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Occasionally Asked Questions

Comparing ORP to FireCalc

What is the key point about how ORP generates it random numbers?

ORP uses the difference between the observed mean from Shiller's market data and the user's specified mean from the ORP parameter form to estimate a revised standard deviation for the random number generator. That in turn will affect the random numbers being generated.

Why are ORP's Monte Carlo results more pessimistic than FireCalc's?

Trying to do a precise reconciliation between two stochastic processes is a fool's errand. Validation of ORP's results is important. It is addressed in a couple of places on ORP's web site. In particular, for ORP's Monte Carlo method see this.

The paper is a sequel to the paper by Dorman, et al that compares the performance of 36 stochastic simulators and shows their collective performances to be all over the map, with a majority flat out wrong. The paper maps ORP onto Dorman's process and shows that ORP got the right answer, according to Dorman's standards, i.e. ORP is in the minority of simulators, that correctly predicted the hypothetical plan would fail.

Personally, I pay little attention to ORP's Monte Carlo option because the whole concept is flawed, as is well documented in the literature. OTOH, the 3-PEAT simulator is a useful tool, which IMHO usefully measures ORP's optimal plan against historical market eras.

After all, what are we trying achieve here? A precision reconciliation of two random processes? Or a reasonable measure of a mathematical model's results of the real world?

ORP Succession Plan

  1. How old are you?
  2. What is your succession plan for ORP?

  1. I am an octogenarian, well past my euthanize-by-date.
  2. The ORP succession plan is that ORP may survive my ascension to the Pearly Gates for a time.

      The roles of the ORP web master are:

      1. Answer email queries about ORP's results and possible anomalies. Edit the documentation when questions indicate the text is muddled. Implement bright ideas that come in from the field.
      2. Update the Federal tax table annually.
      3. Modify the formulation of the tax module whenever Congress mucks about with the tax code.
      4. Rebuild the system whenever a new server operating system requires it.

      When the Roll is Called Up Yonder, Role #1 will no longer be honored. Role #2 can be fulfilled by who ever is doing the hosting; it is a simple update of a CSV file. Any requirement for the other roles will be fini for ORP.

Savings Account Contributions

The contribution to my tax deferred account seems to be deposited into the "After Tax" account rather than the expected tax-deferred account.

Near the end of ORP's Extended form, in the Taxes section, lies the parameter "Current Marginal Personal Income Tax Rate". This is your pre-retirement (current), marginal tax rate on your current income. This is basically your current or next higher tax bracket.

The default value is 24%.

The short answer to your question "is increase this number".

ORP balances your pre-retirement taxes against the retirement taxes that it computes when it decides how to make savings withdrawals. If your pre-retirement tax rate is low compared to your retirement tax rate then ORP will pay taxes now on Roth or taxable contributions, not the higher taxes on 401K withdrawals in retirement. On the other hand, said the one armed financial adviser, if your pre-retirement tax rate is higher then your retirement tax rate, then ORP will grab the tax-deferred deduction now in the form of tax-deferred savings and pay taxes on withdrawals later.

If you have a large tax-deferred account balance or a large pension, or both, then your retirement tax rate will be high and ORP will favor saving in your Roth IRA or taxable account.

Medicare Income Related Monthly Adjustment Amount (IRMAA)

Does ORP model IRMAA?

Most people will pay the standard Medicare part B premium amount. Medicare Part B covers certain doctors' services, outpatient care, medical supplies, and preventive services. You pay a premium each month for Medicare Part B. If you receive Social Security benefits, your Part B premium will be automatically deducted from your benefit payment. If you do not get these benefit payments, you will get a bill from Medicare.

If your Modified Adjusted Gross Income (MAGI) is above a certain amount, you will pay an additional Income Related Monthly Adjustment Amount (IRMAA).

ORP does not model Medicare premiums, with or without IRMAA, because IRMAA belongs on the expenditure side of the ledger and ORP does retirement income management. From ORP's perspective IRMAA is a reduction in spending, important to the retiree, but which does not affect the computation of maximum spending any more than groceries or housing costs do.

