Quant View -- Investing by the Numbers -- Archives: March '04 Stating the Obvious

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March 2004
What was
the Best Allocation

"I could have had class. I could have been a contender."
--Budd Schulberg
On the Waterfront (film, 1954)

 

UY AND HOLD INVESTING DOESN'T get a lot of positive press these days. With more and more information so easily accessible, volatility has been on the rise and short-term strategies have taken the forefront. Indeed, it's often argued that buy and hold is strategy that no longer works in the current environment.

Nevertheless, many investors still adhere to the buy and hold approach. That's a good thing since many people are reluctant investors anyway. Their employer may force them to handle their own retirement savings through their 401(k) or they may make an effort to save for their children's college education, but for most it's certainly not a chore they'd seek on their own. For them, buy and hold is the easiest and most effective strategy.

So given that buy and hold is here to stay, is there one "best" mix for the long-term investor? We thought we'd find out.

You've Got to Have Class

As with any enterprise like this, it's necessary to start with a few assumptions. First and foremost, while there may have been a "best mix" of individual assets, with thousands to choose from, it would certainly be impossible to find it. It's much more reasonable to seek the best combination of classes of assets such as large company stocks and government bonds.

That's the way we framed our search. Since buy and hold is favored by small investors, we only included potential holdings they would actually use in their portfolios.

Based on a second assumption that most investors are relatively conservative, we narrowed the list of potential holdings by eliminating things such as commodities, real estate, and even junk bonds. While these are fine assets, they aren't often found in 401(k)s or small investors' portfolios. Archive Index

Instead, they usually gravitate towards plain vanilla holdings such as intermediate term government bonds, long corporate bonds, large domestic stocks, small domestic stocks, and stocks of companies in developed foreign countries. These, therefore, are the five classes we considered.

To represent them, we used Ibbotson data for the Lehman Intermediate Government Bond Index, the Lehman Aggregate Bond Index, the S&P 500, the Russell 2000, and the MSCI EAFE Index, respectively. The common start date for these series was January 1978, so there was 25 years of data.

You might find the next assumption a little more debatable. Despite adhering to a buy and hold strategy, we didn't assume investors don't trade, but rather that they periodically rebalance. In other words, while they don't jump in and out of hot stocks, they do occasionally trim their winners and add to their losers to keep their portfolio in line -- at least they should.

This is an important assumption since without it, all we'd be doing is backtesting for what would have been the best mix on January 1, 1978, not the best ongoing allocation. More on why this is so important in a moment.

How often do investors rebalance? There's no set timeframe, so we picked one: annually. Even the most conservative buy and hold investor looks at his or her portfolio at least once a year whether it's at year-end, during tax preparation, or on some other yearly occasion. For our purposes here, we chose to assume year-end rebalancing.

Finally we assumed that investors using the buy and hold approach are not big risk-takers. By the same token, they aren't totally risk-averse, either. In other words they aren't necessarily looking for the highest return but rather a comfortable balance between risk and return.

A Point on a Line

Armed with these assumptions, it's possible to use the historical index data to come up with a group of efficient portfolios and then narrow them down to the "best" asset allocation. To do this, we fed the Ibbotson data into a mean variance optimizer to create a frontier of efficient portfolios.
Chart 1
THE EFFICIENT FRONTIER
1979 - 2003

Graph -- Efficient Frontier, 1979 - 2003
Data Source: Ibbotson Associates

In plain English, the optimizer shows what asset mix would have produced the highest return for each level of risk. At this point, there's not one, but a whole range of efficient portfolios tied to varying levels of risk. If you line them all up, you get the red line shown on Chart 1.

Each of these portfolios is a combination of the five asset classes shown on the chart. Not every portfolio uses all five, but they could have.

The portfolios falling along the frontier (red line) are "efficient" because any other mixes will not produce as high a level of return without additional risk. In other words, other mixes will fall below the frontier, yielding less return and/or greater risk.

