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The perfect portfolio » PRINT

By Jeff Merriman-Cohen
August, 2003

Great chefs know that it takes more than the right ingredients to make an outstanding meal. If you put everything together in just the right way, ordinary ingredients can turn into magic. In this article, Jeff Merriman-Cohen shows how the same thing is true for investing.

The ideal portfolio may be different for every investor, but that doesn't mean there are 150 million perfect variations.

Nevertheless, based on the Suggested Portfolios on our Web site and the strategies we manage for clients, there are probably at least 60,000 combinations that could qualify.

How can an investor choose the right one?

In this article, I'll walk through the steps I use when I'm meeting for the first time with a client. I hope this will give you some good ideas on how to put together a combination that's just right for you.

The first conversation I have with any new client is about risk. It's the most basic part of investing, the topic that most of the industry (and most investors) would be happy to avoid altogether.

Let me be blunt about this: Investors who don't understand risk can't understand the decisions and choices they must make.

I ask the client to imagine that he (or she) is in a bank applying for a loan. Soon you realize that at the next desk, Bill Gates is also applying for a loan. Which borrower is likely to be more attractive to the bank? Bill, of course.

The bank would always rather lend its money to him than lend it to you, because there is simply no question about his ability to pay the money back. He's as close to a risk-free borrower as the bank could have.

But Bill Gates is not the sort of person who would hesitate to take advantage of his position. If he told the bank he wouldn't pay more than 3 percent interest, and you were willing to pay 5 percent, what would the bank do?

In this case, the bank is in the same position as an investor. It can lend money to Bill Gates and earn 3 percent in a risk-free transaction. Or it can lend money to you and collect 5 percent in a transaction that has some risk.

The bank has to decide whether the extra return is worth the extra risk.

This is exactly the challenge that smart investors face, over the whole spectrum of investment choices.

In a bond, there are two main risks: maturity and credit. Maturity refers to the fact that rising interest rates tend to depress the prices of longer term bonds more than shorter-term bonds. This makes long-term bonds riskier than short-term bonds.

Credit risk refers to the fact that repayment from a blue-chip company is more reliable than repayment from a company struggling to find enough customers to meet its obligations.

In a stock, there are many risks. But in the aggregate, smaller companies are more risky than bigger ones, and "value" companies are more risky than growth companies.

Because these risks are well known, over long periods of time value stocks and small-company stocks offer higher returns than growth stocks and large-company stocks.

At this point in the conversation, I show the client a graph called "Theoretical Balance of Risk and Return." You'll see it in Figure 1A, below.

This is pretty simple, but you'll need to understand this graph in order to follow the upcoming discussion.

The top end of the dotted line in Figure 1A represents the risk and return level of the Standard & Poor's 500 Index from 1973 through 2002, while the bottom end represents the risk and return of Treasury notes.

The area on the right side of this graph represents higher risks; the area on the left represents lower risks. Similarly, the area at the top represents higher returns, the bottom represents lower returns.

Once you understand this, you'll see that the perfect investment strategy would wind up in the upper left corner of this graph, where risk is lowest and return is highest.

We'll be looking at a series of graphs laid out this same way, always looking for combinations of assets that have more return (closer to the top) and less risk (closer to the left).

By looking at the ends of the dotted line in Figure 1A, you can easily see that, just as you would expect, T-notes have much less risk (on the left side of the graph) but also have lower return (lower on the graph) than the Standard & Poor's 500 Index.

The point in the middle of that line shows what you might expect from a 50/50 combination of T-notes and the S&P 500 Index. This represents the halfway point of both risk and return between T-notes and the index.

However, it doesn't work out that way in real life. You'll see that in Figure 1B below, which shows a solid line based on actual combinations of these two assets.

The solid line in Figure 1B is bent toward the left and toward the top of the graph. You can see that a 50/50 combination of the S&P 500 Index and T-notes produced more than the average of the two returns, at less than the average risk of these two assets.

In Figure 1C below, you'll see where various combinations of these two assets land on the graph. Every intermediate combination is higher than - and to the left of - where it would fall on the straight dotted line we saw in Figures 1A and 1B.

You can think of the bend in the solid line as a benefit of diversification. As we will see, this phenomenon is not limited to these two particular assets. In fact, these three graphs illustrate a fundamental point that investors need to understand: Smart diversification lets you mix two assets together and achieve a higher return at less risk than the average of those two assets.

Before I show a client more examples of this, I pull out a chart, which you'll find in Figure 2 below, called "Which Investment Would You Prefer?" It shows a theoretical graph of return over time of two investments, each of which starts out at $100,000 and winds up worth $200,000.

Many clients have a hard time choosing one of these, and for good reason. They are mirror images of each other, each with ups and downs. The choice between them isn't critical, because they wind up in the same place. I then flip the card over and show them a graph called "Perfect Diversification," which you will see in Figure 3. The straight line right up the middle represents the progress of a 50/50 combination of the two investments.

These two assets have identical long-term rates of return. But in the short term, they are negatively correlated. In plain English, that means they do the opposites of each other.

Perfect diversification like this doesn't exist in real life. But it's a worthwhile goal. By itself, each asset eventually produces the same result, along with a good deal of angst along the way. Put together, they achieve the same result without any angst.