However, there is a manual procedure by which your IRMAA can be incorporated into your ORP planning. ORP's Maximum Spending can be reduced by your IRMAA in the following manner:

  1. Compute your MAGI: ORP's version of your MAGI can be computed from ORP's Withdrawal report. Go to the first line of this report (the first age of retirement) and compute your MAGI as the sum of the Taxes and Spending amounts.
  2. Estimate your IRMAA: once you have your MAGI you can get a rough estimate of your IRMAA from this table:
    MAGI Limit Annual
    Single Married Premium
    $85K$170K$1.608K
    1072142.250
    1342673.215
    1603204.060
    Otherwise5.143

For IRMAA details and a more accurate computation consult medicare.gov

Why does ORP not account for IRMAA as affecting disposable income?

IRMAA is a constant cost to the ORP model in that raising or lowering IRMAA changes Disposable Income (DI) by exactly the same amount.

Basically ORP's Withdrawal Report says:

Withdrawals + Income - Taxes = $DI

For example Earned Income, although constant, needs to be in the model because it increases Disposable Income by less than the gross additional income, because the progressive tax code increases the tax rate. A $E increase in earned income, increases personal income taxes by $E - t(E). The impact on Disposable Income (DI') of adding $E to the model is

Withdrawals' + (Income + $E) - (Taxes' + t(E)' = $DI'
where the prime variables are computed by the ORP optimizer and the others are input assumptions.

The revised disposable income, when income is increased by $E, is:

DI' = DI + $E - t(E)'

So an increase in $E increases $DI by $E - t(E)' where $E - t(E)' is the increase in disposable income for every dollar increase in Earnings. Because ORP is an optimizer, Withdrawals and Taxes will change as $E changes, although the change in Income is constant (indexed to inflation).

On the other hand, said the one armed economist, if the change is a cost (C) (not a income reduction) then t(C) is zero and DI + C = DI'. Most importantly the withdrawal and tax portion of the model do not change when t(C) = 0, so the model's withdrawal schedule does not change. The user has to be cognizant of the fact that disposable income has changed by a constant amount and reduce the spending budget by the premium amount, in this case.

Actually, isn't this all mostly invisible to the retiree? SSA computes your Medicare premium (and IRMAA) and deducts it from your benefits. When you run ORP you specify SSA's gross benefits as specified in your annual statement. When you budget spending you use SSA's net amount for computing your annual surplus, while deducting living costs such a green fees, housing, transportation, bribes, etc.

Yes, taxes are a spending item but taxes and income are tightly bound together so that changing one changes the other. So ORP consider taxes as part of income management.

Occam's razor (Philosophy's law of parsimony; don't make unnecessary assumptions.) is a factor in my thinking here. The ORP Extended Form has more than 110 input values, each of which potentially sends the user off to the help file and generates cynical comments about ORP's complexity. I struggle mightily to keep from adding new input fields. I avoid adding features where $t is zero.

In summary IRMAA reduces your disposable income but has no effect of the income side of the model; IRMAA is a cost only and ORP is a retirement income manager.

Affordable Care Act (ACA)

Why do IRA to Roth IRA conversions exceed my ACA income limits for some years but not others?

Basically what is going on here is that ORP takes a guess at what your fixed income will be during ACA years (e.g. interest income, earned income, pensions, etc.) and estimates when your income will likely be too large to qualify for ACA. For those years ORP takes off that constraint and allows unlimited taxable income. For years with income estimated to be within the ACA limit the constraint is enforced. IRA withdrawals, which are optional, and Roth IRA withdrawals, which are not taxed, are not included in this estimate.

The reason for this is to allow for partial ACA, i.e. for the years in which you qualify and relaxes the other years. ORP offers some guidance for managing retirement income to take advantage of at least some ACA subsidies.

Tax Free Pensions

Where do I enter my non-taxable VA pension in the ORP? It is not subject to federal or state tax and is indexed to inflation.

Since your VA pension has no tax consequences it won't affect anything going on in the model. Leave it out altogether, except manually add it to ORP's computed maximum spending as shown on the first page of ORP's results.

Questions About 3-PEAT

I do not quite understand the 3PEAT modeling data result. Is the disposable income listed for each year the amount of money that I can safely spend that year? So, in my model are we saying that the mean amount of money I can spend each year is $120,000 in today's money?

You have 3-PEAT by the wrong end of the stick.

ORP's Withdrawal Report is a projection into the future, using fixed rates for various things such a rates of returns on savings. If you invest conservatively, with rates more or less approximating ORP's fixed rates then this is a reasonable forward looking report. If you follow the 3-PEAT method then only the first line of the Withdrawal Report contains any actionable information.

