monte carlo final

7/30/2019 Monte Carlo Final

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Given the Mean Annual Return of two investments (like Stocks and Bonds) and the annualized Volatil(orStandard Deviation) of each and a degree ofCorrelation between the two the Monte Carlo (MC) sheet picks random annual returns* for each, over the next umpteen years and,

assuming some split between the two investment types - like 75% of the former and 25% of the latter -(and an annual rebalancing to maintain this split), sees how much would be in your portfolioif you invest annually (this amount increasing annually with inflation) and you give the spreadsheet some hoped-forFinal Portfolio (starting at some Initial Portfolio) and it does this hundreds of times to see what fraction of these iterations

would yield a Final portfolio less than $50K, or less than $100K or $500K or even more than your hoped-for Final Portfolio : )

(These amounts are the BreakPoints.)See: http://home.golden.net/~pjponzo/Monte-Carlo.htm for "the Math"

Since it takes some time, you can ask for just ONE run (of umpteen hundred iterations you decide h

or a collection of runs, using three different Stock/Bond splits and three different Investment Amounts(that makes NINE scenarios, eh?).There's also a chart of some sample portfolios.The red graph on this chart is the deterministic portfolio evolution: it uses an Annualized Return

then sets both Standard Deviations to zero. The Monte Carlo simulations fluctuate about thisP.S. The software needs the Average (or Mean) annual returns. If you know the Annualized returns, y

can Click a Button and get 'em changed to Average.* Note: the (random) returns are Log-normally distributed but you can also ask for a Normal di

This spreadsheet began life as a child ofRichard Pritz with help from Peter Van and Peter Ponzo.


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ity

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tribution.


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You'll want to know how often yourFinal Portolio was greaterthan (for example) $100K or $200K or $300K, etc.To allow you to do this, change the minimum amount in cell T2and the increment in cell R5 like so:

The spreadsheet will calculate how often the Final Portfolio wasless than (for example) $100K, $200K, etc.

Neat, eh?


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Okay, here's another variant:

A standard Monte Carlo simulation uses a fixed Mean Return and Standard Deviation and Distributionover the 10, 20, 30, etc. years considered by the simulation

You don't like that?Then how about selecting, for yourStock gain, at random, monthly gains from a collection of monthly gfrom Jan, 1926 to May, 2001? (At last count, there's 905 of 'em and they live in column AI as "1+MontYou like that? Remember, that includes the 1929 crash!!

You can put your own (1+MonthlyReturn) data in column AI. Just be sure to first delete the data t

If you'd like to see the effect of that choice (where you don't assume some fixed Mean, Standard Deviatbut use real, live historical returns), then instead of typing N orL in cell B9, type S (forS&P, eh?).

The MC software will, when calculating an annual Stock gain, multiply together a dozen monthly selecti(at random, of course) from the collection of905 S&P 500 gains (which live in column AI).The annual Bond gain, however, will be the standard Log-normal distribution with your choiceof Mean and Standard Deviation.

P.S. For the past umpteen years (since 1926) appropriate, nominal (as opposed to inflation-adjusted) "Average S&P Stock Return: 10.9% Standard Deviation: 20%Bonds - 5 year U.S. treasuries: Average Return: 5.5% Standard Deviation: 6%Correlation: 8%See Richard's page for more data: http://www.geocities.com/snarkll/


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(Normal? Log-normal?)

ains of the S&P 500,

ly Return")

at's there!

ion or Distribution,

ons

nnual" numbers are:


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toc s on s ** If B2/C2 are Annualized Returns **

Average Annual Return = 8.0% 4.0%

Annual Standard Deviation = 20.0% 8.0% Enter the Volatilities : Stocks & Bonds

Correlation = 15% Enter the Correlation : Stocks & Bonds

Annual Inflation = 2.0% EnterInflation Rate (=Investment increase)

Years = 30 Enter the number ofYears to considerIterations/100 = 10 Enter just the number ofHundreds

Change only the data in the boxes Final Portfolio = $1,000,000

Normal,Log-normal, S&P ? L Initial = $0

Annual Investment $10,000 $12,000 $14,000 Probability

25% 25% 50% 73% Final Portfolio

Stock Percentage 50% 40% 65% 77%

75% 52% 71% 79% > $1,000,000

Run ONE: just 25% Stock, $10,000 Annual

Run all NINE Stock Percentages / Investments

Created by Richard Pritz with the assistance of Peter Vann & Peter Ponzo.

0%2%4%6%8%

10%12%

14%16%18%

monte carlo final

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