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Corporate Cash Holding Policy: A Multistage Approach with an Application in the Agribusiness Sector

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##### Corporate Cash Holding Policy: A Multistage Approach with an Application in the Agribusiness Sector

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**Corporate Cash Holding Policy: A Multistage Approach with an**Application in the Agribusiness Sector Astrid Prajogo†, Davi Valladao‡, & John M. Mulvey† QWAFAFEW Meeting February 22, 2011 †Operations Research and Financial Engineering Department, Princeton University. ‡ Electrical Engineering Department, Pontifical Catholic University of Rio de Jainero.**Outline**• Introduction & Motivation • The Model • Notation • Model Assumptions • Mathematical Formulation • An Application in the Agribusiness Sector • Regime Analysis in the Agribusiness Sector • Numerical Results • A Fixed Policy Approximation • Conclusion and Future Work**Introduction**We observe a significant increase in the cash-to-asset ratio of S&P 500 companies between 1993 to 2010. Note: Annual data taken from Compustat Index Fundamentals for S&P 500 from Jan 1993 to Dec 2009. Firm-level quarterly data of S&P 500 constituents taken from Compustat Fundamentals from Jan 2010 to Dec 2010.**Introduction**• A recent study by Standard & Poor’s shows that there’s an all-around increase in corporate cash holding. • Global, and • across all industries • 1 Source: S&P Cross-Market Commentary: The Largest Corporate Cash Holdings Are All Over The Map. Data taken as of Jan. 7, 2011. • 2 Total cash in the latest quarter (Mil. $).**Introduction**Cash holding can be bad for a firm because … • Cash may be better invested elsewhere, earning above risk-free rate returns. • Cash provides managers more freedom in choosing projects, even the ones with negative NPV. • High excess cash levels may be a signal of managerial concerns regarding the uncertainty of future operating cash flows and lack of investment opportunities, hinting at a negative link between cash holdings and returns. • High cash reserves may induce the company to be seen as a prime target for hostile takeovers. • [Jensen & Meckling (1976), Harford (1999), Lie (2002)]**Introduction**Cash holding can be good for a firm because … • Internal cash allows for immediate investments and eliminates the costs incurred from external financing. • Buffer stock during economic crisis. • Cash helps reduce borrowing cost. • [Fazzari et al. (1988), Froot et al.(1993)]**Introduction**A Brief Walk through the Literature • Opler et al. (1999) • Investigates the risk determinants of corporate cash holdings • Finds a positive link between growth opportunities and excess cash. • Harford (1999) • High-cash firms are more likely to make value-decreasing investments. • Mikkelson & Partch (2003) • Investigates that relationship between cash holding and operating performance. • Concludes that cash holding does not hinder operating performance. • Bates (2009) • Documents a dramatic increase in cash holdings of U.S. manufacturing companies from 10% in 1980 to 24% in 2004 • Increase in cash holding among corporations is caused by an increase in cash flow risk and R&D expenditures. • Palazzo (2008) and Simutin (2010) • Independently found that firms with a high excess cash level exhibit higher future stock returns compared to its peers with low excess cash.**Introduction**Source: Simutin (2010). Sample average of regression factors in each cash decile. A few observations: High betas for firms with high excess cash High market-to-book value of assets for firms with high excess cash. Smaller sized firms tend to belong in the lowest or highest decile based on excess cash. High-cash firms tend to have lower debt.**Introduction**Source: Simutin (2010). Value-weighted monthly returns are significant at the 1%-level • Firms with high excess cash exhibit higher stock returns than firms with low excess cash. • The Fama-Macbeth regression factors are unable to explain the stock returns generated by this High-Low portfolio. • No causality argument here.**Introduction**• Two sources of funding for investment and production: • cash (internal financing) and • a single period debt (external financing) • The model endogenously determines the best • production, • investment, • financing, • dividend payout, and • cash holding policies to maximize shareholders’ value over the planning horizon. We propose a model of a firm facing stochastic investment opportunities and stochastic cost of external financing that are dependent on the business cycle (regime-switching framework).