Applying Stats To Financial Planning 97 2003
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Transcript of 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
Copyright 2008 Dennis Foley
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.)
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
19.6% chance of running out of money within 30 years
Monte Carlo is superior than classical “point” estimates.
Copyright 2008 Dennis Foley
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%
Copyright 2008 Dennis Foley
Average less than 1% delta to historical data Proves validity of this Monte Carlo model
Copyright 2008 Dennis Foley
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??
Copyright 2008 Dennis Foley
Need to increase yearly savings to $12,500/year to meet goal
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
Stocks
Bonds
Real Estate
Cash
All 4 groups have sub-groups with various benefits and risks… but this is pretty much the investment universe!
Copyright 2008 Dennis Foley
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…
Copyright 2008 Dennis Foley
Assume: $1K initial and $1K/year for 5 years
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
Assumption: historical data from 1926-2005
Copyright 2008 Dennis Foley
Historical fit of Gold 1986-2006
Data fit from historical returns
Non symmetrical
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
Can run the math… or let Crystal Ball do it for you!
Copyright 2008 Dennis Foley
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 = ?
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
Can do the math or let Crystal Ball (must enter correlation)
Copyright 2008 Dennis Foley
Copyright 2008 Dennis Foley
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”
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley
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
Copyright 2008 Dennis Foley