Valuation procedure - MvcWithdrawalRate

RETIREMENT PORTFOLIO OPTIMAL WITHDRAWAL RATES INVESTIGATIONS PROCEDURE

TERMINOLOGY, MODELLING PROCEDURE, METHODOLOGY AND ASSUMPTIONS

This programme investigates retirement portfolio optimal withdrawal rates for different dis-investment strategies.
Initial withdrawal rate = (Initial withdrawal value)/(Initial retirement portfolio value). No payment is assumed to be made at time of retirement, the initial withdrawal value is used to link payments at future time steps through an escalation rate and strategy rules. Payments start at the next withdrawal time, and subsequent time steps thereafter. The withdrawal frequency per year will determine the number of time-steps used in modelling. In cases where payment is first made at initial time, the withdrawal value entered in the system will be the recurring payment made at that time and the initial portfolio value entered in the system must be the portfolio value at that time just after deduction of withdrawals, expenses and tax.
At subsequent time steps (other than initial time), the withdrawal rate is defined in this system as: Withdrawal rate=(Withdrawal value before strategy rule adjustment)/(Portfolio value just before deductions for withdrawals, expenses and tax).
Optimal initial withdrawal rates are optimised initial withdrawal rates that are high enough, while at the same time making sure that the probability of the portfolio surviving till the end of the projection period is within the chosen confidence level limit.
This programme implements forward tests through stochastic modelling to determine the portfolio future progression for given initial withdrawal rate, and optimises the initial withdrawal rate based on the chosen confidence level.
The system allows tests to be performed on a portfolio of up to 5 equity indices, investment grade corporate bonds(in credit rating categories of: AAA, AA,A, and BBB), risk-free sovereign bonds, and risk-free cash bond.
Investigations can be done on impact of different levels of allocated expenses, portfolio management expenses, and asset-class tax rates.
Impact of longevity is not explicitly considered since the goal is to establish optimal initial withdrawal rate that enables the retirement portfolio to last for a fixed period not until death. Longevity can implicitly be factored into the analysis by either increasing the length of the period of investigation, or increasing the thresh-hold end-of-period portfolio value so that it includes the appropriate longevity-risk cost. As an example, if we are investigating optimal portfolio drawdown pattern for a client aged 55 years and chose a fixed period of 30 years, the client will be aged 85 years at the end of the projection period. If the client is worried about longevity risk, we can deal with this in two possible ways:
1. We can simply increase the fixed period of investigations from 30 years to 45 years, which means the retiree will be aged 100 years at the end of the projection period and consider the proportion of paths for which the end-of-period portfolio value is above zero.
2. Alternatively, we can fix the period of investigation at 30-years, calculate the actuarial value of longevity risk by weighting the draw-down values of the client beyond the age of 85 by applicable survival probabilities to get the longevity risk cost. We then set the end-of-period portfolio threshold value that must be exceeded by surviving paths to equal the longevity-risk-cost.
The different dis-investment strategies implemented by this programme are listed below

CONVENTIONAL PORTFOLIO RE-BALANCING DIS-INVESTMENT STRATEGY

Establish initial asset-class allocation amongst equities, fixed income securities, and cash.
Withdrawals from an asset-class are made in proportion to its target asset allocation at projection time set at the outset.
Expenses and taxes are assumed to be paid at withdrawal times.
The portfolio is re-balanced to its target asset-class allocation weights just after withdrawals, expenses and tax are deducted.
Asset-class value multipliers are calculated, for equities it will be the value allocated just after rebalancing divided by the simulated price. Asset class value multipliers for fixed-income securities and cash will be the value allocated.
The withdrawal value is increased by the escalation rate to get the withdrawal value at the next withdrawal time. The escalation rate may be linked to the retirees' personal circumstances, that is, his or her average consumption basket annual cost increases or some other inflation index assumption.
Under this strategy, asset classes either live together till the end of the projection period or die together before the end of the projection period.
This strategy may be suitable for investors whose risk tolerances are constistent with the projected target allocation evolution into the future and therefore content with a portfolio re-balanced that way.

