# Back Issues

##### Defining Luck

By: Jim Otar

*While asset allocation is important for large pension funds, it has shortcomings when applied to individual retirement portfolios because of significant differences in the dynamics of cash flow, management costs, investor behaviour, and the luck factor. Jim Otar examines this.*

“Research has shown that asset allocation is the single largest contributor to a portfolio’s success. In fact, one study concluded that asset allocation accounted for more than 90 per cent of the difference in a portfolio’s investment return.”

Different variations of this quote appear in articles, sales brochures, and newsletters in our business. Each time I read it, I imagine myself at an auction and I can almost hear the auctioneer shouting “I have 90 per cent for asset allocation, do I hear 100 per cent!”

What was this research? It is based on the study by Gary P. Brinson, Randolph L. Hood, and Gilbert L Beebower, ‘Determinants of Portfolio Performance II (Financial Analysts Journal, January/February 1995). This was a follow-up study to their original one in 1986.

What did this research encompass? It analyzed data from 91 large corporate pension plans with assets of at least $100 million over a 10-year period beginning in 1974. While this study is important for large pension funds, it has shortcomings when applied to individual retirement portfolios because of significant differences in the dynamics of cash flow, management costs, investor behaviour, and the luck factor.

Each of these elements has a profound effect on the ‘success’ of a retirement portfolio. In engineering terms, a pension fund can be modeled as ‘isobaric’ (constant pressure) whereas an individual retirement portfolio is ‘isentropic’ (constant entropy).

To get a better handle on the different factors affecting the success of a retirement portfolio, we must first redefine ‘success.’

**‘Probability Of Survival’**

I define success as ‘the probability of survival’ of a retirement portfolio. The lower the probability of depletion; the more succ e s s - ful is the portfolio. However, in cases where withdrawals are less than the sustainable withdrawal rate, we can define success as ‘the growth’ of the portfolio.

Let’s start with a specific example.

Sam, 65, is retiring this year. He has saved $500,000 for his retirement. He needs to withdraw $30,000 in the first year of his retirement, indexed to CPI in following years. He wants his money to last until age 90. Assume he is holding a balanced portfolio of 60 per cent fixed income and 40 per cent equities. His equities perform the same as the Dow Jones Industrial Average. Using the actual historic data starting in 1900, I calculate the portfolio life if Sam were to retire in any of the years since 1900.

I then calculate the probability of running out of money by age 90. It works out as 66 per cent.

**The ‘Luck’ Factor**

If I use for all portfolios for each retirement year since 1900 the same asset allocation, the same asset selection, and the same management costs, the only variable is the timing of retirement. If Sam is lucky enough to retire at the beginning of a secular bull market, such as 1949 or 1982, his portfolio will likely be successful. If he happens to retire at any other time period, then it does not matter what he does with asset allocation, he will likely run out of money. I define this as the ‘Luck Factor.’

**The ‘Asset Allocation’ Factor:**

Now, let’s figure out the contribution of the Asset Allocation Factor.

Say Sam makes the wrong asset allocation decision. Instead of the optimum asset mix, he invests all his money into equities. What is the probability of running out of money by age 90? My calculation shows that it increases from 66 per cent to 72 per cent. This ‘wrong’ asset allocation decision costs Sam an additional six per cent in probability of depletion. The contribution of the Luck Factor (66 per cent) is 11 times that of the Asset Allocation Factor (six per cent).

**The ‘Asset Selection’ Factor:**

Say instead of a ‘buy-and-forget’ strategy, Sam follows his mutual funds closely with a disciplined system. He keeps only the best performing equity funds in his portfolio. As a result, the equity side of his portfolio outperforms the benchmark index by four per cent each year.

Sam’s probability of running out of money by age 90 is 35 per cent. Sam’s disciplined asset selection system creates a 31 per cent reduction in the probability of his portfolio’s failure, calculated as 66 per cent minus 35 per cent. The contribution of the Asset Selection Factor (31 per cent) is about five times that of the Asset Allocation Factor (six per cent).

It is important to note that I am not suggesting that one can outperform the index by four per cent merely by paying more attention to the asset selection process. I used four per cent as a possible upper limit only for calculation purposes.

**The ‘Cost’ Factor:**

Over the long term, the cost of portfolio management eats away some of the portfolio growth. Let’s assume that Sam buys an equity mutual fund that underperforms the index by two per cent because of its management expenses (MER).

What is the probability of running out of money by age 90? It is 77 per cent. Thus, the contribution of the Cost Factor is 11 per cent, calculated as 77 per cent minus 66 per cent. This 11 per cent Cost Factor is about twice that of the Asset Allocation Factor.

When we combine these factors so that they add up to 100 per cent, the Luck Factor contributed 58 per cent, the Asset Selection Factor 27 per cent, the Cost Factor 10 per cent, and the Asset Allocation Factor five per cent to the success of Sam’s portfolio. These findings are vastly different from the ‘asset allocation’ anthem of the retail financial industry.

Here are some important observations:

Luck: The contribution of Luck is minimized near the sustainable withdrawal rate. After that, the higher the withdrawal rate, the more important is the Luck Factor.

Asset Selection: The contribution of the Asset Selection is steady up to a six per cent withdrawal rate. After that, the higher the withdrawal rate, the less significant is the Asset Selection Factor.

Management Cost: The longer the portfolio survives, the larger the cumulative management costs over the life of the portfolio. Therefore, the contribution of the Management Cost Factor is steady up to a sustainable withdrawal rate. After that, it is inversely proportional to the withdrawal rate.

Asset Allocation: It peaks near the sustainable withdrawal rate. After that, it sharply declines.

I find peace of mind in recognizing and quantifying the Luck Factor for individual retirement portfolios. In the majority of cases, it is the largest contributor to the success of a retirement portfolio. Regretfully, far too many retirees are blindsided with unrealistic expectations and decide to take out the commuted value of their pensions. Financial planning professionals must tell their clients the truth about luck instead of blindly projecting future portfolio values like a fortune teller, claiming that “more than 90 per cent of success is in asset allocation.”

*Jim Otar is a financial planner, a professional engineer, a market technician, a financial writer, and the founder of www.retirementoptimizer.com.*

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