The 3-PEAT simulator is backward looking and has no predictive relevance at all. All it says is if you go back in time, to year 2000 in your case, then this is how your particular plan would have behaved. Would your retirement plan have been safe? The only thing of interest that the simulator's report provides is that if, starting in 2000, had you followed the 3-PEAT procedure:

  1. Would your savings run out of money?
  2. How many years did disposable income fall below your essential spending level.

Don't read any more into it than that. You and the stock market will never again see this particular set of returns so there is no decision making relevance in there.

The main 3-PEAT simulation report is in nominal dollars, i.e. inflation has not been removed. These are the numbers that the 3-PEAT practitioners see every year while executing the 3-PEAT method.

The summary at the bottom is in real dollars, i.e. inflated dollars, as measured by the consumer price index, has been removed. When processing data across time if inflation is not removed then the recent data would carry more weight than historical data which would bias the results.

If I do not need the spending amount that ORP calculates that I could take, which account should I withdraw from first?

The answer lies where ORP tendencies overlap with conventional wisdom. Conventional wisdom says distribute your after-tax account first, followed by your IRA and, when that is gone, your Roth IRA. There is good logic behind this rule of thumb, having to do with account appreciation and tax efficiency, and all things being equal ORP agrees.

What are the advantages and disadvantages of Monte Carlo compared to 3-PEAT? It's the same data and the same period under examination. I recognize that MC looks at every n-year period in the entire data set whereas 3-PEAT looks at one n-year period.

First off, 3-PEAT is a method for managing retirement income whereby:

  1. the retiree tells ORP of her current financial situation
  2. ORP computes an optimal, constant spending plan for the remaining years of retirement, and
  3. the retiree implements the plan's decision variables from the first year of ORP's new plan.

Each year the retiree repeats these three steps.

The 3-PEAT simulator simulates the actions taken by a 3-PEAT practitioner over some historical period.

The Monte Carlo method (MC) (a simulator) and 3-PEAT's simulator address retirement spending from two different directions. MC computes a statistical report summarizing many constant spending levels for randomly generated rates of return. MC offers no clues as to how it arrived at its results.

The 3-PEAT simulator's value is that it reports important decision variables such as annual savings withdrawals, disposable income, and estimated taxes for each simulated year. The 3-STEP simulator reports these decision variables in the context of the economic environment in which they were made. This information does not exist in MC.

Secondly, a true Monte Carlo method does not rely on historical data because that data is actually a small, not particularly representative, sample of a much larger universe of possible outcomes. A true MC (such as ORP's) will generate random values that hopefully are characteristic of the full range of outcomes.

It is well to remember that while MC generates probabilities of success (or failure) of constant spending plans, your retirement has only one success or failure outcome.

When I ran ORP's Constant Consumption , areport was produced that detailed my annual spending as X. In reality, I understand that the annual spending changes. So, in which year or years am I allowed to spend X? How does that annual spending change from year #1 through the end of plan?

Let's change your word "allowed" to "plan". Then your expectation is that you spend "X" every year of retirement, indexed to inflation. Of course, blindly spending the same amount every year implies equally blindly withdrawing a constant amount from savings every year without regard to changing market conditions and your personal situation. This offers a high probability of prematurely depleting your savings -- plan failure.

3-PEAT's alternative is that if you can accommodate variability in your actual annual spending then plan failure can be avoided altogether.

The reality is that you make decisions and take action for this year only. Next year, under the 3-PEAT method, you run ORP again, produce a new constant disposable income plan, now one year shorter. Again, you make decisions and take actions for just one year, but made in context of a new plan. Because of changes to external, environmental variables your new plan will differ from year 2 of last year's plan.

The 3-PEAT simulator simulates the 3-PEAT method for as many years as your planned retirement. Whereas ORP uses constants for savings rates of returns, bond interest, inflation, and Social Security's COLA, 3-PEAT solves an LP problem for each year of retirement using historical data for these values. ORP projects the future using constant data while 3-PEAT demonstrates what would have happened had your retirement begun in 1935, or 1984, or whenever. You want to know, if under these economic conditions, did your plan fail:

  • Were your savings prematurely deplete?
  • Did your disposable income fall below your essential spending needs?
  • The simulator addresses these questions for a particular sequence of historical data, anecdotal evidence, if you will, but still evidence.

