated investment timing in earlier stages in order to mitigate under-investment problems in later stages.

Investment, Tobin's q, and Interest Rates

We study the impact of stochastic interest rates and capital illiquidity on investment and firm value by incorporating a widely used arbitrage-free term structure model of interest rates into a standard q theoretic framework. Our generalized q model informs us to use corporate credit-risk information to predict investments when empirical measurement issues of Tobin’s average q are significant (e.g., equity is much more likely to be mis-priced than debt), as in Philippon (2009). We find, consistent with our theory, that credit spreads and bond q have significant predictive powers on micro-level and aggregate investments corroborating the recent empirical work of Gilchrist and Zakrajšek (2012). We also show that the quantitative effects of the stochastic interest rates and capital illiquidity on investment, Tobin’s average q, the duration and user cost of capital, and the value of growth opportunities are substantial. These findings are particularly important in today’s low interest rate environment.

Dynamics of Entrepreneurship under Incomplete Markets

An entrepreneur faces non-diversifiable business risk and liquidity constraints. We provide a unified framework that embeds these frictions to study interdependent business start-up/entry, capital accumulation/asset sales, portfolio allocation, consumption/saving, and business exit decisions. Liquid wealth mitigates financial constraints and critically influences the entrepreneurs decision making. An entrepreneur invests less in business, consumes less, and allocates less to the market portfolio in order to preserve liquidity for precautionary purposes. We develop the counterpart of the q theory of investment for firms run by non-diversified entrepreneurs, and propose corresponding measures for average q and marginal q. Corporate investment depends on both marginal q and the marginal value of wealth. The wedge between average q and marginal q is non-monotonic in liquidity. With illiquid capital stock, the endogenous liquidation option provides significant flexibility for the entrepreneur to manage downside risk, causes firm value to be convex in liquidity and investment to decrease in liquidity near the endogenous exit boundary. The flexibility to accumulate wealth before entering entrepreneurship is highly valuable, and the wealth effect is significant for entrepreneurship. The optimal entry decision critically depends on the outside option, the start-up cost, risk aversion, and wealth. Heterogeneity among entrepreneurs is thus important. Our model yields an operational framework to calculate the private equity idiosyncratic risk premium. Quantitatively, the interactive effects of incomplete-markets frictions and capital illiquidity on investment and value are significant.

The Pricing and Timing of the Option to Invest for Cash Flows with Partial Information

This paper extends real options theory to consider the situation where the mean appreciation rate of cash flows generated by an irreversible investment project is not observable and governed by an Ornstein-Uhlenbeck process. Our main purpose is to analyze the impact of the uncertainty of the mean appreciation rate on the pricing and investment timing of the option to invest under incomplete markets with partial information. We assume that an investor aims to maximize expected discounted utility of lifetime consumption. Based on consumption utility indifference pricing method, stochastic control and filtering theory, under CARA utility, we derive the implied value of cash flows after investment, and then obtain the implied value and the optimal investment threshold of the option to invest, which are determined by a semi-closed-form solution of a free-boundary PDE problem. We show that the solutions are independent of the utility time-discount rate. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations show that partial information leads to a significant loss of the implied value of the option to invest. This loss increases with the uncertainty of the mean appreciation rate. In contrast to standard real options theory, a high volatility of cash flows decreases the implied value of the option to invest as well as the implied information value.

Optimal ownership structure in private equity

We develop a tractable model to analyse the valuation of a general partner (GP) and the ownership allocation in a private equity (PE) fund. Our results indicate that holding ownership will increase GPs value. We further explore the influential factors that affect GPs optimal ownership decision. Our model predicts that GPs managerial skill has positive effects on GPs shareholding choice. Factors such as leverage, unspanned risks, GPs compensation have negative impacts on GP ownership decision. The funds maturity has a non‐monotonic and concave influence. Moreover, the widely used performance measures implied by our model are consistent with empirical findings.

Investment-based optimal capital structure

ABSTRACT This paper extends the classical capital structure model by introducing the output of firm with ‘AK’ production technology dynamically depends on the endogenous investment decision and capital accumulation. Based on our calibration, it shows that the flexibility of dynamic investment and capital accumulation induces the firm to take the lower leverage at financing time and makes the leverage estimate closer to empirically observed leverage ratios, which provides an effective explanation for the ‘under-leverage puzzle’. In addition, this model predicts that the market leverage behaves in a U-shaped manner with capital liquidity, which provides a novel empirical test.

Real Options under a Double Exponential Jump-Diffusion Model with Regime Switching and Partial Information

We consider an irreversible investment in a project, which generates cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We show a method to measure the information value, i.e. the difference between the values of the option to invest under the two cases. We present numerical solutions by finite difference methods if jumps are absent. By numerical analysis, we find that: (i) The value of the option to invest increases with the belief on economic boom; (ii) If investors are more uncertain about the state of the economy, information is more valuable; (iii) The more likely the transition from boom to recession, the less the value of the option; (iv) The bigger the dispersion of the expected return, the higher the information value; (v) A higher cash flow volatility induces a less information value.

Liquidity default, liquidity management and smooth dividends policy

ABSTRACT Our article models liquidity financing constraints with the real options framework. By conducting a comprehensive investigation of the effects of shocks to liquidity constraints on the firm’s optimal investment, financing and dividend policies, our model highlights the importance of liquidity management and extends the liquidity management approach to hedge liquidity default risk. We find that being concerned about liquidity default risk will significantly change a firm’s behaviours, including those related to investment and the optimal capital structure. A firm that is concerned about its liquidity default risk will become more cautious: it will choose to delay investment and have higher leverage when internal liquidity is very low, but choose earlier investment and lower leverage when liquidity is high enough. The dividends policy can alleviate risks from both the external market and internal project volatility and provides an alternative explanation for the ‘smooth dividends policy puzzle’ commonly reported in empirical research.

Liquidity and Risk Management, Executive Compensation, and Investment with Inalienable Human Capital: Optimal Contracting and Corporate Valuation

We formulate a dynamic nancial contracting problem with risky inalienable human capital. We show that the inalienability of the entrepreneur’s risky human capital not only gives rise to endogenous liquidity limits but also calls for dynamic liquidity and risk management policies via standard securities that rms routinely pursue in practice, such as retained earnings, possible line of credit draw-downs, and hedging via futures and insurance contracts.