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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.

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Corporate cash holding policy a multistage approach with an application in the agribusiness sector l.jpg

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.


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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


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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.


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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. $).


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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)]


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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)]


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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.


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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.


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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.


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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).


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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.


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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.


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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.


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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


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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:


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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


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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.




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The Model Notation

t=0

t=1

t=2

s = 1

s = 2

s = 3

s = 4

s = 5

s = 6



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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.


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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.


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The Model

Cash flow constraint

Production constraint


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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:


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An Application Base Case Parameters

Base case parameter values


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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)


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Numerical Results Solution Ratios Base Case Parameters


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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


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Numerical Results Solution Ratios Base Case Parameters


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Numerical Results Solution Ratios Base Case Parameters


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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


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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


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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%


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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. Firm-level quarterly data of S&P 500 constituents taken from Compustat Fundamentals from Jan 2010 to Dec 2010.


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Conclusion & Future Work Motivation

  • 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?


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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, 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.


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THANK YOU Motivation


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The Model Notation Motivation


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Appendix Cost Per Unit Motivation

  • 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:


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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.


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Aappendix Profit Margin Scenario Trees



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