Modeling the After-tax Account

My After-tax Account is invested in solid dividend paying stocks. 60% of its returns are from dividends and 40% are from value appreciation. How do I model this in ORP?

ORP's view of the After-tax Account is that it is divided between stocks and bonds.

  1. Stocks are bought before retirement, and held until they are sold to fund a distribution. You specify the stocks' cost basis. The growth in value of stocks is from their compounding Rate of Return (ROR). The difference in the value of stocks at distribution and their cost basis is subject to capital gains taxes. ORP further assumes that through conservative, active asset management that account value volatility is low so that the constant ROR is a reasonable assumption.
  2. Bonds' annual interest is taxed as personal income and contributes to disposable income. Bonds are held to maturity and redeemed at their original investment value. The ratio of stock and bonds in the account is held to target throughout retirement.

The tricky part is that your real life brokerage account will contain bonds, which fluctuate in price and are sold before maturity thus taking on some characterisics of a stock, and contain stocks that pay significant dividends, with low price volatility, i.e. act like a bond in some ways.

Your mission is to characterize to ORP the behavior of your After-tax Account so that it looks to ORP the way it actually behaves in real life. ORP provides you with knobs that can be adjusted to approximate that. The knobs are % of the account held in stocks, stocks' rates of return, bond interest rate, and cost basis.

With the glide path parameters, you might characterize the account as 60% bonds where the dividends are construed as interest and assets are sold for their purchase price. The remaining 40% is stocks where there are no dividends but with capital gains profits. In other words by setting the percentage of stocks and bonds in the account, and coming up with rates of return and interest rates that are reflective, not of a pure stock/bond situation, but of the behavior of your investments. I realize this is a hell of a load to dump on the casual ORP user but that is the best I can offer. (This sort of fudging goes on in the Operations Research world all the time.) It doesn't matter what you call it as long as its behavior is characteristic of the situation being modeled.

Comparing ORP to Other Retirement Calculators

Why does ORP's Monte Carlo method give worst-case withdrawal rate so much lower than what I have seen published in every other tool or writing I have seen about withdrawal rates?

The quality and relevance of your answers depends on how you state the problem (See the saga of the garganuation super computer Deep Thought that was tasked with finding the meaning of life, the universe and everything and, because the problem was not well stated, came up with the answer "42". Douglas Adams, Hitchers Guide to the Galaxy.)

Positing the retirement income management problem as a percent of assets withdrawn during the first year of retirement is a flawed way of stating the problem. You are essentially making a wish, your initial withdrawal amount (converted to a rate), and calculating a success value. Your results are either the age when your money runs out or how much you are leaving your ungrateful heirs.

With ORP you specify your estate at plan end and ORP computes your maximum` disposable income. The wishing step is omitted.

If you go back to Bengen's original paper you will see that the 4% rule is very narrowly defined and applies only to a specific set of assumptions including exactly a 30 year retirement period and not one year more. Essentially the 4% rule maintains a savings buffer big enough so that there will be sufficient funds to see you through the worst stock market recorded to date; not the worst market that can occur. Most of the time the 4% rule will leave a whopper estate, great for your heirs, not so much for you.

The other calculators are simulators that take a particular set of assumptions and compute its unique answer. ORP is an optimizer. Essentially this means that ORP has fewer assumed parameters to be specified by the user and ORP computes the optimal value for the unspecified parameters.

Simulators do it this way because that is all they can do. Their basic design restricts them to this statement of the problem. The big assumption that simulators make, and that ORP computes, is the initial withdrawal amount for each of the retirement savings accounts; IRA, Roth, and Taxable accounts. ORP not only computes income taxes, ORP minimizes income taxes, values that simulators either ignore or require the retiree to estimates.

The Monte Carlo method is a wrapper around their simulator that does a bunch of runs with the simulator and presents a statistical analysis. If the underlying simulator is flawed rerunning it a thousand times will not make its answers any more valid.

In general, IMHO ORP fits the retirement income management problem better than the simulators. Comparing ORP to a simulator really only measures the simulators' oversimplification of the problem.