PORTFOLIO RULE DIS-INVESTMENT STRATEGY

Establish initial asset-class allocation amongst equities, fixed income securities, and cash.
Expenses and taxes are assumed to be paid at withdrawal times.
Following a period between withdrawal times where positive portfolio return is achieved such that equities or bonds exceed target weighting, sell excess and place in cash to meet future withdrawals.
Portfolio withdrawals are funded in the following order:
1. Overweighting in equity assets from prior withdrawal time. Overweighting in this case is defined relative to the projected target-asset-class weight at that time. The weight considered is the asset-class weight in the porfolio just-before withdrawals, expenses and tax.
2. Overweighting in fixed income assets from prior withdrawal time. Overweighting in this case is defined relative to projected target-asset-class weight. The weight considered is the asset-class weight in the porfolio just-before withdrawals, expenses and tax.
3. Cash
4. Withdrawals from remaining fixed income securities
5. Withdrawals from remaining equity assets in order of prior period performance. The prior period performance in this programme is defined as = [(Equity asset class value just before withdrawals)-(Equity asset class value just after withdrawals, taxes, expenses and rebalancing at previous withdrawal time)]/(Equity asset class value just after withdrawals, taxes, expenses and rebalancing at previous withdrawal time).
6. Rebalancing under this portfolio rule is done by calculating the over-weighting in asset classes and dis-investing them into cash, calculate the cash balance, deduct withdrawals, deduct expenses and taxes, test if the cash balance is negative, set it to zero if it is negative and carry the excess negative balance to the next asset in the withdrawal priority list. Repeat the process over until the last asset in the priority list, and if it is negative then set the whole portfolio process to zero and the path is dead thereafter(ie portfolio value is zero at subsequent time-steps).
7. Asset-class value multipliers are calculated, for equities it will be the re-balanced value divided by the simulated price. Asset class value multipliers for fixed-income securities and cash will be the re-balanced value.
Other than cash, any asset-class whose value is less than or equal to zero at rebalancing is set to zero, and remains so at subsequent time steps. The cash balance can be zero at one stage, but there will be future re-investment into it as over-weight portions of other assets are converted into cash.
This strategy will likely result in a future portfolio that is skewed towards equity investments as the withdrawal priorities require that they are the last to be sold when resources are insufficient, and will suit retirees whose risk-tolerance matches that. It is also likely to result in higher initial optimal withdrawal rates for the same initial asset allocation relative to the conventional portfolio rebalancing rule due to its future skewness towards equity investments other things being equal.

