Betting Management - PowerPoint by zqc88403

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									Betting on the Future with a
Cloudy Crystal Ball?
     Spending, Taxing, Saving, and
              Borrowing
            A balanced budget
           Portfolio management
                  Hedging
               Self-insurance
           Optimal spending rules
                                      Fred Thompson & Bruce Gates
                            Atkinson Graduate School of Management
                     Next page                 Willamette University
Lesson
• Trying to balance budgets (match spending
  to taxing) one year at a time leads to manic-
  depressive spending and taxing patterns
• This is costly, both directly in terms of the
  expedients taken to balance budgets and
  indirectly from a macroeconomic
  perspective
• The problem faced by budget makers
  derives from volatility in revenue growth.



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Lesson
• Economists cannot accurately
  predict revenue growth from one
  year to the next or the timing of the
  business cycle, but we can make
  actuarial predictions
• Mean/variance analysis



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 Example: Classical Multiplicative
 Decomposition
Conceptual Decomposition:       yt  Trend t  Cyclet  Seasonalt  Irregulart

        Trend:       Long-term growth/decline
        Cycle:       Long-term slow, irregular oscillation
        Seasonal:    Regular, periodic variation w/in calendar year
        Irregular:   Short-term, erratic variation
                                yt  Trend t  Seasonalt
                                ˆ
     Conceptual Forecast:

                                                   s1 
                                                  s 
                                yt  b0  b1t   2 
                                ˆ
                                                  
      Forecasting Model:                           
                                                   sL 




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Example: Classical Multiplicative
Decomposition
Conceptual Decomposition:     yt  Trend t  Cyclet  Seasonalt  Irregulart
                   1600

                   1500

                   1400
                   1300

                   1200
            Data



                   1100

                   1000

                   900

                   800

                   700

                   600
                          1996:01
                          1996:02
                          1996:03
                          1996:04
                          1997:01
                          1997:02
                          1997:03
                          1997:04
                          1998:01
                          1998:02
                          1998:03
                          1998:04
                          1999:01
                          1999:02
                          1999:03
                          1999:04
                          2000:01
                          2000:02
                          2000:03
                          2000:04
                          2001:01
                          2001:02
                          2001:03
                          2001:04
                                           Period



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Example: Classical Multiplicative
Decomposition    Visual Representation

                  1600                              1.25

                  1400
                                                    1.15




                                        Seasonal
                  1200




       Trend
                                                    1.05
                  1000

                                                    0.95
                   800

                   600                              0.85


                  1.25                              1.25


                  1.15                              1.15




                                        Irregular
       Cyclical




                  1.05                              1.05


                  0.95                              0.95


                  0.85                              0.85




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Example: Classical Multiplicative
Decomposition, Model
Interpretation
                        s1                                   0.9794
                       s                                     0.9236
     yt  b0  b1t   2 ,
     ˆ                            yt  731.9291  18.5017t  
                                  ˆ                                    
                                                            0.8913
                                                                    
                        sL                                   1.2057 

  Model Interpretation

             Initial, time-zero (1995:Q4) level is $731.92 million
             Increasing at $18.5 million per quarter
             Seasonal pattern
                         Peak in Q4 21% over trend
                         Trough in Q3 11% below trend



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Example: Classical Multiplicative
Decomposition, Forecasts
                                         s1                                       0.9794
                                        s                                         0.9236
                      yt  b0  b1t   2 ,
                      ˆ                                yt  731.9291  18.5017t  
                                                       ˆ                                    
                                                                                 0.8913
                                                                                         
                                         sL                                       1.2057 
Forecasts
            1996 : Q1 t  1    y1  731.9291  18.5017( 1) 0.9794   750.4309 0.9794  735.00
                                 ˆ
                                      
            2002 : Q1 t  25 y25  731.9291  18.5017(25) 0.9794  1194.4727  0.9794  1169.90
                               ˆ


            2002 : Q 2 t  26 y26  731.9291  18.5017(26) 0.9236  1212.9744 0.9236  1120.32
                                ˆ


            2002 : Q3 t  27  y27  731.9291  18.5017(27) 0.8913  1231.4762 0.8913  1097.60
                                ˆ


            2002 : Q 4 t  28 y28  731.9291  18.5017(28) 1.2057  1249.9779 1.2057  1507.07
                                ˆ




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Forecast Model
Assessment
Residual analysis:
 Residual (Error) = Actual – Forecast

Assessment possible for any type of
 forecasting process.