**An Application The Agribusiness Sector**• The agribusiness sector is intended to include those firms whose operations involve the use of agriculture commodities. • We define the companies in this sector as those U.S. companies that are classified within the Global Industry Classification Standards (GICS) subsectors: • Agricultural Chemicals (15101030), • Agricultural Products (30202010), and • Packaged Foods and Meats (30202030). • Data compiled using CRSP and Compustat. • 70 unique agribusiness companies to be included in the sample from January 1990 to March 2010. • The agribusiness sector index return at the end of month t is calculated as the market-cap-weighted average of the stock returns of the companies that are identified to be in the agribusiness sector during month t.**An Application Descriptive Statistics**We observe a similar increase in the cash-to-asset ratio of the agribusiness companies between 1990 to 2010, although the increase is not as dramatic as in the S&P 500.**An Application The Agribusiness Sector**• The relationship between the agribusiness index and the S&P 500 can help us determine business cycles in the agribusiness sector.**An Application Hidden Markov Model**• The uncertainty of the risk factors is assumed to be dependent on the business cycle of the agribusiness sector Use a Hidden Markov Model (HMM) pt,r pe,t pe,e pr,r pt,t Recession Transition Expansion pr,t pr,e**An Application Hidden Markov Model**• Let the S&P 500 and Agribusiness sector returns, rt,Aand rt,M , be our observed variables and the regimes as the latent variable, Rt. Rt-1 Rt Rt+1 [rt-1,A , rt-1,M] [rt,A , rt,M] [rt+1,A , rt+1,M] • The regimes follow the discrete probability transition matrix P, where • Pi, j = Prob{Rt = j | Rt-1 = i}. • Consider K regimes in the agribusiness sector. Then, we write the joint distribution of the monthly returns, rt,Aand rt,M as:**An Application HMM Calibration Results**Transition Probability Matrix • HMM calibration results using S&P 500 and cap-weighted Agribusiness Index monthly total returns. • Sample data from January 1, 1990 to March 31, 2010. Expansionary Period Transition Period Recessionary Period**An Application HMM Calibration Results**• Red denotes market recession, Blue denotes market transition, and Green denotes market expansion in the agribusiness sector. • The regimes’ persistence is gives us comfort that the chosen variables may indeed hold some information on the business cycles of the agribusiness sector.**The Model Notation**t=0 t=1 t=2 s = 1 s = 2 s = 3 s = 4 s = 5 s = 6**The Model Assumptions**• Production, Qt • Quantity of production during period t is decided at time t-1 and sold at time t. • Production quantity is constrained by the capacity function, which depends on the capital level. • Financing/Borrowing, Dt • Single-period debt. • Non-negative debt. • Investments, It • Investing increases the production constraint during period t by increasing the amount of capital: • But the cost of investment is stochastic: • Investments are cheaper during recessions and more expensive during expansions. • Dividends, Et • Non-negative dividends, i.e. no equity issuance.**The Model Cash Flow at t**The cash flow of the firm at time tafter all decisions can be written as follows: Accrued interest on cash savings + Revenue from production during period t - Payment for debt outstanding + New borrowing - Cost of production during period t+1 - Investments for production during period t+1 - Dividend Payout = Cash at time t.**The Model**Cash flow constraint Production constraint**Modeling the End-Effect**• Stochastic programming requires a finite planning horizon T. • There’s a need to address the effect of production, dividends, etc. after T on the objective value. We call this the “end-effect.” Solution: Aggregate the constraints for t > T. Production Constraint: Cash Constraint: Investment Constraint:**An Application**Base Case Parameters Base case parameter values**An Application**Base Case Parameters Problem Size • 2,560 scenarios • 1,518,957 constraints • 143,360 variables, and • 3,186,392 non-zeros • Solving time: 358.9 seconds (using 8GB memory 266GHz Intel Core i7 MacBook Pro)**Numerical Results Solution Ratios**t=0 t=1 t=2 s = 1 ρ1,1=ρ1,2 Take the average, conditioned on regime 1: γ1(1)= (ρ1(1)+ρ1(2)+ρ1(3) +ρ1(4)) / 4 and γ1(2)= γ1(3)= γ1(4)= γ1(1) R1,1 = R1,2 = 