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Safe Withdrawal Rates for Concentrated Portfolios.

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Safe Withdrawal Rates for Concentrated Portfolios.


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This article was posted on June 1, 1999. Revised July 13, 1999

An emerging trend sees investors fleeing mutual funds and purchasing individual stocks and bonds. While this often reduces fees and commissions, some investors are making the switch to place a concentrated bet on a few issues. Is this wise? Can anyone play this game, or should it be left to the young? What does the increased volatility of a concentrated portfolio do to "safe" withdrawal rates in retirement?

From the Motley Fool Bulletin Board:

Screw diversification

Took this slow learner many years to figure this one out. Of the top ten richest people in the US, three got there by holding Microsoft, one Dell Computer, one Berkshire Hathaway and five are from Wal-Mart.

No guts, no glory. Find the best stocks and place your bet.

Another poster observed, "diversification may preserve wealth, but concentration builds wealth." Warren Buffett himself said during an appearance at the University of Washington in 1998 that most people will only see 2 or 3 truly great investment opportunities in thier lifetime. When a good opportunity arises, "it's not the time to be reading a textbook on diversification."

There's no question about it. Investing in an S&P500 index fund means you won't beat the market. Of course, you won't lag the market averages either, like 85% to 90% of professional money managers. But, if you want superior performance, you'll have to buy the lottery ticket of a concentrated portfolio.

Safe Withdrawal Rates for Concentrated Portfolios

The biggest problem that concentrated portfolios pose for retirees is increased volatility. Increased volatility adds risk for an individual looking to withdraw annual distributions from a retirement portfolio. A concentrated portfolio may have superior total returns, but the increased volatility means annual withdrawals must be reduced as a percentage of assets to ensure survivability. This is necessary to insure that a stock market drop doesn't prematurely deplete the portfolio.

Most of the studies on safe withdrawal rates in retirement have used the S&P 500 index as the proxy for the equity portion of the retirement portfolio. However, many retirees prefer to hold a portfolio of individual stocks instead of an S&P 500 index fund. Is it safe to hold a concentrated portfolio in retirement? How does one calculate the "safe" withdrawal rate for a concentrated portfolio?

Diversification vs. Non-Market Risk

Nobel Laureate William F. Sharpe's 1972 paper on "Risk, Market Sensitivity, and Diversification" (Financial Analysts Journal, Jan/Feb 1972, pp. 74-79) appears to be the best place to start in evaluating the "safe" withdrawal rate for a concentrated portfolio. Sharpe derived the formula relating non-market risk to diversification:

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where D = the effective diversification of the portfolio and,

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where V = the relative value of each position in the portfolio, and

R = the relative non-market risk

Beta vs. Non-market Risk

Relative non-market risk, R, is the ratio of the non-market risk of an individual security to the non-market risk of the typical security. Unlike beta values, there is no readily available source for the value of the non-market risk of an individual security. It seems reasonable to assume that securities with greater than average market sensitivity (beta) also exhibit more non-market risk than the typical security. For the purposes of this study, the relative non-market risk of a security is assumed to be equal to its "beta."

While this may seem to be a heroic assumption, "a number of inaccurate estimates for securities may combine to form an exceptionally accurate estimate for a portfolio, thanks to the law of large numbers." As the number of securities in a portfolio increases, so does the accuracy of our estimate of the effective diversification of the portfolio.

Beta values can be obtained from a variety of sources. The most convenient may be The ValueLine Investment Survey available at many public libraries.

Some readers may be familiar with Sharpe's well known plot relating non-market risk to number of securities. It's a graphical representation of 1/(SQRT D) and is reproduced below.

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Sample Calculation

Using Sharpe's formulas, we can calculate the the effective diversification, D, for a $100,000 portfolio consisting of $23,000 in a money market fund and $77,000 in four Dow stocks (i.e., a Motley Fool Foolish Four portfolio.)

