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.
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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.
We observe a significant increase in the cashtoasset 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. Firmlevel quarterly data of S&P 500 constituents taken from Compustat Fundamentals from Jan 2010 to Dec 2010.
Cash holding can be bad for a firm because …
Cash holding can be good for a firm because …
A Brief Walk through the Literature
Source: Simutin (2010). Sample average of regression factors in each cash decile.
A few observations:
High betas for firms with high excess cash
High markettobook 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.
Highcash firms tend to have lower debt.
Source: Simutin (2010). Valueweighted monthly returns are significant at the 1%level
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 (regimeswitching framework).
An Application The Agribusiness Sector
An Application Descriptive Statistics
We observe a similar increase in the cashtoasset 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
An Application Hidden Markov Model
pt,r
pe,t
pe,e
pr,r
pt,t
Recession
Transition
Expansion
pr,t
pr,e
An Application Hidden Markov Model
Rt1
Rt
Rt+1
[rt1,A , rt1,M]
[rt,A , rt,M]
[rt+1,A , rt+1,M]
An Application HMM Calibration Results
Transition Probability Matrix
Expansionary Period
Transition Period
Recessionary Period
An Application HMM Calibration Results
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.
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
Numerical Results Solution Ratios Base Case Parameters
Numerical Results Solution Ratios Base Case Parameters
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
Numerical Results Solution Ratios Base Case Parameters
Numerical Results Solution Ratios Base Case Parameters
A Fixed Policy Approximation Motivation
A Fixed Policy Approximation Model Overview
At each time t, the fixed policy requires the firm to maximize dividends while satisfying the target cashtoasset and investmenttoasset ratios.
Target
cash ratio
Target
Investment ratio
A Fixed Policy Approximation Motivation
Introduction Motivation
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. Firmlevel quarterly data of S&P 500 constituents taken from Compustat Fundamentals from Jan 2010 to Dec 2010.
Conclusion & Future Work Motivation
Bibliography Motivation
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, 19852021.
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), 141206.
Froot, K.A., Schartstein, D.S., & Stein, J.C. (1993). Risk Management: Coordinating Corporate Investment and Financing Policies. The Journal of Finance, 48(5), 16291658.
Harford, J. (1999). Corporate Cash Reserves and Acquisitions. The Journal of Finance, 54(6), 19691997.
Jensen, M. & Meckling, W. (1976). Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure. The Journal of Financial Economics, 3, 305360.
Lie, E. (2002). Excess Funds and Agency Problems: An Empirical Study of Incremental Cash Disbursements. Review of Financial Studies, 13, 219247.
Mikkelson, W. H. & Partch, M. M. (2003). Do Persistent Large Cash Reserves Hinder Performance? The Journal of Financial and Quantitative Analysis, 38(2), 275294.
Opler, T., Pinkowitz, L., Stulz, R. & Williamson, R. (1999). The Determinants and Implications of Corporate Cash Holdings, The Journal of Financial Economics, 52, 346.
Palazzo, D. (2009, January). Firms’ Cash Holding and the CrossSection 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) 11971222.
The Model Notation Motivation
Appendix Cost Per Unit Motivation
Appendix Profit Margin
Aappendix Profit Margin Scenario Trees
Numerical Results Solution Ratios Profit Margin