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
I.
Introduction & Motivation
II.
The Model
1. Notation
2. Model Assumptions
3. Mathematical Formulation
III.
An Application in the Agribusiness Sector
1. Regime Analysis in the Agribusiness Sector
2. Numerical Results
IV.
A Fixed Policy Approximation
V.
Conclusion and Future Work
2
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.
3
Introduction
Top Global Companies (excl. Financials) by Cash
Holding1
Company Name
Total
cash2
Industry
classification
Headquarters
General Electric
Co.
78,392.0
Industrial
conglomerates
U.S.
Toyota Motor Corp.
48,304.8
Automobile
manufacturers
Japan
China Mobile Ltd.
46,786.0
Wireless telecom
Hong
Kong
Microsoft Corp.
43,253.0
Systems
software
U.S.
Cisco Systems Inc.
38,925.0
Communications
equipment
U.S.
Petroleo Brasileiro
S.A. - Petrobras
34,658.9
Intgrtd oil & gas
Brazil
Volkswagen AG
34,632.2
Automobile
manufacturers
Germany
General Motors Co.
33,476.0
Automobile
manufacturers
U.S.
Google Inc.
33,380.0
Internet software
& svc
U.S.
Total S.A.
27,081.0
Intgrtd oil & gas
France
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. $).
4
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)]
5
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)]
6
Introduction
A Brief Walk through the Literature
1. Opler et al. (1999)
•
Investigates the risk determinants of corporate cash holdings
•
Finds a positive link between growth opportunities and excess cash.
2. Harford (1999)
•
High-cash firms are more likely to make value-decreasing investments.
3. Mikkelson & Partch (2003)
•
Investigates that relationship between cash holding and operating performance.
•
Concludes that cash holding does not hinder operating performance.
4. 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.
5. 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.
7
Introduction
Source: Simutin (2010). Sample average of regression factors in each cash decile.
A few observations:
1. High betas for firms with high excess cash
2. High market-to-book value of assets for firms with high excess cash.
3. Smaller sized firms tend to belong in the lowest or highest decile based on excess cash.
4. High-cash firms tend to have lower debt.
8
Introduction
Period
Low
High
HighLow
19602006
0.852%
1.253%
0.401%
19601982
0.913%
1.242%
0.220%
19822006
0.794%
1.262%
0.469%
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.
9
Introduction
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).
•
Two sources of funding for investment and production:
1. cash (internal financing) and
2. a single period debt (external financing)
•
The model endogenously determines the best
1. production,
2. investment,
3. financing,
4. dividend payout, and
5. cash holding policies
to maximize shareholders’ value over the planning horizon.
10
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:
1.
Agricultural Chemicals (15101030),
2.
Agricultural Products (30202010), and
3.
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 marketcap-weighted average of the stock returns of the companies that are identified to be in
the agribusiness sector during month t.
11
An Application
Descriptive Statistics
Cash-to-Asset Ratio in the Agribusiness Sector
Sample data 1/1/1990 to 3/31/2010
9.0%
8.0%
7.0%
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
01/01/10
05/01/09
09/01/08
01/01/08
05/01/07
09/01/06
01/01/06
05/01/05
09/01/04
01/01/04
05/01/03
09/01/02
01/01/02
05/01/01
09/01/00
01/01/00
05/01/99
09/01/98
01/01/98
05/01/97
09/01/96
01/01/96
05/01/95
09/01/94
01/01/94
05/01/93
09/01/92
01/01/92
05/01/91
09/01/90
01/01/90
0.0%
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.
12
3/1/2002
10/1/2009
3/1/2009
8/1/2008
1/1/2008
6/1/2007
11/1/2006
4/1/2006
9/1/2005
2/1/2005
7/1/2004
12/1/2003
5/1/2003
10/1/2002
Agribusiness Index
8/1/2001
1/1/2001
6/1/2000
11/1/1999
4/1/1999
9/1/1998
2/1/1998
7/1/1997
12/1/1996
5/1/1996
10/1/1995
3/1/1995
8/1/1994
1/1/1994
6/1/1993
11/1/1992
4/1/1992
9/1/1991
2/1/1991
7/1/1990
12/1/1989
Total Returnn
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.
Total Return of the S&P 500 and the Agribusiness Index
S&P 500
7.29
2.70
1.00
Date
0.37
13
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)
pe,e
pt,r
pe,t
Expansion
pr,r
pt,t
Recession
Transition
pr,t
pr,e
14
An Application
•
•
Hidden Markov Model
Let the S&P 500 and Agribusiness sector returns, rt,A and 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,A and rt,M as:
15
An Application
• HMM calibration results using S&P 500
and cap-weighted Agribusiness Index
monthly total returns.
HMM Calibration Results
Transition Probability Matrix
• Sample data from January 1, 1990 to
March 31, 2010.
Expansionary Period
Transition Period
Recessionary Period
16
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.
17
An Application
Descriptive Statistics
18
An Application
Descriptive Statistics
19
The Model
Notation
t=0
t=1
t=2
s=1
s=2
s=3
s=4
s=5
s=6
20
The Model
Notation
21
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.