Table 1.
Effective Diversification Calculation
Motley Fool Foolish Four
No. Security Current
Value
(V)
Relative
Value
(R)
Beta
(V x R)^2 Comments
1 VMMXX $23,000 0.2300 0.05 0.00013 Vanguard Money Market Fund
2 CHV $19,250 0.1925 0.67 0.01664 Chevron
3 XON $19,250 0.1925 0.75 0.02084 Exxon
4 EK $19,250 0.1925 0.50 0.00926 Eastman Kodak
5 GM $19,250 0.1925 0.88 0.02870 General Motors
- Total $100,000 1.0000 - 0.07557 = Sum(V x R)^2

Effective Diversification, D = 1/(SUM (V x R)^2) = 1/(0.07557) = 13.2

Non-market Risk = 1/(SQRT (D)) = 1/(SQRT 13.2) = 27%

Beta value for Money Market Funds

Note that the non-market risk (which we're calling "beta") for the money market fund is estimated to be 0.05. Some would argue that a money market fund has a non-market risk of zero since it approximates the "risk free rate." However, there is a small risk that a money market fund could suffer a loss independent of the direction of the market (i.e, the default risk), so a nominal beta of 0.05 was chosen.


Safe Withdrawal Rates for Concentrated Portfolios

In using this relationship to examine the safe withdrawal for a concentrated portfolio, four assumptions are made:

  • 1) The safe withdrawal rate for a portfolio with D=50 or more approximates the the safe withdrawal from a portfolio at the "efficient frontier" using the the S&P 500 index as a proxy for the equity allocation. See Table 2. below.

Table 2.
Withdrawal Rates and Survivablity

for portfolios invested at the "Efficient Frontier" using an S&P500 index fund for the stock allocation of the portfolio. Fixed Income portion of portfolio invested in 4 to 6 month commercial paper. Annual expenses assumed to be 0.20% of assets. Survivability was calculated using over 125 years of data from 1871-1998. (From the Retire Early Study on Safe Withdrawal Rates.)
- - Inflation Adjusted Annual Withdrawal
Pay Out
Period
Percent
Stock
(100% Surv.) (95% Surv.) (90% Surv.)
50 yrs. 82% 3.37% 4.28% 4.56%
40 yrs. 77% 3.54% 4.44% 4.82%
30 yrs. 71% 3.81% 4.45% 4.95%
20 yrs. 66% 4.75% 5.26% 5.63%
10 yrs. 44% 7.56% 8.12% 8.65%

Note (1): A portfolio invested at the "Efficient Frontier" contains the mix of stock and fixed income securities that results in the maximum 100% survivable inflation adjusted withdrawal rate for the pay out period selected.

Note (2): Survivability refers to the chance that the portfolio will still contain funds at the end of the pay out period. For a 100% survivable withdrawal rate, there was no pay out period from 1871-1998 in which the portfolio was depleted. A portfolio is 90% survivable if 10% of the pay out periods examined from 1871-1998 resulted in the portfolio being depleted prior to the end of the pay out period.

  • 2) The safe withdrawal rate for a portfolio consisting of a single "high-beta" stock (e.g. "penny stock") approaches zero.

  • 3) The relationship between non-market risk and the safe withdrawal rate is a continuous function.

  • 4) The reduction in safe withdrawal rate is proportional to the increase in non-market risk.

Based on the four assumptions above, the equation for calculating the withdrawal rate for a concentrated portfolio is as follows:

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  • where Wportfolio = the withdrawal rate for a concentrated portfolio and,

  • WS&P500 = the withdrawal rate for a portfolio using the S&P500 as the proxy for the equity allocation of the portfolio and,

  • Rportfolio = the non-market risk for the concentrated portfolio and,

  • RS&P500 = the non-market risk for a portfolio using the S&P500 as the proxy for the equity allocation of the portfolio and,

  • Rmax = the non-market risk for a portfolio of a single "penny stock." It approaches 100%.

This relationship is shown in the plot below. The left hand scale measures non-market risk while the right hand scale shows the corresponding "safe" withdrawal rate for that level of diversification.

[Graph]

Sample Calculation of Safe Withdrawal Rate for a Concentrated Portfolio.

Exercise: Determine the "95% safe" withdrawal rate for a retiree holding the Motley Fool Foolish Four portfolio in the example above. Our retiree has a 40 year pay out period.

