Stay Low

By Craig L. Israelsen
Reprinted from Financial Planning Magazine
January 2008

ow correlation between the assets in an investment portfolio is a good thing. This study examines the benefits of low correlation in retirement portfolios during the distribution phase--when a retirement portfolio is in "withdraw mode" as money is being systematically withdrawn. Analyzing portfolio durability post retirement has often been overlooked. In fact, the vast majority of mean-variance research has been based on buy-and-hold portfolios during the pre-retirement accumulation phase. A portfolio in "withdrawal mode" is far more sensitive to portfolio volatility (i.e., account value losses) than a buy-and-hold portfolio.

A fundamental premise of portfolio construction is to utilize assets that have low correlation with each other. A primary benefit of assembling a portfolio with low correlation between the constituent assets is a reduction in the volatility of the overall portfolio returns, which, in turn, reduces the portfolio's standard deviation of return. While this advantageous domino effect may have intuitive appeal, it may be difficult for many investors to put a specific value on. More simply, most investors are probably unable to articulate the material benefits of reducing the standard deviation of their portfolio's returns, though they undoubtedly have a general sense that doing so is a "good thing."

This article examines the aggregate correlation among various assets in a variety of portfolios and the corresponding impact on: portfolio performance as measured by standard deviation of annual returns, internal rate of return, maximum portfolio draw-down in any single year, frequency of loss, and probability of portfolio recovery following a loss. I'm suggesting that three of these measures of portfolio risk-maximum portfolio draw down, frequency of loss, and probability of recovery from a loss-are more intuitively useful to the average investor than is standard deviation of return.

The time frame covered in this study was the 37-year period from 1970-2006. Assets included in this analysis were large-cap US equities, small-cap US equities, non-US equities, US intermediate term bonds, cash, real estate, and commodities (see Table 2). The 37-year historical performance of large-cap US equities is represented by the S&P 500 Index, while the performance of small-cap US equities is captured by using the Ibbotson Small Companies Index from 1970-1978, and the Russell 2000 Index from 1979-2006. The performance of non-US equities was represented by the Morgan Stanley Capital International EAFE Index (Europe, Australasia, Far East) Index. U.S. intermediate term bonds were represented by the Ibbotson Intermediate Term Bond Index from 1970-76 and the Lehman Brothers Intermediate Term Bond index from 1977-2006.

The historical performance of cash is represented by 3-month Treasury Bills. The performance of real estate was measured by using the annual returns of the NAREIT Index (annual returns for 1970 and 1971 were estimated as the NAREIT Index (National Association of Real Estate Investment Trusts) did not provide annual returns until 1972). Finally, the historical performance of commodities was measured by the Goldman Sachs Commodities Index (GSCI). As of February 6, 2007, the GSCI is now known as the S&P GSCI Commodity Index. The primary data source for this study was Morningstar Principia. Raw data were also obtained from "Stocks, Bonds, Bills, Inflation" by Ibbotson Associates.

The bivariate correlations between each asset are reported in "Correlating the Correlations". The aggregate correlation for the entire portfolio (as calculated by computing the average of the 21 bivariate correlations) was 0.128.

As shown in "Risk & Reward", there is a clear correlation between each individual asset's 37-year annualized buy-and-hold return and its worst three-year cumulative percentage return. Higher return comes at the price of a larger worst-case loss. Small cap US equity, for example, had an impressive 37-year average return of over 12%, but also endured a three-year period in which the account value fell by more than 40%. Many investors won't be able to emotionally endure such a loss and will bail out at exactly the wrong time. For that reason, the ultimate goal needs to be risk-controlled asset growth.

Also included in "Risk & Reward" are three portfolios: an equally-weighted portfolio including all seven assets (shown by the black square); a 40% large stock/60% fixed bond portfolio (plum square); and a 60% large stock/40% bond portfolio (bright blue square). The 40/60 portfolio is a common asset allocation model among "conservative allocation" funds, such as Vanguard Wellesley Income or Franklin Income. The 60/40 portfolio is typical among "moderate allocation" funds, such as Vanguard Wellington or Dodge & Cox Balanced. The equal-weighted seven-asset portfolio had an allocation of 42% equities, 29% fixed income, and 29% in "alternative" assets.