1 s = 2 s = 3 R0 = 1 ρ1,3 =ρ1,4 R1,3 = R1,4 = 1 s = 4 Take the average, conditioned on regime 2: γ1(5)= (ρ1(5)+ρ1(6) ) / 2 and γ1(6)= γ1(5) s = 5 ρ1,5 =ρ1,6 R1,5 = R1,6 = 2 s = 6**A Fixed Policy Approximation**Motivation • Drawback of the Original Problem • Curse of Dimensionality • Difficult to interpret the solution provided by a stochastic program • Difficult to test the robustness of a stochastic program solution • An Alternative using Fixed Policy (“FP”) Rules • Use policy rules on a set of Monte Carlo simulated independent paths. • Fixed policy rule using Monte Carlo simulation by setting a target: • cash ratio, and • investment ratio • at each stage for each regime. • Use the average cash and investment ratios under each regime given by the SP. • Sub-optimal solution**A Fixed Policy Approximation**Model Overview At each time t, the fixed policy requires the firm to maximize dividends while satisfying the target cash-to-asset and investment-to-asset ratios. Target cash ratio Target Investment ratio**A Fixed Policy Approximation**Motivation • Fixed Policy vs Original Problem • The policy rule provides us with a sub-optimal solution. • We measure the Objective Gap between the two approaches: • (Objective(xorig) – Objective(xFP)) / Objective(xorig) • Objective(xorig) = 520.46 • Objective(xFP) = 473.72 • Objective Gap = 8.9%**Introduction**Companies may not be acting optimally based on our model. Could cash savings be motivated by fear? Could cash savings be a leading indicator of market returns? Note: Annual data taken from Compustat Index Fundamentals for S&P 500 from Jan 1993 to Dec 2009. Firm-level quarterly data of S&P 500 constituents taken from Compustat Fundamentals from Jan 2010 to Dec 2010.**Conclusion & Future Work**• Conclusion • Our model shows that there is a benefit to corporate cash holding. • In particular, firms save cash in order to facilitate investments during recession, when external financing is costly. • The fixed policy rule might be a good approximation of the optimal solution. • Future Work • Extensions: incorporating equity issuance, hedging policy, etc. • Investigate a firm’s true objective function by calibrating the model to real (cash) data? • The stochastic programming approach presents to us some difficulties in computing error bounds. Policy rules will address this problem. How can we combine the two approaches?**Bibliography**Bates, T.W., Kahle, K.M., & Stulz, R.M. (2009). Why Do US Firms Hold So Much More Cash than They Used To? The Journal of Finance, (64)5, 1985-2021. Fazzari, S. M., Hubbard, R. G., Petersen, B. C., Blinder, A. S. & Poterba, J. M. (1988). Financing Constraints and Corporate Investment. Brookings Papers on Economic Activity 1988(1), 141-206. Froot, K.A., Schartstein, D.S., & Stein, J.C. (1993). Risk Management: Coordinating Corporate Investment and Financing Policies. The Journal of Finance, 48(5), 1629-1658. Harford, J. (1999). Corporate Cash Reserves and Acquisitions. The Journal of Finance, 54(6), 1969-1997. Jensen, M. & Meckling, W. (1976). Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure. The Journal of Financial Economics, 3, 305-360. Lie, E. (2002). Excess Funds and Agency Problems: An Empirical Study of Incremental Cash Disbursements. Review of Financial Studies, 13, 219-247. Mikkelson, W. H. & Partch, M. M. (2003). Do Persistent Large Cash Reserves Hinder Performance? The Journal of Financial and Quantitative Analysis, 38(2), 275-294. Opler, T., Pinkowitz, L., Stulz, R. & Williamson, R. (1999). The Determinants and Implications of Corporate Cash Holdings, The Journal of Financial Economics, 52, 3-46. Palazzo, D. (2009, January). Firms’ Cash Holding and the Cross-Section of Equity Returns. Retrieved November 1, 2010, from http://ssrn.com/abstract=13739618. Simutin, M. (2010). Excess Cash and Stock Returns. Financial Management, 39(3) 1197-1222.**Appendix Cost Per Unit**• Assume that the agriculture commodity index is a good proxy for the unit cost of raw materials used in production. • Volatility clustering behavior motivates the use of the GARCH(1,1) model. • Calibration results using sample data from 1/1/1990 to 2/28/2010:**Appendix**Profit Margin • Unit sales price follows the formula , where is the gross profit margin. • The quarterly data of Gross profit margin = (Revenue – COGS) / Revenue is available from each company’s income statement compiled in the Compustat database. • Due to the small number of data points, we choose to simulate the profit margin from the sample data.