PORTFOLIO RULE WITH CAPITAL-PRESERVATION DIS-INVESTMENT STRATEGY

The rules are the same as portfolio rules with the following additions
When the current withdrawal rate is guardRate*100% or more above the initial withdrawal rate and not in last waiver period years up to maximum age, the current year withdrawal value is reduced by withdrawalAdjustmentRate*100%, which then becomes the new base amount e.g. if guardRate is 0.2, withdrawalAdjustmentRate is 0.1, Initial withdrawal rate is 5% which has increased to 6%, cuts back to 5.4% = (1.0-0.1)*6% if the period between successive withdrawal times is one year. For this to happen the waiver period rule should not be breached, for example if the retirement age is 55 years, the waiver period is 15, the maximum age is 90 and we are at projection time that is 15 years into the future, the capital preservation rule will operate because we are still outside the waiver period of 15 years, that is (90-(55+15))=20. If we are at projection time that is 30 years into the future, the capital preservation rule will not operate because we are now within the waiver period (90-(30+55))=5. The withdrawalAdjustmentRate parameter that is entered in the system is a yearly withdrawal adjustment rate parameter. If one enters the withdrawal adjustment rate parameter as 0.1, and the period between successive withdrawal times is 1 year, the result is a 10% cut in withdrawal rate if the current withdrawal rate is guardRate*100% or more above the initial withdrawal rate. If the period between successive withdrawal times is not equal to one year, but some period equal to Delta years, the adjustment rate to be applied at withdrawal times if the conditions for the capital preservation rule to operate are satisfied is calculated by the system to equal 1.0-(1.0 - withdrawalAdjustmentRate)^Delta, where the symbol ^ is a power symbol. This ensures that if there are f Delta periods in a year, and the withdrawal rate is guardRate*100% or more above the initial withdrawal rate over all such periods, the cumulative cut in withdrawal value over that year will be withdrawalAdjustmentRate*100%. If for example, the yearly withdrawal adjustment rate is entered as 0.1 and the period between successive withdrawal times is 0.25 years, the withdrawal value adjustment applied at withdrawal times is: 1.0-(1-0.1)^0.25 = 0.0260.
If the withdrawal rate increases, it means the portfolio value has reduced relative to the level of withdrawals, so we are withdrawing more resources from a lower asset base. We can preserve some value in our asset by cutting back on withdrawals if the guard rate level is breached. The guard-rate level that needs to be breached in order for the capital preservation rule to start operating is = (Current withdrawal value before strategy rule adjustment)/((1.0 + guardRate)*InitialWithdrawalRate). In this programme, this is called the lower-guard-rail because the portfolio value has to fall to a value below it for the rule to start operating.
This strategy will result in a higher optimal initial withdrawal rate when compared with other strategies, other things being equal. What the retiree is doing is trading-off the possibility of future cuts in withdrawal values for higher initial levels of drawdowns. This strategy will suit an investor whose drawdown pattern, due to life-style and other obligations, is high initially just after retirement, and reduces as he or she progresses into the future after adjusting his or her lifestyle and re-calibrated his or her obligations.

PORTFOLIO RULE WITH PROSPERITY DIS-INVESTMENT STRATEGY

The rules are the same as portfolio rules with the following additions
When the current withdrawal rate is -guardRate*100% or worse below the initial withdrawal rate, the current year withdrawal is increased by withdrawalAdjustmentRate*100%, which then becomes the new base amount e.g. if guardRate is 0.2, withdrawalAdjustmentRate is 0.1, Initial withdrawal rate is 5% which has fallen to 4.2%, it increases to 4.62% = (1.0 + 0.1)*4.2%. The withdrawalAdjustmentRate parameter that is entered in the system is a yearly withdrawal adjustment rate parameter. If one enters the withdrawal adjustment rate parameter as 0.1, and the period between successive withdrawal times is 1 year, the result is a 10% increase in withdrawal rate if the current withdrawal rate is -guardRate*100% or less below the initial withdrawal rate. If the period between successive withdrawal times is not equal to one year, but some period equal to Delta years, the adjustment rate to be applied at withdrawal times if the conditions for the prosperity rule to operate are satisfied is calculated by the system to equal (1.0 + withdrawalAdjustmentRate)^Delta - 1.0, where the symbol ^ is a power symbol. This ensures that if there are f Delta periods in a year, and the withdrawal rate is -guardRate*100% or less below the initial withdrawal rate over all such periods, the cumulative increase in withdrawal value over that year will be withdrawalAdjustmentRate*100%. If for example, the yearly withdrawal adjustment rate is entered as 0.1 and the period between successive withdrawal times is 0.25 years, the withdrawal value adjustment applied at withdrawal times is: (1 + 0.1)^0.25 - 1.0 = 0.0241.
If withdrawal rate reduces, it means the portfolio value has increased relative to the level of withdrawals, so we are withdrawing less resources from a higher asset base. We can reward ourselves by increasing the value of our withdrawals if the guard rate level is breached. The guard-rate level that needs to be breached in order for the prosperity rule to start operating is = (Current withdrawal value before strategy rule adjustment)/((1.0 - guardRate)*InitialWithdrawalRate). In this programme, this is called the upper-guard-rail because the portfolio value has to increase to a value above it for the rule to start operating.
This strategy will result in optimal initial withdrawal rate that is lower than that for capital-preservation but similar to that for portfolio rule only, other things being equal. The similarity with the portfolio rule only is because the paths that breach the upper guard rail have shown a relative increase in portfolio values and are therefore likely to survive till the end of the projection horizon. The number of surviving paths are therefore similar to those for portfolio rule only, and since optimisation is based on the proportion of surviving paths, the optimal withdrawal rates are therefore similar. What the retiree is doing is profit-taking following a good run of portfolio returns. This strategy will suit a retiree who likes profit taking and due to the portfolio rule favouring equities, profit taking may be a good thing to do for most retirees given the risky nature of equity investments. Do not forget to reward yourself after a period of very good returns.

