Portfolio Survival During

Retirement

Which will last longer?

Your portfolio…

…or you?

Steady 5% Earnings, Annual Withdrawals Equal to

7% of Initial Portfolio Value Deterministic 75/25 Portfolio

$-

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15

Does

that resemble

the real world?

Actual Returns on a $1,000 Initial Investment from 1965 to 1978

$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

$1,400.00

$1,600.00

$1,800.00

Monte Carlo Simulation

More in Gear with Reality?

The ModelThe Model•S&P 500 and Long-Term Corporate Bond Returns from

1926-1995

•Returns were adjusted for inflation using the Consumer Price Index

•Mean returns and standard deviations were calculated for portfolios consisting of:

•100% Stocks

•75% Stocks, 25% Bonds

•50% Stocks, 50% Bonds

•25% Stocks, 25% Bonds

•0% Stocks, 100% Bonds

Portfolio Survivability was then tested

“Success”=Balance >$0at end of desired number of years

Each portfolio was tested for 15, 20, 25, and 30 year spans.

Each portfolio was given a $1,000 initial balance. Withdrawals were made in terms of the percentage of the

initial balance. This withdrawal amount stayed the same. Since the stock and bond returns had been

adjusted for inflation, this simulated maintaining steady purchasing power.

Tested withdrawal rates were 3%, 4%, 5%, 6%, 7% and 8%.

What makes this a linear algebra problem?Randomness

The standard deviation is multiplied each “year” by a lognormally distributed random number as part of a transformation matrix.

This is what makes the model a Monte Carlo process.

Five different portfolio blends?

Six different withdrawal rates?

Four different time spans tested?

Hmm… that comes to 120 different scenarios…

Then I tested each scenario 10,000 times…

100% Stock, 30 Years, 3% withdrawal

Final Portfolio Value is in $10,000 increments

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50/50 Stocks/Bonds, 20 years, 6% withdrawal

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The probability of survival drops to 76%.

50/50 Stocks/Bonds, 20 years, 5% withdrawal

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A 1% reduction in the withdrawal rate increases the probability of success from 76% to 90%.

Suppose you wanted a more conservative

portfolio.

100% Bonds, 25 years, 5% withdrawal rate

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38% of these portfolios did not survive the 25 year time frame.

How Realistic are these

Simulations?

The Trinity Study

“Real Life” Results

Researchers from Trinity University calculated the probability of portfolio survival using actual inflation-adjusted returns of the S&P 500 and Long-Term Corporate Bonds between 1926 and 1995. This is the same data upon which our Monte Carlo simulation was based.

The researchers used a “rolling time period” format. They began with 1926 and counted forward 15 years for one 15-year time period. Then they began in 1927 and counted forward another 15 years, getting another time frame to evaluate.

1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936…

Monte Carlo Simulation Results Simulation Results in Black; Trinity Study Results in Blue

Withdrawal Rate 3% 4% 5% 6% 7% 8%

100% Stocks 15 Years 99 97 93 87 79 70

100 100 88 75 79 70 20 Years 98 93 85 76 66 56

100 100 88 75 63 53 25 Years 95 88 78 67 57 47

100 100 87 70 59 46 30 Years 92 84 73 61 51 41

100 95 85 68 59 41 75% Stock/25% Bonds

15 years 100 99 96 90 81 70 100 100 100 95 82 68

20 years 99 95 87 76 64 51 100 100 90 75 61 51

25 years 97 90 78 65 52 39 100 100 85 65 50 37

30 years 95 85 72 57 44 32 100 98 83 68 49 34

50% Stock/50% Bonds 15 years 100 100 98 93 83 68

100 100 100 93 79 64 20 years 100 97 90 76 60 42

100 100 90 75 55 33 25 years 99 92 79 61 43 28

100 100 80 57 37 20 30 years 96 86 68 50 33 20

100 95 76 51 17 5 25% Stock/75% Bonds

15 years 100 100 99 94 82 64 100 100 100 89 70 50

20 years 100 98 90 73 49 29 100 100 82 47 31 16

25 years 99 93 74 51 28 14 100 93 48 24 15 4

30 years 97 84 60 36 18 8 100 71 27 20 5 0

100% Bonds 15 years 100 100 98 91 74 52

100 100 100 71 39 21 20 years 100 97 84 60 36 18

100 90 47 20 14 12 25 years 98 87 62 35 17 7

100 46 17 15 11 2 30 years 94 73 44 21 8 3

80 20 17 12 0 0

As the length of time we want the portfolio to survive increases, the discrepancy between the model and the Trinity Study also increases. The discrepancy is larger for bonds than for stocks.

As the length of time we want the portfolio to survive increases, the discrepancy between the model and the Trinity Study also increases. The discrepancy is much larger for bonds than for stocks.

100% Stocks vs. 100% BondsMonte Carlo Simulation Results

Simulation Results in Black; Trinity Study Results in Blue

Withdrawal Rate 3% 4% 5% 6% 7% 8%

100% Stocks 15 Years 99 97 93 87 79 70

100 100 88 75 79 70 20 Years 98 93 85 76 66 56

100 100 88 75 63 53 25 Years 95 88 78 67 57 47

100 100 87 70 59 46 30 Years 92 84 73 61 51 41

100 95 85 68 59 41

100% Bonds 15 years 100 100 98 91 74 52

100 100 100 71 39 21 20 years 100 97 84 60 36 18

100 90 47 20 14 12 25 years 98 87 62 35 17 7

100 46 17 15 11 2 30 years 94 73 44 21 8 3

80 20 17 12 0 0

Shortcomings of MC Simulation

Monte Carlo simulations assume independence between each year. In reality, prevailing economic conditions can impact returns for several consecutive years.

Bonds went down five years in a row twice

during this 20 year period.

Value of $1,000 Initial Investment

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

Returns Converge on Assumed

MeanOver shorter time periods, results can vary dramatically. The model shows

only probabilities over large numbers.

TIPS and I-bonds now offer protection against inflation. These improvements aren’t

captured in our historic mean assumptions.

This model considers only two asset classes.

Portfolio survivability can be improved by adding more asset classes.

Many experts believe future equity returns

will be lower than those in the time

period considered.

Where Monte Carlo Simulations Shine

Equity Mutual Fund Expense Ratios

Industry Average: 1.26%

Vanguard Average: 0.20%

Bond Mutual Fund Expense Ratios

Industry Average: 1.08%

Vanguard Average: 0.22%

100% Stocks, 30 years, 5% withdrawal

• Vanguard Industry Ave.• 92% Success Rate 82% Success Rate

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75% Stocks/25% Bonds, 30 years, 5% withdrawal

• Vanguard Industry Ave.

• 84% Success Rate 71% Success Rate

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50% Stocks/50% Bonds, 30 years, 5% withdrawal

• Vanguard Industry Ave.

• 72% Success Rate 55% Success Rate

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25% Stocks/75% Bonds, 30 years, 5% withdrawal

• Vanguard Industry Ave.

• 56% Success Rate 40% Success Rate

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100% Bonds, 30 years, 5% withdrawal

• Vanguard Industry Ave.

• 40% Success Rate 25% Success Rate

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Ignore Wall Street hype

Keep Investing Costs Low

Consider All Your Retirement Assets

Consider Your Willingness and Need to take Risk

MC Simulations can be a valuable part of the process; they aren’t the whole process.