Portfolio Survival During Retirement

Which will last longer? Your portfolio… …or you?

Steady 5% Earnings, Annual Withdrawals Equal to 7% of Initial Portfolio Value

Does that resemble the real world?

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

Monte Carlo Simulation More in Gear with Reality?

The Model S&P 500 and Long-Term Corporate Bond Returns from 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 >$0 at 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

50/50 Stocks/Bonds, 20 years, 6% withdrawal The probability of survival drops to 76%.

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

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% Bonds

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.

Returns Converge on Assumed Mean Over 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 VanguardIndustry Ave. 92% Success Rate82% Success Rate

75% Stocks/25% Bonds, 30 years, 5% withdrawal VanguardIndustry Ave. 84% Success Rate71% Success Rate

50% Stocks/50% Bonds, 30 years, 5% withdrawal VanguardIndustry Ave. 72% Success Rate55% Success Rate

25% Stocks/75% Bonds, 30 years, 5% withdrawal VanguardIndustry Ave. 56% Success Rate40% Success Rate

100% Bonds, 30 years, 5% withdrawal VanguardIndustry Ave. 40% Success Rate25% Success Rate

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.