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INSIGHT: Why ‘Risk’ Aversion Should Cause a High Percentage in Stocks

March 16, 2020, 1:00 PM

For most investors, the most relevant definition of “risk” is that of not achieving one’s long-term financial goal. Most individuals will not be able to reach their objective with a portfolio containing entirely Treasury Inflation Protected Securities (TIPS), the only truly riskless asset. Despite the accompanying increase in dispersion, stocks are necessary to increase the dollar amounts of possible “end-point” portfolio values, including the lower-end. Short-term stock market fluctuation actually has an advantageous effect because of rebalancing and dollar cost averaging. Pre-retirement, the portfolio should have a high percentage, possibly 100%, in equities.

After retirement, a fixed-income cushion eliminates or mitigates reverse dollar cost averaging by someone who regularly withdraws the same dollar amount from her portfolio. A retiree or imminent retiree must balance this benefit against the need for stocks’ higher long-run return to avoid the risk of running out of money before death.

A defined-benefit pension, including Social Security, is similar to a fixed-income holding. Someone with an adequate pension has the equivalent of a huge bond investment. The non-pension part of her portfolio should probably be 100% in equities for her entire life. Hereinafter, the term “retiree” refers to a retired individual with a pension benefit (including Social Security) insufficient for her needs.

I shall discuss three alternate definitions of portfolio “risk”: (1) short-term volatility, e.g., daily, weekly, or monthly, (2) dispersion around end-point expected value, and (3) the risk of not achieving one’s financial goal, e.g., paying a child’s college tuition or not running out of money before death.

The definition an investor chooses affects the mix of equities and fixed-income.

Someone averse to short-term portfolio fluctuation (the first definition) would use bonds to dampen volatility. Bonds vary in price less than stocks.

The second definition is dispersion around the portfolio’s “expected value” at the end of the investor’s “time horizon,” e.g., death or the date of a particular expense. I shall call this future time the “end-point.”

End-point “expected value” is the average of the possible portfolio values weighted by their probabilities. The relevant risk is the dispersion of possible values around this “expected value,” the size of the range of possible higher or lower amounts.

To illustrate, suppose the end-point is a child’s college tuition bill. For simplicity, assume this is one lump sum due on a certain future date. To calculate the “expected value” of the portfolio on that day, one would create a table of possible values with accompanying probabilities adding up to 100%: 10% chance of $X, 20% chance of $Y, 15% chance of $Z, etc. The “expected value” would be the weighted average of these values and probabilities—the “average” outcome. The risk is the dispersion or range of these possible outcomes around the “expected value.” The greater the variation, the higher the risk. A mathematical way to measure this dispersion is variance or standard deviation.

A higher ratio of stocks to bonds increases both “expected value” and dispersion around it. Nevertheless, the dispersion of end-point share values should be much lower than their short-term volatility (although, as the end-point approaches, the two should gradually converge). Therefore, using end-point dispersion as the definition of risk will raise one’s ratio of equities to fixed-income.

The third alternative definition of risk is that of not achieving one’s long-term financial objective. A retiree wishes to avoid running out of money before death on an unknown future date. A parent wants enough to pay a child’s tuition.

The second and third definitions of risk are similar, but have the following difference:
(1) The second definition looks at the dispersion around “expected value.”
(2) The third looks at both the dispersion below “expected value” and the level of the lower range of possible future values.

For most, if not all, investors, the third is the most relevant definition. That is the one on which I shall now focus.

TIPS are the only truly risk-free security. With a large enough portfolio consisting entirely of TIPS, the investor can guarantee having a certain real value at a future date (although not necessarily enough to pay for college tuition if it rises faster than general inflation). With a large enough TIPS portfolio relative to spending, a retiree can insure that she will not run out of money even if she lives a long time.

Most individuals have too small a portfolio to reach their goal with 100% in TIPS. Currently, the real yield on TIPS is tiny or negative. Even at a real return of, say, 1%, $1 million in TIPS generates an annual real yield of only $10,000 before any tax.

