Investment Simulation

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.

AUSTMOD - Stochastic and Historical Investment Simulation Model

The model is an Excel workbook that displays up to 60 years of historical (past) and 40 years of simulated (future) investment performance for 15 “sectors”:

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 February 2018 Institute of Actuaries of Australia (IAAust) paper “Australian Investment Performance 1959 to 2017 (and Investment Assumptions for Stochastic Models)”. A slightly updated version of this paper was presented to the June 2018 International Congress of Actuaries in Berlin– CLICK HERE.

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 X, includes many new features, for example:
  • Three auto-correlation options
  • Three skewness options
  • Two kurtosis options
  • Inflation-linked bonds and hedged (and unhedged) international shares
  • 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 AUSTMODX algorithms is summarized below:

1.Random numbers. If seeds are used, random numbers are “controlled” by selecting 4000 random numbers, then calculating a second set of numbers equal to one minus these and mixing both sets together so that all 8000 have near zero auto-correlation.

2. Normal.  First, the model generates independent Normal random variables for each sector.

3. 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).

4. 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 2017 (and Investment Assumptions for Stochastic Models)”.

5. Shape.  For sectors Q, F, G, J, L, C, N and B the shape of the distribution may then be slightly improved by reducing both the skewness and kurtosis - refer paragraph A13 of “Australian Investment Performance 1959 to 2017 (and Investment Assumptions for Stochastic Models)”.

6. 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).

7. 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.

8. 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.

9. 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.

10. 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.

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

12. Repeats.  Steps 2 to 11 are repeated 144 times to give a 144-year single scenario with no auto-correlation.

13. Auto-correlation.   48-year scenarios with auto-correlation may then be generated using the methodology described in Appendix B, paragraphs B7 to B9, of “Australian Investment Performance 1959 to 2017 (and Investment Assumptions for Stochastic Models)”.

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

15. 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).

Important Information
Lynken Counsellors
provides the asset allocation and simulation services; SuperEasy® does not provide them. SuperEasy® does not have any liability in respect of Lynken Counsellors' services or for any information, product or service offered by any third party on or through Lynken Counsellors; The information provided on this website does in no way constitute SuperEasy® recommending or proffering any advice. Similarly, Lynken Counsellors does not have any legal liability in respect of SuperEasy® activities and services.

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