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Second section: portfolio
theory




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Lesson
• Most states cannot significantly
  reduce volatility in revenue growth
  by substituting one tax type for
  another (e.g. a broad-based foods
  and services taxes for in income
  tax, or vice versa).



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Lesson
• Unsystematic volatility in revenue
  growth can be significantly reduced via a
  well-designed portfolio of tax types.
  • Diversification of tax types can reduce
    revenue volatility: most states rely on a
    portfolio of tax types.
  • How does diversification of tax portfolios
    work? The answer is that portfolio
    volatility is a function of the covariance
    or correlation, , of its component
    revenue sources
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  Diversification of tax types
                Table 1: An Illustrative, Two-Tax Portfolio
                          Prob.    Income        Alcohol      Portfolio
     Recession             0.10     -22.0%         8,0%        -7.0%
     Below Average         0.20       -2.0          4.0         1.0
     Average               0.40       10.0          0.0         5.0
     Above Average         0.20       18.0          -4          7.0
     Boom                  0.10       30.0         -8.0         11.0
      Expected Growth                 8.0            0          4.0


•Expected growth is the weighted average of the growth rates or four
percent.
•The volatility of the portfolio, = 3.1 percent -- much less than the
volatility of either the income tax (13.4 percent) or the income and alcohol
taxes combined (8.9 percent). It is less even, than the volatility of the
alcohol tax alone (4.4 percent)




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Implications of
portfolio theory
• In general, tax sources have 0.65, so adding taxes to the
  portfolio tends to reduce but not eliminate volatility.
• It is possible to construct an efficient growth frontier,
  showing an efficient linear combination of growth rates and
  volatilities ranging from zero volatility, to a state’s optimal
  volatility at its current growth rate and beyond
• All one needs is information on the covariance of the
  growth rates of each of the different tax types and designs
  that obtain in different states.
• Only if we look at efficient tax portfolios is there a
  necessary tradeoff between stability and growth.




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                 Efficient Tax Portfolios
Expected
Portfolio
 Growth


                      PE          PEF            Theoretically feasible



                                                    PY
                                          OR                                    CY
                                        CS


                   SE                            PE = Efficient Portfolio
                                                 PEF = Efficient and Fair Portfolio
            Efficiency frontier                  OR = Current tax portfolio
                                                 CY = Corporate income tax
                                                 PY = Personal income tax
                                                 CS = Broad-based consumption tax
                                                 SE = Selected excises




                                                                   Volatility, 

            Figure 6: Feasible and Efficient Tax Portfolios

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Lesson
 • Average volatility will usually be
   reduced by adding tax sources,
   except where the two taxes are
   perfectly correlated, r = +1.0
 • A two tax portfolio could in theory
   be combined to eliminate revenue
   volatility completely, but only if r =
   -1.0 and the two taxes were
   weighted equally

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Lesson
• Once an efficient tax-portfolio
  frontier has been identified,
  changes in the portfolio of tax
  types to increase tax-equity will
  also increase volatility in revenue
  growth



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Lesson
• Even the best-designed tax portfolio
  would not eliminate all volatility. In the
  absence of a policy of borrowing and
  lending at the risk free rate, the best tax-
  portfolio designers could do is eliminate
  the unsystematic or random portion of
  the variation in revenue growth.
• The systematic portion would remain. By
  systematic we mean, the portion
  correlated with some underlying variable

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Lesson
• GNP growth is the main underlying
  variable -- which has two components
   • Trend (mean)
   • Cyclical
• Predicting the timing and amplitude of business
  cycles is no easier than predicting the growth
  of the economy from one year to the next




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Third Section: Hedging and
self insurance
One way to eliminate systematic volatility in revenue
growth is with a revenue flow of equal and opposite
volatility. This is called hedging.
If we could find two tax types which produced revenue
flows of the same size that were perfectly, but inversely
correlated with each other, we could eliminate all volatility
in revenue growth. Unfortunately, there are no such tax
types.
Is it possible to design a hedge against the systematic
component of revenue volatility?
                             Next page
Lesson
• It is theoretically possible to do so
  using forwards, futures, or options




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Lesson
• It is theoretically possible to do so
  using forwards, futures, or options
• It is not practically feasible to do
  so at this time




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Lesson
• It may never be politically
  feasible to do so




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Hedging with options
& futures contracts
• Futures
• Options                        See C. Hinkelmann & Steve Swidler,
                                 “Macroeconomic Hedging with Existing
                                 Futures Contracts,” Risk Letters,
                                 forthcoming;
                                 “State Government Hedging with
                                 Financial Derivatives,” State and Local
                                 Government Review, volume 37:2,
                                 2005; “Using Futures Contracts to
                                 Hedge Macroeconomic Risks in the
                                 Public Sector,” Trading and
                                 Regulation, volume 10, number 1,
                                 2004.