Among the stand-alone assets (the dots), there is a clear pattern between higher annualized return and larger losses. The benefit of creating diversified portfolios is demonstrated by the location of the squares. For example, the 7-asset portfolio (black square) and the 40/60 portfolio (plum square) eliminated a cumulative loss over any three calendar-year period during the 37-year time frame of this study--while still maintaining a level of performance that was comparable with the individual equity assets. As expected, the 60/40 portfolio had a higher return than the 40/60 portfolio (by 63 bps), but at the price of experiencing a much larger three-year loss (-13.9% vs. -0.40%). The modest additional return in the 60/40 portfolio (relative to the 40/60 portfolio) comes at a high price. Best of all, the seven-asset portfolio produced an average annualized return of 11.5% and a worst-case three-year loss of +2.09%.

Asset allocations of 100% in bonds or 100% in cash eliminated large portfolio losses over any three-year period, but the performance of bonds or cash was significantly lower than individual equity assets and the three portfolios. Without sufficient portfolio growth, the likelihood of outliving one's retirement portfolio obviously increases. Thus, the classic risk/return tradeoff can, in large part, be successfully dealt with through portfolio diversification rather than hibernating in cash.

Finally, we examine a portfolio in the post-retirement distribution phase (i.e., a withdrawal portfolio). A starting balance of $500,000 is assumed, with an initial withdrawal at the end of the first year of 5% of the starting portfolio balance (in this case, $25,000), and an annual increase in the withdrawal of 3% to account for annual inflation. Thus, the second year withdrawal in this analysis was $25,750, the third year withdrawal was $26,523, and so forth. (There are many opinions about an appropriate withdrawal rate. The 5% rate used here is illustrative, rather than prescriptive).

The step-by-step results of building increasingly diversified portfolios (and thereby achieving successively lower correlation within the portfolio) are shown in "The Correlation Scorecard". The most dramatic impact occurs when adding commodities as the seventh asset class. This multi-asset portfolio (the black square in "Risk & Reward") was comprised of large US equity, small US equity, non-US equity, US Int. term bonds, cash, REITs, and commodities--each asset having a portfolio weighting of 14.3%.

The 7-asset portfolio had the highest IRR (11.25%), the lowest standard deviation of return (8.67%), the lowest aggregate correlation (.128), the smallest maximum one-year draw-down (-10.2%) and a zero frequency of a 10% loss (as measured by IRR) over one, two, and three-year periods. (The -10.2% maximum portfolio draw-down is, by necessity, calculated differently than IRR).

The location of the 7-asset portfolio in "Seeking the Northwest Corner" is significant inasmuch as the upper left hand corner represents the ideal combination of risk and return. In this case, the Y-axis represents the 37-year IRR of each portfolio during the withdrawal phase, whereas the X-axis shows the worst single % loss in the portfolio during the 37-year withdrawal period.

In a withdrawal portfolio, the probability of recovery from a 10% loss within 3 years is lowest in the five-asset and seven-asset portfolios (54.3%), but the margin of difference is slim between the highest probability of 62.9% and the lowest at 54.3%. The key point here is that highly diversified portfolios with low aggregate correlation tend to avoid losses, which essentially negates the need for a high recovery probability. In sum, the probability of recovery from a 10% loss within three years is slightly lower in the more diversified portfolios, but the frequency of 10% or higher losses is essentially eliminated.

In addition to reducing the volatility of year-to-year performance (as observed by the fact that the seven-asset portfolio had the second lowest standard deviation of return), what are the additional benefits of a low correlation portfolio?

With reductions in correlation and standard deviation of return come dramatic reductions in the worst-case single year portfolio draw-down. The maximum portfolio draw-down was reduced by 67%, from -30.8% in a two-asset portfolio to -10.2% in the seven-asset portfolio. Moreover, the likelihood (or frequency) of experiencing a portfolio loss was reduced in portfolios with lower aggregate correlation. Both of these issues-reduced magnitude of loss as well as reduced frequency of loss-are important to all investors, but particularly to retirees in withdrawal mode for whom the mathematics of recovery following a portfolio loss are much more demanding.

The raw performance of each portfolio in "The Correlation Scorecard" was surprisingly consistent as each additional asset was included. In fact, given the assets used in this analysis and the sequencing of their inclusion, greater diversification ultimately enhanced performance (particularly when adding the sixth and seventh assets--REITs and commodities). However, the real benefit of adding each additional asset to the retirement portfolio was a substantial reduction in portfolio volatility (as measured by standard deviation of return), improved loss protection (as measured by worst case single year portfolio draw-down), and a lower frequency of loss.

Some may correctly suggest that several of the portfolios do not represent sensible retirement portfolios because of their modest exposure to bonds. Agreed. To address this issue, consider the last two portfolios in the table-a "conservative allocation" 40/60 portfolio and a "moderate allocation" 60/40 portfolio.

