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  1. 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.

  2. 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

  3. 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.

  4. 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. $).

  5. 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)]

  6. 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)]

  7. 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.

  8. 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.

  9. 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.

  10. 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).

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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:

  16. 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

  17. 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.

  18. An Application Descriptive Statistics

  19. An Application Descriptive Statistics

  20. The Model Notation t=0 t=1 t=2 s = 1 s = 2 s = 3 s = 4 s = 5 s = 6

  21. The Model Notation

  22. 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.

  23. 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.

  24. The Model Cash flow constraint Production constraint

  25. 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:

  26. An Application Base Case Parameters Base case parameter values

  27. 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)

  28. Numerical Results Solution Ratios

  29. 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

  30. Numerical Results Solution Ratios

  31. Numerical Results Solution Ratios

  32. 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

  33. 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

  34. 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%

  35. 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.

  36. 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?

  37. 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 Simutin, M. (2010). Excess Cash and Stock Returns. Financial Management, 39(3) 1197-1222.


  39. The Model Notation

  40. 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:

  41. 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.

  42. Aappendix Scenario Trees

  43. Numerical Results Solution Ratios