Timing of Actual Withdrawals and Paying Taxes

Why does ORP have me taking a substantial amount out of my tax deferred account for the first year of retirement, paying taxes on it, then putting what I don't spend in my after tax account? This yields a very large tax bill in year one

Starting at age 70 you have $102K of other income (Social Security income and your pension) coming in and an equal RMD. That's $204K of money that has to go somewhere. $30K is going to taxes and $160K is your after inflation lid on spending. That leaves roughly a $15K surplus. ORP's only option at this point is to stuff it into the After-tax Account.

Since you have capped spending, ORP goes into its maximize estate mode which means it's only too happy to push your surplus into the After-tax Account. It also means that ORP will honor the RMD but as it does so it will try to leave as much as possible in the tax-deferred account without breaking any IRS regulations and while minimizing taxes, i.e. keeping your taxable income in the 28% bracket. (Your heirs, not you, pay taxes on estate money left in the tax-deferred account, thereby reducing your tax burden while increasing theirs. Their taxes are outside the model, ORP is reducing your taxes.)

This leaves your original question: "What is going on before age 70, before the RMD and before Social Security income?" This is where life gets complicated. ORP prefers to pay taxes early in the plan, rather than later; up to a point. In your case the "point" is the top of the 25% bracket. ORP is attempting to keep taxable income at the top of the 25% bracket and failing; there is quite a bit of leakage into the 28% bracket. In the first year your taxable income is at the top of 33% bracket. Except for ages 66-70, your taxable income, after all transfers, is at the top of the 28% bracket for ages 67-70. After age 70 ORP, with the beginning of Social Security income is working the top of the 25% bracket, while minimizing withdrawals to build up the estate.

The force behind ORP's desire to pay taxes early is that tax brackets' upper bounds grow at the rate of inflation (2.5%) and savings grow at the Rate of Return (7%). Thus, in the lower brackets ORP pays taxes to the top of a lower bracket early in the plan. But the ROR higher than inflation means that money taken out of the tax-deferred account later in the plan will, after a point (28%), be taxed at a higher rate than money in the After-tax Account.

As an experiment, if you set your inflation rate equal to your ROR you will cool ORP's enthusiasm for doing early transfers.

The message here is that ORP is doing a balancing act amongst conflicting requirements and coming down somewhere in the middle, which is what optimization is all about.

You might consider allowing Roth conversions. It probably won't have that much effect on your estate size but it may leave your estate more favorably situated from your heirs' economic point of view.

ORP's results may be intuitively uncomfortable but ORP's mission is to make you aware of and to get you thinking about issues like this even though you may decide not to act on ORP's results.

I am going to start withdrawing from my retirement savings this year. I plan to do Roth conversions at the end of the year and to start selling after-tax assets right now, I plan to sell $10K at a time or as we need them for income. Since I'm going to half what I will owe in capital gains withheld by Vanguard, how much should I sell?

When it gets down to estimating actual withdrawals and actual taxes there are several programs around to help you; Quicken, Turbo Tax, and their ilk. The timing of withdrawals and conversions is up to you. ORP works on an annual basis and assume everything, except change in market value, takes place at the first of the year.

ORP is not an accounting program, it generates guidelines.

Effects of Inflation

Increasing inflation decreases annual spending, but why does the initial After-tax account balance increase?

You have your finger on a central problem of retirement income planning. ORP is working with nominal, i.e. inflated, dollars. The only real, non- inflated, value in ORP's report is Initial Spending on the first page of the report.

Your initial spending drops from $43K to $39K in real dollars thanks to your inflation increase from 0% to 1%. Because your initial withdrawals are lower, your early savings balances will be higher. From then on you can't really compare because of the nominal dollar problem.

If you deflate your After-tax Account annual balances you will see a big drop in real balances.

Because of the inability to compare plans with different inflation rates, many academic researchers work in real dollars only. However, the actual live real-world planner is dealing with a nominal world so that is how ORP, and everybody else, works.

Inflation is death to retirement. Long live the Federal Reserve. If the Republicans get their way and put the money supply under the control of Congress you can kiss your retirement as you planned it goodbye.

Accounting for taxes

How does ORP account for taxes paid?

Taxes are money going to the state and Federal governments, which is the same as disappearing into the air as far as your plan is concerned. Taxes are paid by decreasing spending, while increasing withdrawals from all sources. Taxes go up, assets go down, subsequent spending goes down

Maintaining original asset allocations in accounts.

Is there a way to set ORP's asset allocation initially and include rebalancing so that the asset allocation for the portfolio as a whole remains specified rather than each individual fund-type?