PORTFOLIO RULE WITH BOTH CAPITAL-PRESERVATION RULE AND PROSPERITY-RULE DIS-INVESTMENT STRATEGY

The rules are the same as rules for both portfolio-rule-with-prosperity and portfolio-rule-with-capital-preservation ,
This strategy will result in optimal initial withdrawal rate that is similar to that for capital-preservation, other things being equal. It should be easy to figure out from the similarity between portfolio-rule, and portfolio-rule-with-prosperity why this is so. This strategy has both upper and lower guard rails in operation. It can be recommended to a retiree who has drawdown structure similar to that for portfolio-rule-with-capital-preservation, with an extra dimension of profit taking.

PORTFOLIO RULE WITH FREEZES DIS-INVESTMENT STRATEGY

The rules are same as for portfolio-rule-with-capital-preservation only that in this case the withdrawal value is set to its previous value when the lower guard rail is breached, and the guard-rail-rate is linked directly to the fall in portfolio value instead of indirectly through an increase in withdrawal rate.

OTHER KEY MODELLING CONSIDERATIONS

The modelling of equity prices is the usual real-world projection of share prices at the risk-adjusted-discount-rate plus a shock process that is consistent with the assumed correlation structure.
The modelling of bond prices is different from the usual bond valuation modelling in other applications. There is no mention at all of coupon rates, principal value payment at maturity, and coupon payment frequency. Instead, the modelling of bond prices done here is in the same setting as that done for share prices, and their correlated shock process are generated together. The bond's present value is projected at the real world risk-adjusted-discount rate plus a shock process, whose volatility is the volatility of forward bond price returns. The risk-adjusted-discount-rate used in bond price projection is the risk-free forward interest rate plus a credit spread that depends on the credit rating of the bond.
The credit spread that is added is the spread above the risk free rate that when added to the risk free yield curve, and used to discount cash flows from a bond of maturity equal to the projection horizon, makes their value equal to the current bond price in that credit rating category.
The introduction of the shock process is the usual technique of adding -0.5*VarianceRate*DeltaPeriod + Volatility*Z(0,1)*Sqrt(DeltaPeriod). The Z(0,1) is the normally distributed random number simulated by the system, and is correlated to the shock processes in other securities, based on the correlation coefficients entered. This makes it easy to establish correlation with other securities.
Coupons are assumed to be re-invested in the same asset class under this model, making their timing and frequency irrelevent, and variations in reinvestment rates are assumed to be due to variations in the levels of the yield curve which are captured by the introduced shock process.
The maturity values of bond payments(Principal value plus coupon) are known, but since we are projecting the bond prices from their current prices forward as opposed to discounting from maturity to present, the certainty in the maturity values of our bond is captured by the volatility structure used to project the bond prices forward.
To get the volatility structure, we first note that the forward bond price volatility used in bond option pricing is given by BondVolatility=ForwardBondModifiedDuration*ForwardBondYield*ForwardBondYieldVolatility.
The proportionality of forward bond price volatility to duration, suggests we use a volatility at projection time of the following functional form in this model: BondVolatility = Constant*(MaturityPeriod-ProjectionTime)/MaturityPeriod = V(t,T)
The functional form of volatility means as the projection time approaches maturity, the volatility applied to the shock process approaches zero, so towards maturity, we will essentially be projecting the then present value of the bond forward at the applicable forward rate as the effect of the shock process diminishes to zero.
The value of the constant in our volatiltity, function is the annualised global-fit volatility parameter to be entered into the system. The system automatically weights it according to the above mentioned functional form.
To get the value of the constant, we use a spectrum of actively traded market instruments such as caps and bond options that span the projection horizon, whose prices are readily available.
We substitute the functional form of volatility to get analytic pricing formulae for lets say n instruments as P(1),P(2),.....,P(n). Their respective market prices are Q(1),Q(2),....,Q(n).
The objective function we want to minimise is F(1,2,....,n) = (P(1)-Q(1))^2 + (P(2)-Q(2))^2 +,.....,+ (P(n)-Q(n))^2. The value of the constant on the functional form of volatility that minimises this objective function is the global-fit parameter that is entered in the system as annualised volatility parameter.
For an alternative method of estimating the volatility parameter, see the section below on calibration of the system for the UK and US market.
The above mentioned calibration procedure assumes that fixed-income securities that have maturities equal to the projection horizon are available in the market. In practice, securities available in the market have maturities that do not necessarily match the projection horizon. As a guide on how to calibrate the system, the system is already calibrated to calculate optimal withdrawal rates investigations for the UK market and USA market.

