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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 47 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 2007 Institute of Actuaries of Australia (IAAust) paper “Australian Investment Performance 1960 to 2007 (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 U, 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 30/6/1960
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 AUSTMODU algorithms is summarized below:
1. Normal. First, the model generates independent Normal random variables for each sector.

2. Cross-correlation. These 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. May then be added using formula [2] or [4] as described in Appendix A of “Australian Investment Performance 1960 to 2007 (and Investment Assumptions for Stochastic Models)”.

4. Shape. For sectors F, G, J, L and M the shape of the distribution may then be improved by reducing both the skewness and kurtosis - refer paragraph A13 of “Australian Investment Performance 1960 to 2007 (and Investment Assumptions for Stochastic Models)”.

5. Forces. The resultant standardized random variables (denoted srv) are then converted to annual forces using the formula mu + sigma*srv.

6. Mixture. The annual force for the mixture or portfolio is then determined by weighting the sector forces by the proportions for each sector.

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

8. Repeats. Steps 1 to 7 are repeated 108 times to give a 108-year single scenario with no auto-correlation.

9. 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 1960 to 2007 (and Investment Assumptions for Stochastic Models)”, but with references to 16, 32 and 96 changed to 18, 36 and 108 respectively.

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

11. Refinement. The CPI and AWOTE auto-correlations may be further improved by increasing their cross-correlation with the D sector by .13 (refer paragraph B11 of the above paper).

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

SuperEasy Pty Ltd is not licensed to provide advice on investments, or legalities of the types of investments that you can have. SuperEasy® strongly recommends that you seek professional advice before making any investment choice or decision.

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