Extremely conservative investors would create portfolios with low risk falling along the lower left regions on the frontier. More aggressive investors would be comfortable with higher levels of risk and would seek mixes towards the right end of the frontier.

In assuming the average buy and hold investor is not overly conservative or aggressive, it's reasonable to assume he or she would be comfortable somewhere in the middle of the frontier. Given this, the midpoint on the frontier has a standard deviation of .1227 and a corresponding historical annual return of 14.59%.
Chart 2
THE "BEST" MIX

Graph -- The 'Best' Mix, 1979 - 2003
Source: Quantview

Chart 2 shows the components of this optimum mix. Four of the five potential holdings are utilized. Only the most conservative, intermediate term government bonds, is excluded. (This is interesting since it lends further support to our earlier research regarding the use of government bonds in portfolio construction.)

The overall split is 75% stocks, 25% bonds. Based on our work on loss-aversion and time horizons, this looks like the appropriate mix for an investor with a 16 to 17-year investment horizon. That's consistent with buy and hold investors who traditionally take a long-term approach.

It's not too surprising that intermediate government bonds aren't included in the mix. The Lehman Aggregate Bond Index includes some government bonds and its average maturity and duration aren't too different from the Lehman Intermediate Government Bond Index. Although the two plot differently on Chart 1's efficient frontier, intermediate government bonds are only included in the most conservative portfolios.

The 6% holding in foreign stocks isn't something we would have normally included. This isn't because of an aversion to foreign stocks, but rather because of the small percentage.

Positions that are less than 10% of the overall mix usually have minimal (if any) impact on overall portfolio performance. Still, the MSCI EAFE series has a relatively low correlation with domestic bonds, and this was obviously enough for the optimization process to include it.

From a behavioral standpoint, a 6% foreign holding also makes sense. Many investors believe enough in the benefits of diversification that they want to hold at least some foreign stocks -- just not too many. Six percent is a level that can satisfy this desire without making a buy and hold investor uncomfortable.

Actual Results

The comfort level is important for buy and hold investors. If you're planning to build a portfolio to hold for years to come, you don't want to agonize over the short-term twists and turns of the market. The "Best" Mix seems to fill the bill.

The 14.59% average annual return may make it appear risky, but don't get carried away by that number. Remember it's based on the period 1979-2003, a period generally viewed as above-average for equities. Also remember the risk level is at the midpoint of the efficient frontier so it's hard to call it excessive.

In fact, we'd suggest the risk level is more important that the potential return for buy and hold investors. In general, they'd be willing to forego the potential for market-beating returns in order to maintain acceptable levels of risk.
Chart 3
ANNUAL RETURN HISTORY
1979 - 2003

Graph -- 'Best' Mix Return Histogram, 1979 - 2003
Source: Quantview

Buy and hold investors aren't totally risk averse. Like most investors, they have an asymmetric attitude toward risk: They don't mind it when it yields above average returns, but they shun it when it results in below average returns -- especially losses. (For a detailed explanation of "good" and "bad" risk, click here.) In other words, they aren't risk averse, they're loss averse.

Given this, the "Best" Mix is certainly something buy and hold investors can handle. Chart 3 is a histogram showing the number of its annual returns falling within 5% ranges. As you can see, of the 25 years, only five ended with negative returns. Of these five, only one -- 2002 -- was down more than 5%.

The return profile is definitely skewed toward positive results (although statistically, it's said to be negatively skewed). Six years saw returns in the 15-20% range while eight were in the 20-30% range.

So what do the annual returns look like? For the period 1979-2003, the average return was 14.6% with the best occurring in 1985 (+30.9%) and the worst in 2002 (-13.3%). With a standard deviation of 12.2%, returns should fall within the range of +2.3% to + 26.7% 68% of the time.

Again, it's important not to put too much weight on the actual return numbers since the measurement period was uncommonly good for stocks. What is significant is the fact that at least historically, returns from this portfolio are much more likely to be positive than negative. That's certainly a comfort for anyone employing a buy and hold strategy.