22
The Model
Cash Flow at t
The cash flow of the firm at time t after 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.
23
The Model
Cash flow
constraint
Production
constraint
24
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:
25
An Application
Base Case Parameters
Base case parameter values
26
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)
27
Numerical Results
Solution Ratios
Cash Ratio
100
%
Mean
Median
CI 95%
50
0
0
1
2
3
4
5
4
5
4
5
t
Debt to Asset Ratio
%
50
0
0
1
2
3
t
Investment to Asset Ratio
%
100
50
0
0
1
2
3
t
28
Numerical Results
t=0
Solution Ratios
t=1
t=2
s=1
ρ1,1= ρ1,2
R1,1 = R1,2 = 1
R0 = 1
ρ1,3 = ρ1,4
R1,3 = R1,4 = 1
ρ1,5 = ρ1,6
R1,5 = R1,6 =
2
s=2
s=3
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)
s=4
s=5
s=6
Take the average,
conditioned on regime 2:
γ1(5)= (ρ1(5)+ ρ1(6) ) / 2
and
γ1(6)= γ1(5)
29
Numerical Results
Solution Ratios
Average Cash-to-Assets Ratio
Average Investment-to-Assets Ratio
35
25
Regime 1
Regime 2
Regime 3
Regime 1
Regime 2
Regime 3
30
20
25
15
%
%
20
15
10
10
5
5
0
1
2
3
4
0
5
t
0
1
2
3
4
5
t
Average Debt-to-Assets Ratio
15
Regime 1
Regime 2
Regime 3
10
%
0
5
0
0
1
2
3
t
4
5
30
Numerical Results
Solution Ratios
Cash-to-Asset Ratio
Time
Regime 1
(Expansion)
Regime 2
(Transition)
Regime 3
(Recession)
0
NaN
0.1098
NaN
1
NaN
0.2335
0.0077
2
0.0000
0.3206
0.0346
3
0.0029
0.3398
0.0579
4
0.0129
0.3335
0.0586
5
0.0318
0.2717
0.0606
6
0.0453
0.1254
0.0006
Investment-to-Asset Ratio
Time
Regime 1
(Expansion)
Regime 2
(Transition)
Regime 3
(Recession)
0
NaN
0.0000
NaN
1
NaN
0.0000
0.2395
2
0.1386
0.0000
0.1956
3
0.0725
0.0000
0.1731
4
0.0152
0.0000
0.1772
5
0.0098
0.0000
0.1683
6
0.0031
0.0000
0.6880
31
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:
1. cash ratio, and
2. 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
32
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
33
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%
34
Introduction
S&P 500 Companies: Cash-to-Asset Ratio and Return
Sample data 12/1/1993 to 12/31/2010
14.00%
4.50
Companies may
not be acting
optimally based on
our model.
13.00%
13.04% 4.00
Could cash savings
be motivated by
fear?
11.00%
12.28% 3.50
12.00%
11.55%
10.75%
10.37%
10.00%
9.00%
3.00
2.50
10.35%
9.39%
9.39%
2.00
1.50
8.95%
9.01%
1.00
8.81%
8.00%
7.81%
0.50
7.00%
0.00
12/01/93
08/01/94
04/01/95
12/01/95
08/01/96
04/01/97
12/01/97
08/01/98
04/01/99
12/01/99
08/01/00
04/01/01
12/01/01
08/01/02
04/01/03
12/01/03
08/01/04
04/01/05
12/01/05
08/01/06
04/01/07
12/01/07
08/01/08
04/01/09
12/01/09
Could cash savings
be a leading
indicator of market
returns?
11.82%
Cash-to-Asset Ratio
Return
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.
35
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?
36
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.
37
THANK YOU
The Model
Notation
39
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:
40
Appendix
Profit Margin
•
Unit sales price follows the formula
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.
, where
is the
Histogram of Monthly Agribusiness Profit Margin during Expansion
30
20
10
0
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
0.36
0.38
0.4
0.36
0.38
0.4
Histogram of Monthly Agribusiness Profit Margin during Transition
3
2
1
0
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Histogram of Monthly Agribusiness Profit Margin during Recession
8
6
4
2
0
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
41
Aappendix
Scenario Trees
Dividends
40
40
20
20
0
$
$
Cash
0
1
2
3
4
5
0
6
0
1
200
100
100
50
0
0
1
2
3
4
5
0
6
t
Investment
4
5
6
0
1
2
3
4
5
6
t
Production profit
50
$
Units
50
0
3
t
Capital
$
$
t
Debt
2
0
1
2
3
t
4
5
6
0
-50
0
1
2
3
4
5
6
t
42
Numerical Results
Solution Ratios
Cash Ratio
%
100
50
0
0
1
2
3
4
5
6
5
6
5
6
t
Debt to Asset Ratio
%
100
50
0
0
1
2
3
4
t
Investment to Asset Ratio
%
100
50
0
0
1
2
3
4
t
43