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INVESTMENT SIMULATOR

AUSTMOD - Stochastic and Historical Investment Simulation Model


SuperEasy’s Actuarial Partners, Lynken Counsellors provide asset allocation and investment simulation services, through their qualified and experienced actuaries, Colin R. Grenfell and Ken G. Dance, using the Austmod simulation model.

The model is an Excel workbook that displays up to 50 years of historical (past) and 40 years of simulated (future) investment performance for 15 “sectors”:

B

 Bill rate (90-day bank) in middle of year

C

 Cash sector

D

 10-year bond rate in middle of year

F

 Fixed interest sector

G

 Government semis 0-3 years (SBC/UBS Warburg index SSG03)

I

 International shares sector  (MSCIAI prior 30/6/88)

J

 International bonds sector

L

 Loans sector

M

 Mortgage trust (valued on a hold to maturity basis)

N

 Inflation linked bonds (all maturities) UBS index

P

 Direct property (one-third NM/AXA, two-thirds AMP)

Q

 Property trust accumulation index  (from 31/1/01 S&P/ASX 300,    from 30/6/02 GICS)

S

 Shares sector  (All Ordinaries accumulation index prior 31/3/65)

W

 AWOTE by quarter (= av. 1.5 mths. lag), not seasonally adjusted,

full-time adults, males original (pre 9/81), AWE males (pre 1/75)

X

 CPI index by quarter



The model results are displayed in both table and chart forms. The simulated model scenarios depend on nominated assumptions for means, standard deviations, cross-correlations, auto-correlations, skewness, kurtosis, taxation and investment fees. The historical results are analysed and documented in Colin Grenfell’s September 2009 Institute of Actuaries of Australia (IAAust) paper “Australian Investment Performance 1959 to 2009 (and Investment Assumptions for Stochastic Models)”.

Appendix A of Colin’s Oct/Nov 1997 IAAust paper “Uses of S.I.S. (Superannuation Investment Simulations)” has a specification of the then version O of Austmod.

The latest model, version V, includes many new features, for example:
  • Three auto-correlation options
  • Three skewness options
  • Two kurtosis options
  • Inflation linked bonds
  • An exempt tax option (with or without imputation credits)
  • Historical results at quarterly intervals back to 30/6/1959
  • Results with or without investment fees
  • Three cross-correlation options (one with lagged AWOTE and CPI)
  • Means plus or minus an additional rate if required
  • Compound and arithmetic means
  • Sixteen superannuation and investment simulation output alternatives
  • Stochastic, deterministic and “historical random start” simulation options
  • Five net cash flow input alternatives (or cash outflow for pensions)
  • Choice of 8, 40, 200 or 1,000 simulations
  • Updated assumptions and proportions.
Mathematical Structure

For the technically-minded -

The model has an annual time scale. The mathematical structure of the underlying AUSTMODV algorithms is summarized below:
  1. Normal.  First, the model generates independent Normal random variables for each sector.

  2. Cross-correlation.  These random variables are then converted to dependent Normal random variables using the Cholesky decomposition formula (refer Wilkie A D, 1988, JIA 115. Part 1, page 51).

  3. Skewness and kurtosis.  These random variables may then be converted to dependent non-Normal random variables using formula [2] or [4] as described in Appendix A of “Australian Investment Performance 1959 to 2009 (and Investment Assumptions for Stochastic Models)”.

  4. Shape.  For sectors Q, F, G, J, L, N and C the shape of the distribution may then be improved by reducing both the skewness and kurtosis - refer paragraph A13 of “Australian Investment Performance 1959 to 2009 (and Investment Assumptions for Stochastic Models)”.

  5. Taxation.   The input for each sector includes two tax rates and information for imputation credits. The income tax rate is applied to the long term expected income yield and imputation credits. The deferred tax rate is applied to the total before tax yearly return less the long term expected income yield. This is equivalent to assuming, for tax purposes, that all fluctuations in investment returns are due to fluctuations in the capital appreciation component. The after tax standard deviation for each sector equals the before tax standard deviation * (1 - deferred tax rate).

  6. Additional return.  The before tax standard investment return for each investment sector may be increased (or decreased if negative) by adding an additional return. For tax purposes the additional return is treated as a capital appreciation component and taxed at the deferred tax rate.

  7. Investment fees.  The before tax investment fee for each sector is deducted from the before tax long term expected income yield; the result is then taxed at the income tax rate.

  8. Forces.  After allowing for taxation and any additional return and investment fees, the standardized random variables (denoted srv) from 4. above, are then converted to annual forces using the formula force = mu + sigma*srv.

  9. Mixture.  The annual force for the mixture or portfolio is then determined by weighting the sector forces by the proportions for each sector. The proportions may be specified individually, or default proportions for “Growth”, “Balanced” or “Capital Stable” may be used.

  10. Rates.  The annual forces are then converted to rates using the formula EXP(force) - 1.

  11. Repeats.  Steps 1 to 10 are repeated 108 times to give a 108-year single scenario with no auto-correlation.

  12. Auto-correlation.  A 40-year scenario with auto-correlation may then be generated using the methodology described in Appendix B, paragraphs B7 and B8, of “Australian Investment Performance 1959 to 2009 (and Investment Assumptions for Stochastic Models)”.

  13. Lags.  CPI and AWOTE may then be lagged (refer Section 14 and paragraphs B10 and B11 of the above paper).

  14. Refinement.  The CPI and AWOTE auto-correlations may be further improved by increasing their cross-correlation with the D sector by .12 (refer paragraph B11 of the above paper).

For further information, contact Colin Grenfell on 03 9886 1091, or colin.grenfell@supereasy.com.au



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