applying stats to financial planning 97 2003

January 2008

Copyright 2008 Dennis Foley

Retirement Scenario and Pitfalls Back-test Monte Carlo simulation (1926-2005) More retirement scenarios (audience participation) Normal distributions and best fit of historical data

Savings Time horizon Modern Portfolio Theory Diversification Appetite for risk Fitting gold, individual stock, or other investments Running your own forecast scenarios


Past performance is no guarantee of future returns

Investor returns may be worth more or less than original cost

“Back tested” this Monte Carlo model is correct over 99% of the time from 1926 through 2005

No one really knows what will happen in the future (including me, your broker, financial advisor, barber, guy at work, actively managed mutual fund manager, etc.)


Assumptions Large Cap Stocks: 1926-2005 Bonds: 1926-2005 Nest egg at retirement = $1KK base in 2007 4.5% fixed withdrawal ($45,000) Increased by fixed 3% per year (for inflation) 80% stocks (avg.=10.4%, standard dev.=20.2%) 20% bonds (avg.=5.5%, standard dev.=5.55%) No adjustment in stock/bond ratio over time


19.6% chance of running out of money within 30 years

Monte Carlo is superior than classical “point” estimates.


Fixed withdrawal remains at 4.5%, but reduce yearly increase (for inflation) from 3% to 2% per year

Change stock percentage to 22.8%

3.7% chance of running out of money within 30 years

With minor adjustments, increase certainty of not running out of money from 80.4% to 96.3%


Average less than 1% delta to historical data Proves validity of this Monte Carlo model


Age 45 => 20 years from retirement $175K nest egg Goal of $1KK with >75% certainty in 20 years Previously determined to use:◦ 2008 – 75% stocks, 25% bonds linearly reduce to…◦ 2028 – 45% stocks, 55% bonds

Contribute $10K/year How much should contribution be reduced or

increased to achieve at least $1KK with 75% certainty??


Need to increase yearly savings to $12,500/year to meet goal


Stocks

Bonds

Real Estate

Cash

All 4 groups have sub-groups with various benefits and risks… but this is pretty much the investment universe!


Small cap stocks offer 2.2% greater average return than large cap stocks

But, with more than a 50% increase in dispersion versus large cap stocks

What does this mean? Assume: $1K initial and $1K/year for 5 years Run Monte Carlo to see…


Assume: $1K initial and $1K/year for 5 years


Large Cap has less chance losing money◦ Large Cap = 18.1% chance of less than $6K◦ Small Cap = 28.2% chance of less than $6K

Small Cap has greater chance of upside◦ Large Cap = 2.9% chance of more than $12K◦ Small Cap = 13.2% chance of more than $12K

Investors must decide if they want greater upside or less downside…

Assume: $1K initial and $1K/year for 5 years


Actively managed mutual funds offer endless combinations of stock/bond subgroups

Actively managed funds (vs. index funds)◦ Have much higher tax rates (fund turnover)◦ Have much higher expenses (1.5% vs. 0.25%)◦ Sometimes have loads as high as 5%!

Index funds offers superior long term returns


In the last 5 years:◦ S&P index has outpaced 67% large cap actively

managed Mutual Funds With no advice!◦ S&P mid cap index has outpaced 84% of actively

managed mid cap funds With no financial planning!◦ S&P small cap index has outpaced 79% of actively

managed small cap funds With minimum tax consequences


You don’t need a financial advisor You don’t need actively managed funds It is relatively easy to “do it yourself” You will save more money If retired, you will have more money to

withdraw◦ Depending on the size of your nest egg….◦ It may be as much (or more) than a car payment

You run Monte Carlo simulations to optimize your portfolio

All that you need is the software and a PC


Assumption: historical data from 1926-2005


Historical fit of Gold 1986-2006

Data fit from historical returns

Non symmetrical


Simplification of Modern Portfolio Theory

1990 Nobel Prize Harry Markowitz et. al. All investments can be assigned◦ Expected value◦ Standard deviation (dispersion)◦ Correlation*

Diversification leads to less risk => higher return

*Models shown so far have correlation = 0 Crystal Ball allows setting correlation values


Can run the math… or let Crystal Ball do it for you!


What happens if correlation coefficient 1?◦ Example (assume correlation coefficient = 1):◦ Portfolio = 50% Fund A and 50% Fund B◦ Fund A Past/Expected Return = 20%◦ Fund A historical standard deviation = 26%◦ Fund B Past/Expected Return = 10%◦ Fund B historical standard deviation = 16%◦ Portfolio Expected Return = ?◦ Portfolio Expected standard deviation = ?


Can do the math or let Crystal Ball (must enter correlation)


Expected value is a linear operator◦ Just weighted average

Standard deviation is◦ Square Root of (Weighted average of the variance +

covariance)◦ Can do the math◦ Or just use Crystal Ball!

Diversification among uncorrelated assets:◦ Higher return with less risk!◦ “Efficient Frontier”


Summary ◦ Diversification optimizes your portfolio – provided

that correlation coefficient are less than 1◦ Pick stocks, funds or ETF’s that are not correlated◦ Typical asset classes with low correlation

coefficients to each other Cash Bonds Stocks REIT’s Emerging International


Correlation Coefficients can change over time!◦ International stocks used to have a low correlation

coefficient◦ Now, with globalization, correlation coefficient to US

indexes near 1.0!◦ Need to follow trends and periodically adjust Recent data suggests that international emerging

markets have lower correlation coefficient to US markets


The only proven method to wealth is to save Index Funds/ETF’s provide better returns

than actively managed funds Crystal Ball/Monte Carlo can show:◦ The risk of running out of money◦ The probability of saving enough With periodic saving Depending on portfolio mix◦ The optimized portfolio given your risk tolerance


Saving for Retirement◦ Determine % certainty requirement◦ Determine Lump Sum desired◦ Use Monte Carlo to determine Probability of reaching Lump Sum Extra Savings necessary to achieve goal Optimal portfolio mix


Retirement Withdrawal◦ Determine your goals: Amount of time you want money to last (i.e. 30 years) % probability of running out of money◦ Run Monte Carlo to determine: Optimal portfolio mix Withdrawal amount Withdrawal yearly “raise” for inflation

applying stats to financial planning 97 2003

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