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Self insurance?
• Rainy day fund
• Cooperative cash pool




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Lesson
Self insurance and risk pooling
• Insurance is like a put option.
• A rainy-day fund is simply a form of
  self insurance.
• A rainy day fund large enough to
  prevent all revenue shortfalls would be
  very costly
• Risk pooling would dramatically
  reduce those costs

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Fourth Section: Optimal
Spending




               Next page
Lesson
• States can use savings and/or borrowing to smooth out
  consumption over the business cycle
• Consumption smoothing implies present value balance:
   PV future revenue + net assets ≥ PV future outlays
• Goal should be to balance budgets in a present-value
  sense, using savings and debt to smooth spending
• Hence, the problem faced by budgeters is to identify the
  maximum rate of growth in the spending level from one
  year to the next that is consistent with present value
  balance, given the state’s existing revenue structure and
  volatility.
• where PV future revenues + net assets < PV future
  outlays, permanent reductions in spending or
  permanent increases in taxes are necessary
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Lesson
• This can be done by treating revenue
  growth as a random walk. In which case,
  the problem faced by budget makers can
  be solved mathematically by optimal
  control theory.




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The basic question
How much should we spend next
 year?
State and local governments have few
  degrees of freedom but can focus on
  issues of solvency and liquidity




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Managing spending
• Schunk and Woodward’s (S&W)
  spending rule:
Increase spending no faster than the rate
     of inflation plus the long-term real
  growth rate of the underlying economy
    (put aside the remainder for a rainy
                     day)
    Donald Schunk and Douglas P. Woodward. Spending Stabilization Rules: A Solution to
           Recurring State Budget Crises? 2005. Public Budgeting & Finance 5(4): 105-124.




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                       Managing spending 2
                        Figure 4: Oregon Spending, Actual and
                                   Stabilization Rule

                      8,000
General Fund Budget




                      7,000
                      6,000
                      5,000
                      4,000                                         A
                      3,000
                      2,000
                      1,000
                         0
                              1            2                  3           4           5
                                                       Biennium

                                  Stabilization Rule Outlays            Actual GF Outlays


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Revenue growth is a
random walk
Revenue growth can be modeled as a
Wiener process:
• a continuous-time, continuous-state stochastic
  process in which the distribution of future values
  conditional on current and past values is identical
  to the distribution of future values conditional on
  the current value alone, and
• the variance of the change in the process grows
  linearly with the time horizon.


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         Monte Carlo simulation of Oregon’s future
          spending and revenues, given the adoption
                  of S&W’s spending rule
                                                                        y = 2.6215x
                                                                        R2 = 0.5876
        $1,000



         $800



         $600
Value




         $400



         $200



           $0
                 0   10   20   30    40         50       60   70   80   90            100


        -$200
                                              Time



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An optimal spending rule
Given that we can model revenue growth as
a Wiener process, it is possible to calculate
a spending rule directly using optimal
control theory.
By comparing proposed spending levels
(including tax expenditures and debt
service) against the optimum spending
level calculated using this rule, one can say
whether or not the specified spending level
is sustainable and implicitly assess a state’s
saving and borrowing policies as well.
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Indexes of Revenue, Asset Portfolio Value, and Expenditure
 The blue line shows an index of revenue, the beige line shows an index of
 portfolio value, and the red line shows an index of optimal expenditure. All
                   indexes are normalized to 100 in year 1.




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Practical Implications
• Oregon cannot significantly reduce volatility in
  revenue growth by tinkering with its tax structure --
  at least not without also reducing progressivity
• Hedging -- probably not practical
• Oregon could rely on a rainy day fund of sufficient size
  to mitigate the adverse consequences of cyclical
  revenue shortfalls (if it had one) or meliorate them via
  a program of countercyclical borrowing
• Other things equal, Oregon’s revenue growth trend is
  faster than outlay growth under the S&W rule
• Oregon doesn’t need to increase taxes to offset a
  structural budget deficit -- it could adopt an optimal
  spending rule that would allow it to smooth
  consumption


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