  • WS&P500 = the withdrawal rate for a portfolio using the S&P500 as the proxy for the equity allocation of the portfolio (see Table 2., above) = 4.44% = 0.0444

  • Rportfolio = the non-market risk for the concentrated portfolio (i.e, Motley Fool Foolish Four portfolio) = 27% = 0.2749

  • RS&P500 = the non-market risk for a portfolio using the S&P500 as the proxy for the equity allocation of the portfolio. Assume D=50. Then, 1/(SQRT D) = 1/(SQRT 50) = 0.1414

  • Rmax = the non-market risk for a portfolio of a single "penny stock." = 100% = 1.00

Using the Retire Early Safe Withdrawal Formula for Concentrated Portfolios and substituting the known variables:

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Wportfolio = (0.0444)-((0.2749-0.1414) / (1.00-0.1414))*(0.0444) = 0.0375 = 3.75%

Safe Withdrawal Rates for Some Famous Portfolios

Using the Retire Early Safe Withdrawal Formula for Concentrated Portfolios the "100% safe" inflation adjusted withdrawal rate was determined for several "famous" portfolios. Here's the results.

Safe Inflation Adjusted Withdrawal Rates
for Some Famous Portfolios

A 40 year pay out period was assumed, 77% stock/23% fixed income. Fixed Income portion of portfolio invested in 4 to 6 month commercial paper. Annual expenses assumed to be 0.20% of assets. The 77% stock allocation is substituted for the portfolios listed, ranging from an S&P 500 index fund to MSFT stock.)
Click on Portfolio name to see details.
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Portfolio
S&P 500
Motley Fool
Foolish Four
Motley Fool
Rule Maker
Motley Fool
Rule Breaker
Bill Gates'
Portfolio
MSFT
No. of Securities
in Portfolio
500 4 14 12 1
Effective
Diversification
"D"
83.4 13.2 12.9 2.0 1.4
Initial Inflation Adjusted
Annual Withdrawal
.
"100% Safe" 3.54% 2.99% 2.98% 1.17% 0.63%
"95% Safe" 4.44% 3.75% 3.73% 1.47% 0.79%
"90% Safe" 4.82% 4.07% 4.05% 1.60% 0.86%
Note: The actual Motley Fool Foolish Four portfolio (and the Foolish Four portion of the Rule Maker portolio) are not long-term buy and hold investments. The Foolish Four stocks are mechanically changed each year. This presentation does not reflect that yearly change. Also, the Motley Fool portfolios are virtually 100% stock. They do not match the "efficient frontier" mix of stock and fixed income investments used in this analysis.

The most striking result of this tabulation is the comparison of the Foolish Four Portfolio with the Rule Breaker Portfolio. Even though the Foolish Four has 4 stocks and the Rule Breaker portfolio has 12, the effective diversification for the Rule Breaker portfolio is a dismal 2.0. This is because America On-Line (AOL) and Amazon.com (AMZN) make up over 50% of the Rule Breaker portfolio and are high volatility stocks (i.e., "high beta".) The Foolish Four portfolio, in contrast, has low volatility Dow stocks which actually increase the effective diversification of the portfolio.

This table also illustrates the effect of diversification on safe withdrawal rates. Portfolios with large positions in volatile stocks suffer much lower "safe" withdrawal rates. Indeed, a portfolio with a single low volatility Dow stock (e.g., Chevron or Eastman Kodak) is more diversified and offers a higher "safe" withdrawal rate than a portfolio with equal weightings of 7 internet stocks with betas of 2.0 or more.

What are the reasonable conclusions to draw from this?

Diversification is important for a retiree making annual withdrawals from a portfolio. If you decide to maintain a concentrated portfolio in retirement, reduce your annual withdrawal. If you can't survive on the lower withdrawal rate, then you need to diversify.

However, this doesn't mean you should automatically sell all your winners and buy an index fund when you retire. When I ran this calculation on my own portfolio I got a D = 1.8 and a "95% safe" withdrawal rate of 1.27% for a 50 year pay out period. Since I'm spending less than that, I figure I'm O.K. If you can live comfortably on a 1.50% withdrawal rate and don't mind the risk, you can logically (if, perhaps, not safely) hold the Motley Fool Rule Breaker Portfolio in retirement.

The Retire Early Diversification Spreadsheet

Retire Early has developed an easy to use Microsoft Excel spreadsheet for making the "safe" withdrawal rate calculation described in this article.

Download
Retire Early Diversification Worksheet

(rediver.zip, filesize = 7k, expands to rediver.xls, filesize = 22k.)

You will need pkunzip.exe to expand the file once you download it. The instructions for performing and interpreting the diversification calculation appear in the upper left hand corner of the spreadsheet.


filename = concport.html
Copyright 1999 John P. Greaney, All rights reserved.

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