CALIBRATION OF THE SYSTEM FOR THE UK AND USA MARKET

In addition to allowing users to investigate their own tailor-made solutions for optimal withdrawal rate investigations, the system offers the option for users to investigate optimal withdrawal rates for the UK and USA market using system-calibrated parameters.
The portfolio for the UK market is selected to mimic the following:
1. FTSE All shares index to represent the UK market portfolio
2. FTSE 100 to represent the developed equity market index
3. iShares Core MSCI Emerging Markets (EIMI) to represent GBP denominated emerging markets index
4. FTSE 350 Real Estate (FTUB3510) to represent GBP denominated property index
5. UK GBP denominated cash bond
6. UK Domestic sovereign bonds that are part of FTSE UK Domestic Investment-Grade Bond Index (UKBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
7. UK AAA-rated bonds that are part of FTSE UK Domestic Investment-Grade Bond Index (UKBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
8. UK AA-rated bonds that are part of FTSE UK Domestic Investment-Grade Bond Index (UKBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
9. UK A-rated bonds that are part of FTSE UK Domestic Investment-Grade Bond Index (UKBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
10. UK BBB-rated bonds that are part of FTSE UK Domestic Investment-Grade Bond Index (UKBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
The portfolio for the USA market is selected to mimic the following:
1. S&P 500 index to represent the USA market porfolio
2. S&P 100 to represent the developed equity market index
3. MSCI Emerging Markets (MSCIEF) to represent USD denominated emerging markets index
4. S&P 500 Real Estate (SPLRCREC) to represent USD denominated property index
5. US USD denominated cash bond
6. US Treasury bonds that are part of FTSE US Broad Investment-Grade Bond Index (USBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
7. US AAA-rated bonds that are part of FTSE US Broad Investment-Grade Bond Index (USBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
8. US AA-rated bonds that are part of FTSE US Broad Investment-Grade Bond Index (USBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
9. US A-rated bonds that are part of FTSE US Broad Investment-Grade Bond Index (USBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
10. US BBB-rated bonds that are part of FTSE US Broad Investment-Grade Bond Index (USBIG), bond parameter information is extracted from FTSE Russell Factsheet|September 30, 2023
To calculate correlations between the representatives of the Developed equity markets index, Emerging equity markets index, and The property markets index for both the UK and US markets, index monthly returns data is extracted from https://uk.investing.com/ and respective correlations are calculated.
To calculate market betas for the representatives of the Market portfolio index, Developed equity markets index, Emerging equity markets index, and The property markets index for both the UK and US markets, index monthly returns data is extracted from https://uk.investing.com/ and respective betas are calculated using the formula:MarketBetaOfIndex = Covariance(Market portfolio index returns,Index returns)/VarianceOfMarketPotfolioReturns.
To calculate correlations between equity market indices and fixed income bonds, from our investigations of correlations between bond indices(eg FTSE Actuaries bond index) and equity indices we noted that correlations for these vary over time from very low positive values to slightly negative values. We therefore assume zero correlation between equity returns and fixed-income returns.
To calculate correlations between rated investment grade fixed income bonds with ratings starting from AAA-to-BBB, first we extract rated class bond parameters from the FTSE Russell Factsheet|September 30, 2023. The parameters of interest here are Effective duration, Yield to maturity, Bond volatility, Option adjusted spread. One quick and crude way to estimate correlation of bonds within different rating categories is to note that bonds with similar duration behave the same way to small parallel shifts in yield curves. In this case, we ignore bond rating and concentrate on effective duration of bonds in different rating categories. If for example a AAA-rated bond has the same effective duration as a BBB-rated bond, we expect the BBB bond to behave the same way to small parallel shifts in yield curves as the AAA-rated bond. Principal components analysis shows that parallel shifts in yield curves generally explain more than 80% of differences in bond returns variability. We can crudely assume that all bonds are positively correlated but the degree of correlation differs due to relative differences in effective duration periods. We therefore scale the correlation between bonds of different duration between extremes of 0 and 1. If the bonds have the same effective duration we assume their correlation to be 1, and if the other bond's duration is zero(eg Cash bond) relative to another bond of duration greater than zero, we assume the correlation between them to be zero. Ignoring the rating category of the bond, we therefore can crudely assume the correlation between investment grade bond Y and investment grade bond Z to be given by the following formula Correlation(Bond Y,Bond Z) = Minimum(Effective