# Monte Carlo

January 1, 2005

By Hank Bulmash

Roger McGuinn is one of the brightest people I know. He was a math major in university. Then he studied engineering and founded his own firm. "I'm planning on retiring in about three years," he told m...

Roger McGuinn is one of the brightest people I know. He was a math major in university. Then he studied engineering and founded his own firm. “I’m planning on retiring in about three years,” he told me over coffee.

“It’s my investments that I’ve been losing sleep over,” he confided. “A few years ago my brokerage firm sent me a retirement calculator. According to their guidelines, I should be in clover.”

“What’s a retirement calculator?”

“You dial in three numbers: (1) the expected rate of return of the investment portfolio, (2) how much you want to withdraw each year, and (3) how many years you expect to live after you retire. Based on those parameters, the calculator tells you how long your money will last. If you take out what your investments earn or less, you should never run out of money. My advisor tells me I should be able to earn 8% on my capital. Therefore if I withdraw 8% or less of my capital, the calculator concludes I’ll never run out of money.

“The problem is, it’s wrong,” Roger continued. “Look what would have happened if I retired five years ago. My portfolio was worth $1,000,000 in 2000. I lost 15% in 2000 and 16% in 2001. Then I earned 7% in 2002 and 12% each in 2003 and 2004.”

“So you lost 31% in the first two years and you gained the 31% back in the next three years.”

“But I didn’t gain it back in full. Assuming no withdrawals or contributions, my portfolio was down to $958,000 after five years.”

“That’s because of the way the percentages work. Losing 15% of $1 million costs you $150,000. Gaining 15% on $850,000 earns you only $127,000.”

“That’s right. So dropping 31% and then earning it back leaves me a little below what I started with — five years earlier. But what’s worse is my retirement scenario. My plan was to withdraw $80,000 a year. If I had done that, in 2004 I would have had a nest egg of only $491,000. By 2014, all my money would be gone.”

“The calculator doesn’t take bad years into account,” I said.

“Exactly. If your retirement begins in a bear market, the plan is compromised. Since statistics show that one out of every three years is bad, the calculator’s assumptions are fatally flawed.”

“What if you reduced your withdrawals to 8% of each year’s opening balance, instead of taking out a flat $80,000 a year.”

“That idea occurred to me. My withdrawals would be forced to drop in lockstep with the balance in my account. At the end of five years, I’d have $626,000 in savings instead of $491,000. Not great, but a real improvement. However, my withdrawals would have dropped to an average of $56,000 per year. It would be hard for us to live on so little.”

“But what’s your alternative?”

“That’s the crucial question, isn’t it? How do I know how much to save now that I’ve discovered these return-on-investment calculators don’t really help? I’ve found one solution. It’s called a Monte Carlo simulation.

“It’s a reminder that life is a gamble,” Roger continued. “The simulation takes the expected rate of return for a portfolio and generates all the annual alternatives that might occur. Over a 30-year period, there are an astronomical number of different outcomes. Monte Carlo calculates how likely you are to achieve your goals. For example, following the brokerage’s suggestions would have given me enough for the rest of my life only 55% of the time.”

“And your advisor thought your money would be enough for you, no matter what,” I said.

“Exactly. So I need more capital if I really need to live on $80,000 per year. Or, if I drop my annual withdrawals to $60,000, my portfolio would last for 30 years, 70% of the time. That’s not a sure thing, but it’s better than the advice I was getting.”

“Another alternative is to invest in a lower risk portfolio.”

“True. If I invested in government securities, I wouldn’t have any losing years. But my return would be only about 3% or 4%. The all-debt portfolio is much safer in the short term — you’ll never lose capital. But it’s risky over the long haul compared to a mixed portfolio of debt and equities. The debt portfolio will earn just a little over inflation.”

“You’re making my future seem a lot less secure,” I said.

“In that case,” Roger said, “I’ve done you a favour, and you should reciprocate.”

“You want me to pay for the coffee?”

“That would be fine.”

*Hank Bulmash, MBA, CA is a principal of Bulmash Cullemore, chartered accountants of Toronto, e-mail: hbulmash@bulmashcullemore.com. Contact him for more details about the Monte Carlo simulation and investment.*