Asset Allocation: The Re-Balancing Act

by Craig L. Israelsen
University of Missouri-Columbia

From Financial Planning Magazine, June 2001. Reprinted with permission.

sset allocation, as the phrase is typically used, refers to an investment strategy which integrates two or more different types of assets into an investment portfolio. Ideally the performance histories of the different assets are not highly correlated. Question: Is the allocation decision a one time event, or a periodic one? While there is probably not a "correct" answer, this article suggests that asset allocation is a periodic decision. Specifically, this analysis examines how the assets in an "allocated" portfolio might benefit from annual rebalancing.

The term rebalancing implies a management protocol in which at the end of a certain time period (annually, for example) the amount of money in each asset within a portfolio is either equalized or brought back to a pre-determined percentage of the total portfolio. This is accomplished by withdrawing money from the asset(s) which performed best (or least poorly) and investing it into the account(s) of the asset(s) which performed poorest (or least best). Figure 1 demonstrates the process involved in annual rebalancing. As can be seen, it "forces" one to periodically "sell high and buy low." To avoid the burden of taxation in the current period, this approach is best suited for assets in a tax-deferred accounts, such as IRA's, 401(k), or 403(b) accounts.

The portfolio in Figure 1 has an investor allocate money between large cap U.S. stock, small cap U.S. stock, and non-U.S. equities. The three separate assets had varying success in year 1 (using hypothetical results). The process of rebalancing at the conclusion of the first year required that $78 be withdrawn from the large U.S. stock account and $13 from the small U.S. stock account and invested into the international stock account, thus equalizing the amount of money in each asset at the beginning of year 2. This simple example represents one type of asset allocation model which would necessitate repeated "allocation" decisions.

The particular portfolio being illustrated was chosen because of the relatively low historical correlation between the three assets (see Figure 2). The 31 year correlation between large domestic stock and small domestic stock is .67. A coefficient of 1.0 indicates perfect correlation, such as would be the case between a S&P 500 Index fund and the S&P 500 Index itself. So, a correlation of .67 indicates a moderate correlation. The 31 year correlation of non-U.S. stock with U.S. large cap stock is .51, and between U.S. small cap stock and non-U.S. stock it is .37 - both relatively low correlations.

Assets with low correlation to each other tend to have contrasting performance from year to year. The pistons of an engine do not all move in the same direction at the same time, which is highly beneficial. It is precisely because the pistons fire in different order that the engine can produce power. In like manner, the contrasting performance of different assets from year to year can be beneficial in a portfolio. But, what is the benefit - better return or a reduction in volatility?

Figure 1. The Mechanics of Annual Rebalancing

Figure 2. Correlation of Annual Returns from 1970 - 2000

	Large U.S. Stock Account	Small U.S. Stock Account	International Stock Account	Total Value of Portfolio
Start of Year 1	$1,000	$1,000	$1,000	$3,000
Return in Year 1	14.5%	8.0%	-2.4%	6.7%
Value at End of Year 1	$1,145	$1,080	$976	$3,201
Value at End of Year 1	$1,145	$1,080	$976	$3,201
$3,201 portfolio value at the end of Year 1 $3,201 � 3 accounts = $1,067 per account at start of Year 2
Needed Rebalancing Action at End of Year 1	Withdraw $78	Withdraw $13	Deposit $91
Rebalanced Account Values at Start of Year 2	$1,067	$1,067	$1,067	$3,201

	Large U.S. Stock	Small U.S. Stock
Small U.S. Stock	.67	--
International Stock	.51	.37

Large U.S. Stock: S&P 500 Index
Small U.S. Stock: Ibbotson Small Company Stock (DFA U.S. 9-10 Small Company Fund)
International Stock: Morgan Stanley Capital International Europe, Australasia, Far East Index (EAFE)

Within an asset allocation model which utilizes annual rebalancing the goal may be both return enhancement and risk minimization. For example, as seen in Figure 3, over the 31 year period from 1970 to 2000 large cap U.S. stock (i.e. the S&P 500 Index) produced an average annual return of 12.9%, small cap U.S. stock (Ibbotson Index) averaged 13.5% per year, and non-U.S. stocks (EAFE Index) had an annual average return of 12.2%. An asset allocation model of 33% large U.S. stock, 33% small U.S. stock, and 34% non-U.S. stock had, over the same time frame, an average annual return of 13.4%, which represents a return enhancement compared to large U.S. stock and non-U.S. stock. Moreover, the 33/33/34 portfolio generated its return with less risk (as measured by standard deviation) than either U.S. small cap stock or non-U.S. stock. Hence, over a relatively long time period, an asset allocation model utilizing annual rebalancing generated a return equal, or superior to, the individual investment assets but with comparable or lower risk than any individual component.

Over the ten year period from 1991 - 2000 the annually rebalanced portfolio produced an average annual return which was inferior to a sole investment in either large U.S. stock or small U.S. stock. During the 5 year period ending in 2000, the rebalanced portfolio's return was significantly lower than a 100% position in U.S. large cap stock. However, in both the 5 and 10 year periods, the level of risk in the 33/33/34 portfolio was lower than any of the separate assets individually. It may be that performance enhancement is not the compelling feature of asset allocation (or annual rebalancing) but rather the potential for a significant reduction in portfolio risk as measured the volatility in year to year return (which corresponds directly with account value fluctuation).