duration Of bond Y,Effective duration Of bond Z)/Maximum(Effective duration Of bond Y,Effective duration Of bond Z) It is important to note that the yield curve can shift in in different ways that are not necessarily parallel shifts albeit these other shifts bearing less weight in explaining the variability in bond returns. For UK rated bonds we simply use the effective duration of bonds in different rating categories from FTSE Russell Factsheet|September 30, 2023 to calculate correlations. For US bonds, we simply duration-match the rated bonds by placing them in different maturity periods and use the effective duration of the respective maturity periods to calculate correlations. In calibrating our system, we assume rollover of fixed income securitities with similar duration till the projection horizon as opposed to the calibration of fixed income securities with maturities that match our projection horizon which may not be available in the market. We also assume that any credit rating down-grades or up-grades are delt with by re-balancing the fixed income securities portfolio to its target allocation and any bond rating-downgrades that are outside the investment grade result in selling of the security and replacing it with an appropriate investment grade security.
To calculate volatility parameters for equity indices, we simply calculate the volatility of monthly returns and use the following formula to calculate annual volatility: Annual equity volatility = (Monthly volatility)* SquareRoot(12). To calculate the volatility parameter for fixed income securities we first calculate the yield by using the formula BondVolatility=EffectiveDuration*YieldToMaturity*YieldVolatility. For the UK market, we use the standard deviation of the FTSE UK Domestic Investment-Grade Bond Index as bond volatility, and its effective duration and yield to maturity from FTSE Russell Factsheet|September 30, 2023 and invert the formula to get the yield volatility. We assume the same flat yield volatility for bonds in different rating categories and use the previously mentioned formula for bond volatility to calculate the volatilities for different rated bonds including domestic sovereigns. To reflect that we are simulating over a period of over 10 years, we scale up the volatility parameter using the following formula: ScaledUpVolatilityParameter = (Effective duration of over 10 years to maturity bonds)/(Effective duration of bond)*BondVolatility . We do the same for the US bonds by first calculating the yield based on the standard deviation of the FTSE US Broad Investment-Grade Bond Index (USBIG) and scaling up volatilities to reflect that we are simulating over a period exceeding 10 years.
For credit spreads, we simply use the Option-adjusted credit spreads for different rated bonds from FTSE Russell Factsheet|September 30, 2023 . We are using the Sterling gilt yield curve, and the treasury yield curve as our proxy for the risk-free rate and we therefore make no adjustment to the option-adjusted spread, but note that in custom situations where one uses a different risk free curve (eg LIBOR rate - 10 basis points) an appropriate adjustment will need to be made to the option-adjusted spread.
Dividend yields are simply the long-term average dividend yields for different indices. The index level can be any positive number not neccessarily the current index level. This is because we are simulating growth parameters in determining the future portfolio value evolution. As an example, growth at current index level of 10 leads to the same value growth at current index level of 50. That means if we have a portfolio of value V and growth parameter g: (V/10)(10*(1+g))=(V/50)(50*(1+g)) .
To calculate expected market portfolio returns we simply use the long term market portfolio index price returns for the UK and US markets, convert them to their continuously compounded versions and add respective expected dividend yield rates to get long term expected market porfolio total returns. The system automatically assumes re-investment of dividends for different indices but allows the user the option to investigate different dividend re-investment plans. As an example if the index dividend yield is 0.04, the system automatically assumes a dividend re-investement rate of 0.04. If the user chooses the option to input a dividend re-investment rate of 0.01, the system will then adjust the dividend yield to (0.04-0.01) = 0.03 and use that yield rate to simulate price returns. If the user chooses a dividend re-investment rate of 0.05, the system will reject it because it does not allow the user to input a dividend re-investment rate that is greater than the dividend yield. If the user inputs a dividend re-investment rate of zero, the system will simulate equity price returns assuming a dividend yield of 0.04 , which means no dividends are re-invested and therefore we will be investigating optimal withdrawal rates based on price-returns not total returns. The system default option simulates equity prices based on total returns, that is, assuming that all dividends are re-invested.
The asset allocations determine the portfolio risk levels and as the risk level increases the proportion of initial portfolio value invested in equities increases versus the proportion of initial portfolio invested in fixed income securities and cash.