To increase the likelihood of achieving the objective, the portfolio must contain stocks. An increase in the percentage in equities raises the dispersion below end-point expected value. Nevertheless, the dramatic advantage is the increase in both “expected value” and possible future values below “expected value.” With the third definition of “risk,” risk-aversion causes a higher percentage in equities.

Short term volatility, the first risk definition, actually tends to increase end-point “expected value.” If the investor is an employee who regularly contributes the same dollar amount to a 401(k), short-term fluctuation boosts the benefit of “dollar cost averaging.” By purchasing the same dollar amount each period, the employee automatically purchases more shares when stock prices are low and fewer shares when prices are high. As a result, the average price paid per share is lower than the average share price over time. The total number of shares accumulated is larger.

Short-term volatility also magnifies the advantage of periodic rebalancing. Suppose the employee rebalances at fixed intervals to a target of 60% U.S. stock, 30% non-U.S. stock, and 10% fixed-income. At the end of the period, because of price changes, assume she has 70% in U.S. stock, 28% in non-U.S., and 2% in bonds. To rebalance to her target, she must sell U.S. shares and purchase bonds and non-U.S. stock.

Alternatively, assume that, at the end of the period, she has 50% in U.S. stock, 25% in non-U.S. stock, and 25% in bonds. To rebalance to target, she must sell bonds and purchase U.S. and non-U.S. stock.

Periodic rebalancing forces her automatically to sell high and buy low. The greater the share price fluctuation, the larger the rebalancing benefit.

Assume the employee has no fixed-income and a target of, say, 60% U.S. shares and 40% non-U.S. That has at least two advantages: (1) higher return from stocks rather than bonds, and (2) increased gain from dollar cost averaging.

The effect on rebalancing is mixed. While the volatile components of the portfolio are larger, the employee loses the opportunity to rebalance between shares and fixed-income, especially valuable during a stock market crash

Suppose an employee retires and regularly withdraws the same dollar amount from her portfolio. A danger is that dollar cost averaging would operate in reverse. She might automatically sell more shares when stock prices are low and fewer shares when prices are high.

She can eliminate or mitigate this effect by holding some fixed-income and coordinating withdrawals with frequent rebalancing. For spending, she would withdraw from overweight asset classes; then, she would rebalance to target. To illustrate, suppose she has a target of 60% U.S. stock, 30% non-U.S. shares, and 10% bonds. At the end of a month, she has 58% in U.S. stock, 28% in non-U.S. shares, and 14% in fixed-income. For expenses, she would sell bonds; then, she would rebalance to target.

With short and/or small stock swings, coordinating withdrawals with rebalancing would avoid reverse dollar cost averaging. Nevertheless, long-term and/or substantial moves in opposite directions might still have such an adverse result. During a lengthy and/or severe bear market, she might be forced to sell shares at a low price to replenish the depleted bondholding. An initial larger fixed-income target would create a bigger cushion, which the retiree or imminent retiree must balance against the drawback of bonds’ small, tiny, or negative real return.

In short, “risk” has multiple possible definitions. The one chosen affects the investor’s mix of stocks and bonds. For most, if not all investors, the most relevant definition is the risk of not achieving one’s long-term financial objective.
Most individuals have too small a portfolio to reach their goal with 100% in TIPS, the only truly risk-free security. To increase the likelihood of achieving the objective, the portfolio must contain equities. With the proper definition of “risk,” risk aversion causes a higher percentage in stocks.

Before retirement, short-term volatility is actually beneficial because it increases the advantage of dollar cost averaging and of rebalancing (although a portfolio with no bonds at all is unable to rebalance between fixed-income and equities). After retirement, bonds mitigate the adverse effect of reverse dollar cost averaging. The retiree must balance this advantage against the substantial opportunity cost of losing stocks’ higher long-term return.

This column does not necessarily reflect the opinion of The Bureau of National Affairs, Inc. or its owners.

Author Information

William K.S. Wang is an Emeritus Raymond Sullivan Professor at the University of California Hastings College of Law. Wang is also a member of the investment committee of AccessLex Institute, a nonprofit.