Compared to the 40 equity/60 bond portfolio, the seven-asset portfolio had a 190 bps higher IRR (11.25% vs. 9.35%) while only increasing the volatility of return by 56 bps-unlikely to be noticed by even the most fastidious investor. Perhaps more importantly, the probability of recovery from a 10% loss is considerably higher in the seven-asset portfolio (54% vs. 37%) and the worst case single-year portfolio draw-down is lower (-10.2% vs. -12.2%). The frequencies of large losses over one, two, and three-year periods are essentially zero for both portfolios.

The seven-asset portfolio also shines against the 60 equity/40 bond portfolio as evidenced by a 155 bps higher IRR, a 211 bps lower standard deviation of return, a slightly higher probability of recovery from a 10% loss within three years, a significantly lower maximum one-year drawdown (-10.2% vs. -18.9%), and marginally better loss frequencies.

In summary, there are several quantifiable benefits of lowering the correlation of a retirement portfolio's component assets. First, there is a dramatic reduction in the volatility of the portfolio's performance (i.e. lower standard deviation of return). Second, there is a significant reduction in the worst-case portfolio loss, or maximum portfolio draw-down. Third, the likelihood (or frequency) of loss is minimized. Fourth, performance does not suffer if sufficient diversification is achieved.

This study suggests that maximum portfolio loss, frequency of loss, and probability of recovery following a loss are quantifiable measures of the benefits of low portfolio correlation. Furthermore, this study suggests that these three measures may have greater intuitive appeal to investors than standard deviation of return.

Avoiding large losses is of paramount importance during the distribution phase of a retirement portfolio. Achieving low correlation among the assets in a portfolio-a key to avoiding large losses-requires the use of a variety of assets with low correlation. Some of the needed assets may not fit the standard paradigm of a traditional retirement portfolio, namely commodities and REITs.

At least one caution is in order. The time frame of this analysis (1970-2006) was a period of robust returns across the board. Equities averaged annual performance in excess of 11%, intermediate bonds averaged over 8%, commodities generated a 37-year average annual return of over 11%, and REITs had nearly a 13.5% annualized return. These levels of performance may not persist. Nevertheless, the benefits derived from building low correlation portfolios-particularly during retirement-will always be in demand regardless of the performance level of various assets.

Correlating the Correlations

Risk & Reward

The Correlation Scorecard

Equally-Weighted Assets in Withdrawal Portfolio   ($500,000 starting balance, 5% withdraw rate, 3% inflation rate of annual withdrawal)	37-Year IRR  (%)   1970-2006	37-Year Standard Deviation of Annual Returns  (%)	Aggregate Portfolio Correlation	Probability of Recovery from a 10% Loss Within 3 Years (%)	Worst Case Single Year  Portfolio Draw-Down (%)a	Frequency of a  One-Year Loss of 10% or worse (%)b	Frequency of a Two-Year  Cumulative Loss of 10% or worse (%)	Frequency of a Three-Year Cumulative  Loss of 10% or worse (%)
Two-Asset Portfolio Large US Equity, Small US Equity (50% each)	10.74	18.03	.738	62.9	-30.8	10.8	11.1	8.6
Three-Asset Portfolio  Large US Equity, Small US Equity, Non-US Equity (33.33% each)	10.94	17.18	.599	60.0	-29.8	13.5	8.3	8.6
Four-Asset Portfolio Large US Equity, Small US Equity Non-US Equity, US Int. Term Bonds (25% each)	10.60	13.04	.416	60.0	-22.0	8.1	5.6	5.7
Five-Asset Portfolio Large US Equity, Small US Equity, Non-US Equity, US Int. Term Bonds, Cash (20% each)	9.96	10.45	.211	54.3	-16.9	2.7	5.6	2.9
Six-Asset Portfolio Large US Equity, Small US Equity, Non-US Equity, US Int. Term Bonds, Cash, REIT (16.67% each)	10.38	10.61	.258	57.1	-18.8	5.4	2.8	2.9
Seven-Asset Portfolio Large US Equity, Small US Equity, Non-US Equity, US Int. Term Bonds, Cash, REIT, Commodities (14.3% each)	11.25	8.67	.128	54.3	-10.2	0.0	0.0	0.0
40/60 Conservative Allocation Portfolio 40% Large Stock 60% Intermediate Bond	9.35	8.11	.221	37.1	-12.2	0.0	2.8	0.0
60/40 Moderate Allocation Portfolio 60% Large Stock 40% Intermediate Bond	9.70	10.78	.221	51.4	-18.9	2.7	5.6	2.9

Seeking the Northwest Corner

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Craig L. Israelsen, Ph.D., is an Associate Professor at Brigham Young University and Principal at Target Date Analytics, LLP (www.TDBench.com).