This conclusion is verified by the data in Figure 4. Let's look at the data in the 31 year period column. An single initial investment of $333 in 1970 in large U.S. stock grew to a value of $14,334 by the end of 2000 (with no additional money invested and no withdrawals during the 31 year period). Likewise, $333 invested in small U.S. stock in 1970 became $16,918 by 2000, and $334 invested in non-U.S. stock grew to be $11,709. The combined total of the three assets by the end of 2000 was $42,961. By comparison, $1,000 invested into the 33/33/34 portfolio in 1970 with annual rebalancing to keep each asset at its original percentage of the portfolio had an ending value of $49,496 by 2000. This represents a $6,535 improvement relative to investments in each asset separately. Moreover, the portfolio with annual rebalancing had 18.5% less year to year return volatility than the average standard deviation of the three separate accounts. Over the ten and five year period the dollar gain from an annually rebalanced asset allocation portfolio was slightly negative, but in both cases provided sizable reduction in overall risk.

As the last 3 quarters have reminded us, investors can quickly forget about 9 good years in the wake of 9 bad months. Asset allocation can serve the important function of dampening the downside risk without unduly penalizing return. Said more bluntly, if you don't help clients allocate assets according to a logical plan as they get on board, they'll very likely push to reallocate assets illogically during the storm (i.e. panic mode selling). Moreover, by setting a pattern of rebalancing every year clients become accustomed to skimming profits off winners and depositing them into laggards. From this perspective, it's possible clients may look at poorly performing assets in a more positive light - specifically as a buying opportunity. Perhaps most importantly, asset allocation (from a client's perspective) becomes a pro-active management pattern, rather than a reactive, asset-rotation shell game.

Figure 3. Investment Synergy: The Benefit of Re-Balancing

Year	Large Stock S&P 500	Ibbotson Small Company Stock	International Stock EAFE Index	PORTFOLIO 33% Large 33% Small 34% Intl
1970	4.0%	-17.4%	-10.5%	-8.0%
1971	14.3%	16.5%	31.2%	20.8%
1972	19.0%	4.4%	37.6%	20.5%
1973	-14.7%	-30.9%	-14.2%	-19.9%
1974	-26.5%	-20.0%	-22.2%	-22.9%
1975	37.2%	52.8%	37.1%	42.3%
1976	23.8%	57.4%	3.7%	28.1%
1977	-7.2%	25.4%	19.4%	12.6%
1978	6.6%	23.5%	34.3%	21.6%
1979	18.4%	43.5%	6.2%	22.5%
1980	32.4%	39.9%	24.4%	32.2%
1981	-4.9%	13.9%	-1.0%	2.6%
1982	21.4%	28.0%	-.9%	16.0%
1983	22.5%	39.7%	24.6%	28.9%
1984	6.3%	-6.7%	7.9%	2.5%
1985	32.2%	24.7%	56.7%	38.0%
1986	18.5%	6.9%	69.9%	32.2%
1987	5.2%	-9.3%	24.9%	7.1%
1988	16.8%	22.9%	28.6%	22.8%
1989	31.5%	10.2%	10.8%	17.4%
1990	-3.2%	-21.6%	-23.2%	-16.1%
1991	30.5%	44.6%	12.5%	29.0%
1992	7.7%	23.4%	-11.9%	6.2%
1993	10.0%	21.0%	32.9%	21.4%
1994	1.3%	3.1%	8.1%	4.2%
1995	37.4%	34.5%	11.6%	27.7%
1996	23.1%	17.6%	6.1%	15.5%
1997	33.4%	22.8%	1.8%	19.1%
1998	28.6%	-7.3%	20.0%	13.8%
1999	21.0%	29.8%	27.0%	25.9%
2000	-9.1%	-3.6%	-14.2%	-9.0%
Between 1970 and 2000 $1,000 grew to...	$43,046	$50,803	$35,058	$49,496
31 YR AVE ANNUAL RETURN	12.9%	13.5%	12.2%	13.4%
31 YR STANDARD DEVIATION	16.0%	22.3%	21.5%	16.3%
Between 1991 and 2000 $1000 grew into...	$4,997	$5,015	$2,244	$3,974
10 YR AVE RETURN	17.5%	17.5%	8.4%	14.8%
10 YR STANDARD DEVIATION	14.5%	15.8%	14.4%	11.4%
Between 1996 and 2000 $1000 grew into...	$2,321	$1,675	$1,412	$1,795
5 YR AVE RETURN	18.3%	10.9%	7.1%	12.4%
5 YR STANDARD DEVIATION	15.2%	15.9%	13.2%	12.1%

Figure 4. The Re-Balancing Act

	31 Year Period 1970 to 2000 Ending Account Value	10 Year Period 1991 to 2000 Ending Account Value	5 Year Period 1996 to 2000 Ending Account Value
$333 Invested in Large Stock	$14,334	$1,664	$773
$333 Invested in Small Stock	$16,918	$1,670	$558
$334 Invested in Intl Stock	$11,709	$750	$472
Summed Value of Three Separate Accounts	$42,961	$4,084	$1,803
$1,000 Invested in 33/33/34 Portfolio with Annual Rebalancing	$49,496	$3,974	$1,795
Benefit from Annual Rebalancing	$6,535	$-110	$-8
Reduction in Volatility of Annual Returns from Annual Rebalancing	18.5% less volatility	23.5% less volatility	17.7% less volatility

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