DE-RISKING OF THE RETIREMENT PORTFOLIO

De-risking of the retirement portfolio can be done in three ways if a user chooses the customised optimal withdrawal rate investigations option:
1. De-risking can be done by simply increasing the propotion of initial portfolio value invested in fixed income securities and cash relative to the proportion invested in equities and keep the intial portfolio allocations, and target end-of-period portfolio allocations the same.
2. De-risking can also be achieved by first allocating a high proportion of intial portfolio value invested in equities relative to the proportion invested in fixed income securities and cash, and then allocating a very low proportion of end of period target allocation weight invested in equities relative to that invested in fixed income securities and cash. The portfolio weight invested in fixed income securities and cash is then gradually increased as we progress into the future.
3. Another way of de-risking the portfolio is by using a combination of 1 and 2 above.
De-risking of the retirement portfolio can be done in one way if a user chooses the system internally-calibrated optimal withdrawal rate investigations option:
1. De-risking can be done by choosing a low risk level. The option for adjusting target weight as we progress into the future is not available for the internally-calibrated optimal withdrawal rate investigations option.
Follow view-page-by-view-page instructions below to investigate optimal initial withdrawal rates.

Financial solutions home page

Log into your account or if you are a new user, register your account and enable two factor authentication.
Click on the [Optimal withdrawal rate] button, this will take you to the parameters index page.

Parameters index page

Select the withdrawal rule/dis-investment strategy
Select to use internal withdrawal rates investigations or perform customised investigations.
Select to investigate different expense and tax rates with internally calibrated model.
Select to enter dividend re-investment plan or use the default dividend re-investment plan.
Select to optimise initial withdrawal rate, or investigate outcomes of a pre-determined initial withdrawal rate.
Click the submit button, and this will take you to the custom index page if you chose the custom option in 2 or to the dynamic text-block parameters page if you chose internally-calibrated investigations option.

Custom index parameters page

Select to enter time-varying or flat zero rates at inter-path simulation times.
Leave the default selection of pairwise-varying correlations between equity share prices' returns and bond prices' returns.
Enter portfolio projection period in years.
Select the number of underlying equity share price variables/indices in the portfolio.
Select the number of time steps in the simulation paths. For example, if one enters a projection period of 30 years, and number of times-steps as 30, the system will divide the 30 year period into 30 equal periods of 1-year each.
Click the submit button, and this will take you to the array populating page.