Chart 4
HISTORICAL PERFORMANCE vs. BENCHMARKS
1979 - 2003


1 Year 3
Years
5
Years
10
Years
15
Years
20
Years
25
Years
Bear Market
2000-2002
"Best Mix" Portfolio 26% 5% 18% 154% 371% 826% 1,952% -19%
LB Int. Govt. Bond 0% 19% 32% 81% 196% 395% 747% 31%
LB Aggregate Bond 3% 23% 37% 94% 231% 495% 851% 33%
S&P 500 28% -12% -4% 183% 458% 1,041% 2,431% -38%
Russell 2000 47% 20% 41% 146% 374% 594% 2,164% -21%
MSCI EAFE 39% -8% 1% 59% 79% 724% 1,231% -43%
Source: Quantview

Chart 4 shows the historical returns for the "Best Mix" vs. the benchmarks from which it is derived. It's important to note that they are derived by rebalancing the portfolio back to the target mix at the beginning of each year.

To see why this is important, look back at Chart 1. The green line shows the efficient frontier for unrebalanced portfolios. In other words, if you were a true buy and hold investor who never rebalanced your portfolio once you established it back in 1979, this would be your efficient frontier.

The fact that it lies below the efficient frontier for rebalanced portfolios demonstrates the benefits of periodic rebalancing. This is why annual rebalancing is one of the major assumptions underlying the "Best Mix" portfolio.

Looking at Chart 4, there aren't really any surprises. The "Best Mix" portfolio is a combination of stocks and bonds, so lags behind equities when stocks do well (1, 15, 20, and 25-year periods) while beating the bond series. The opposite holds when bonds outperform (3 and 5-year periods).

With the mix tilted towards stocks, it suffered a 19% loss during the 2000-2002 bear market. As you'd expect, its diversification cushioned it relative to equities, but not enough to avoid a loss. This shouldn't trouble buy and hold investors since they look to much longer investment horizons than a mere three years.

Two other things stand out in these returns. First, the "Best Mix" portfolio compares well with the all-stock S&P 500 over the 1, 3, 5, and 10-year periods. Perhaps most importantly, it does this with much less volatility and risk. So much for the belief that long-term investors should be 100% in stocks.

The second thing to notice is how the mix compares to the bond series, especially for periods of 10-years and up. Many conservative investors completely shun stocks, seeking the safety of bonds. For the buy and hold investor willing to rebalance every year, the "Best Mix" portfolio provides substantially greater returns without significantly increasing risk. That's something to think about, especially when you're building a portfolio for the long-term.

Contrary to popular myth, buy and hold investing is not dead and it's not likely to go away, either. Investors wishing to use this approach need to adopt a rational strategy like the one described here. The numbers speak for themselves.

* * *

This really is a strategy you can put to use. All you need to do buy the four proxies for large cap domestic stocks, small cap domestic stocks, foreign stocks, and domestic bonds. We'd recommend using S&P Depositary Receipts (SPDR) for the S&P 500 trading under the symbol SPY. The other series can be represented by iShares, IWM, EFA, and AGG, respectively.

These are all exchange traded funds, known as ETFs. They track their respective benchmarks, have very low management fees, and are truly good proxies. All are listed on the American Stock Exchange and can be traded throughout the day, not just at the close like index mutual funds. Since they trade like stocks, you must pay a commission each time you trade. However, if you follow the regimen of only rebalancing once a year and use a discount broker, this portfolio could actually end up costing less than a collection of index mutual funds.

If you periodically add to your portfolio or if you're systematically dollar cost averaging, you should consider using low-cost no-load index funds such as those offered by Vanguard. Don't make the mistake, however, of using managed funds since they often stray from their stated objectives.

We'll be periodically reporting the "Best Mix" portfolio performance since it will be used as a benchmark for comparison for an actively rebalanced portfolio we'll be launching in May 2004.



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