You are proposing that ORP should withdraw from the accounts in the same proportion as the original balances, to maintain the same ratio of balances in all 3 accounts. Money can flow from the IRA to the Roth or the taxable account but that upsets the proportioning. Account balances have to be maintained by predefined withdrawal scheduling ignoring taxes and all there rest of that economic stuff.

That is a different calculator than ORP. It can be implemented with a spreadsheet.

Federal Tax Report Looks Funny

The problem I see is in the "last year" row of the tax table. Half of the max in the 10% column gets shifted to the 15% column. Why is that?

You specified that both you and your spouse leave the plan at age 92 (the default). Your spouse is one year younger than you. When you hit age 92 you leave the plan and your spouse stays, for your age 93. Her income is reduced and she becomes a single person and is taxed accordingly. Hence the discontinuity.

Separation of Spouse Accounts.

In its reports ORP lumps both the retiree and spouse tax deferred accounts together. When making a withdrawal, does it matter which account the withdrawal comes from, especially regarding a Roth Conversion? The retiree (me) has only 3 years to convert while my wife has several more years.

Internally ORP treats the retiree and spouse IRAs separately. Same for Roth. Not so for After-tax. From the perspective of how ORP is used it doesn't matter which account you withdraw from. Your withdrawal decisions are only for this year. Next year, when you run ORP to do mid course corrections, your withdrawal decisions will be reflected in your updated account balances and ORP will proceed from there. Generally speaking decision implementations are just for this year, made in the context of ORP's overall plan.

Unnecessary IRA Distributions

My pension and Social Security income significantly exceed my spending needs. I have no wish to draw on my savings, notably my IRA and Roth IRA. Why does ORP do three years of IRA to Roth conversions at the start of retirement even though it makes no Roth distributions?

The cause is the IRA Required Minimum Distribution (RMD).

The purpose of the RMD is to drive the IRA balance down over retirement so that the IRS can collect the taxes that were deferred on contributions. Taxes are paid annually on IRA withdrawals, which are based on the IRA balance. ORP reduces taxes on RMD withdrawals by lowering the IRA balance early in retirement, first by conversions, followed by withdrawals above the RMD level. After mid retirement IRA withdrawals are pegged to the RMD.

At the same time ORP maximizes the IRA balance at the end of the plan because no taxes are required on TD account funds left in the in the estate. (Or rather taxes become a problem for the heirs.)

In general, early IRA to Roth conversions reduce taxes in the latter part of the plan at the expense of taxes very early on. There is enough to this topic to warrant a scholarly paper:

http://www.iarfc.org/documents/issues/Vol%2015%20Issue1.pdf

Strange Savings Withdrawal Patterns

When I use the Spend option to put an upper bound on spending I keep getting a withdrawal report indicating that I should withdrawal from my tax-deferred account many thousands of dollars more than I need to spend for the entire year during the first four or five years.

Remember, ORP is an optimizer and not a calculator. As an optimizer ORP tries to maximize something. If you fix your estate ORP will maximize your annual, after tax, disposable income. If you put an upper bound on your spending ORP will maximize your final total asset balance.

If you cap your annual spending then ORP may engage in all manner of inexplicable, unnatural acts as it maximizes your Final Total Asset Balance. As you observed early in your plan ORP transfered tax-deferred withdrawals to your After-tax Account, absorbing the tax consequences in the process. This is a consequence of the constant spending assumption.

The sensible way to use ORP, the 3-PEAT way, is to remember that there is a difference between the end of your plan and your life expectancy. Your planning horizon, the term of your plan, is a conservative statement of your best case longevity scenario. Your life expectancy is younger than that, and the Asset Balance report shows your anticipated estate for each year of the plan. Set your estate to some value that provides a buffer in case you outlive your term. Then let ORP maximize your spending; this is a projected upper bound on your budget for each year of the plan. You are not required to spend it all, just don't plan on spending more. With 3-PEAT these numbers apply only for one year, any unspent funds will increase your savings for the following year.

Monte Carlo Results

Why is the average spending returned by the Monte Carlo simulation less than the normal mode?

These results are caused by variance drag. Average (arithmetic) returns are always above compound (geometric) returns by an amount which increases as the volatility of the portfolio increases. Only in the case of no volatility are they the same. Volatility reduces the returns that investors care about, the compound return that ends up in their pockets.

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