Array populating page

Identifier indices used in this section start identification counting from 0, to make them consistent with programming of array indices.
Enter name of indicated underlying share price variable.
Enter number of discrete dividends before the longest share price projection time (enter zero if none) of indicated underlying share variable. Discrete dividend is, such that, if the underlying share price value just before dividend payment is S, and the value of discrete dividend is D, then the value of the share price just after discrete dividend payment is S-D.
Enter the number of known dividend yields before the longest share price projection time (enter zero if none) of indicated underlying share variable. Known dividend is, such that, if the underlying share price value just before dividend payment is S, and the value of known dividend yield is q, then the value of the share price just after dividend payment is S*(1-q).
Enter initial portfolio allocation of indicated asset classes.
Enter the target end-of-period portfolio allocation of indicated asset classes. The end-of period target portfolio allocation will be used by the system to project the target portfolio allocation at withdrawal times linearly from initial time to end-of-projection time. The target portfolio allocation is used by the system to re-balance the portfolio under the conventional portfolio rebalancing rule, and calculation of over-weight values under the portfolio rule.
Enter portfolio management expense rates for indicated asset classes. For example, if the expense rate is r and the asset class value is V, the charge is r*V, the value you should enter is r.
Enter other allocated expense rates for indicated asset classes. For example, if the expense rate is e and the asset class value is V, the charge is e*V, the value you should enter is e.
Enter tax rates for indicated asset classes. For example, if the tax rate is t and the asset class value is V, the charge is t*V, the value you should enter is t.
Enter credit spreads for indicated asset classes.
Enter continuously compounded zero-rates at share price inter-path simulation times.
Enter pairwise correlations between indicated underlying share price variables and bonds.
Click the submit button, and this will take you to the Optimal withdrawal rates investigations parameters page.

Optimal withdrawal rates investigations parameters page

Select the currency of valuation from the drop-down list.
Enter the name of investment portfolio.
If prompted, enter age of pensioner.
If prompted, enter maximum age for waiver consideration.
If prompted, enter threshold period for waiver consideration.
Enter initial investment portfolio value.
If prompted enter initial withdrawal rate.
Enter withdrawal value annualised escalation rate.
If prompted, enter guard-rail rate.
If prompted, enter yearly withdrawal value adjustment rate.
If prompted enter the continuously compounded expected return on market portfolio.
Enter the confidence-level for optimal withdrawal rate investigations as a percentage.
If prompted enter annualised global-fit volatility paramaters for indicated fixed income bonds.
If prompted enter the initial prices of indicated share price variables.
If prompted enter the continously compounded dividend yields of indicated share price variables. The continously compounded dividend yields together with discrete dividends, and known dividend yields, enable any dividend payment patterns to be accomodated in the pricing model.
If prompted enter the continously compounded dividend re-investment rates of indicated share price variables.
If prompted enter the market betas of indicated share price variables.
Enter the annualised volatilities of indicated share price variables.
If prompted enter discrete dividend values and their timing, and zero rates of dividend timing periods for indicated underlying share price variables.
If prompted enter known dividend yield values and their timing for indicated underlying share price variables.
If prompted select the risk-level.
If prompted select the disinvestment horizon.
If prompted select the domicile.
If prompted enter expense and tax rates for different asset classes
Click the submit button and this will take you to the output display page.

Output display page

You can view pricing model output together with input parameters you entered.
At the bottom of the page you can click on the button to create database record for the current model output. This will take you to the create database record page where you should click on the create button to create the database record.
After clicking on the create button to create the database record, you will be taken to the database records view page, where you can scroll vertically or horizontally to view database records including the one you just created.
You can filter database records according to the currency of valuation using the filter box. You can click on the details link on the extreme right of a particular database record, this will take you to the particular database record details page.