If you remember only one thing from this article, I hope it's this: For diversification to work, it has to be more than holding different things. They have to be different things that behave differently from each other. Figure 3 demonstrates this dramatically.

This is exactly why it doesn't do investors much good to hold several funds that each behave much like the Standard & Poor's 500 Index. Doing so may feel comfortable. But as one of my colleagues sometimes says, three boxes of different brands of cornflakes may look different on the shelf; but in the end all that's inside is cornflakes.

The "mostly cornflakes" problem is more prevalent than you might think. It turns out that institutions fall into the same traps as individuals. Lots of 401(k) plans have multiple options that overlap each other and are focused mostly on large-cap U.S. stock funds.

It's not uncommon to find 401(k) plans that offer half a dozen such funds and perhaps a mid-cap stock fund, but nothing at all in the way of small-cap funds.

International stock funds may or may not be offered, and that's certainly a pity, as I have no trouble pointing out to the clients I meet with.

The next card I show to clients contains what you see in Figure 4 below: A graph showing combinations of large-cap U.S. stocks and large-cap international stocks, represented by the Morgan Stanley Europe Australia Far East Index known as EAFE.

At first glance, this looks very different from Figure 1. But you'll notice that the two ends of the solid curved line could be connected by a straight dotted line similar to that in Figures 1A and 1B. Again, the line in Figure 4 has a very pronounced bend toward the left. The 50/50 combination of these assets is much less risky and a bit more productive than the midpoint of a straight line would be.

This graph should be particularly interesting to anybody who is regularly withdrawing money from a portfolio, because low volatility (represented on the left side of the chart area) is a huge contributor to the ability of a portfolio to survive regular withdrawals.

While the highest return is the S&P 500 Index, a combination of 70 percent U.S. and 30 percent international provides almost the same return with greatly reduced risk.

At this point in the presentation, I show the client two more graphs constructed the same way: Figure 5, showing U.S. large-cap vs. U.S. small-cap stocks, and Figure 6, showing U.S. large-cap vs. U.S. large-cap value stocks.

The shapes of the curves are different. But each line has a distinct bend to the left, and a 50/50 combination produces substantially less risk than would be achieved with a straight line. In each case, the line bends because the assets behave differently from each other.

Now let's return to the subject of risk tolerance. Figure 7, below, is a 12-column table of numbers showing the underlying data behind Figure 1C, which you will recall is the balance of risk and return of fixed income vs. equities.

There is no perfect point on the risk/return curve. Finding the proper balance depends on each person's needs and ability to tolerate risk. The table in Figure 7 is a good way to show exactly how much risk an investor would have taken over the past three decades with various combinations of T-notes and stocks.

The numbers at the bottom of each column in this table show six measures of risk for each portfolio combination. I ask the client to study those numbers and find a column that he or she could live with. Three and a half years ago, I found that people had an exaggerated view of how much risk they could stomach. But the bear market of 2000-2002 taught investors that risk is not just a theoretical concept!

Today, many investors underestimate their ability to tolerate risk, perhaps overcompensating for the ravages of the bear market. A few years ago, I found myself urging investors to assume less risk than they wanted to; now I find some investors so nervous that they want to take less risk than is appropriate for them.

I'd like to spend a little more time looking at Figure 7 and thinking about the topic of risk. This is the core of the most important decisions that investors must make.

Let's start with the assumption that you are comfortable with the very minimal risk of the all-fixed-income portfolio of T-notes, but that you are not satisfied with the 8.7 percent compound return.

I'll also assume that you could be satisfied with the 10.7 percent return of the all-equity portfolio, but that you're not comfortable with the risks.

The question is: Where do you fit in between?

To find the answer, look at the worst-12-months figures for various combinations and find a loss that you could accept. Let's say your maximum acceptable one-year loss is 25 percent, meaning the combination of 60 percent equities and 40 percent fixed-income investments is appropriate for you.

When I'm reviewing this with a client, I would then say: "OK, now imagine that it's one year later and I call you to say we had a totally normal year for your investments, and you've lost 25 percent of your money because of the market. How do you feel about that?"

At this point, the topic of risk becomes a bit more real for somebody contemplating an investment.

Thinking of losses in percentage terms is still too theoretical for some people, and I usually try to drive the point home by posing the question a different way.

As they think about how much they are willing to lose, I ask them to think of the current value of their portfolios and apply the loss figures to that amount. Somebody with a $1 million portfolio, for example, may think she's quite comfortable with a 15 percent loss. But when I ask her if she's willing to accept a loss of $150,000, I sometimes see a look of horror.

That look represents the link between losing money on paper and losing money in reality. On paper, it's no big deal. In real life, it can be a big deal. Many retirees and people near retirement remember very well when $25,000 represented an entire year's wages. And when they think of losing $150,000, they may see it as the equivalent of losing six years' of earnings.

If you have a time horizon of 20 years or more, in theory you should have no issues about risks over periods of one year or five years. What matters is what happens in 20 years when you need the money, not now.

But emotionally, we react differently. Unless we see reassuring interim results, we lose confidence that we're on the right road.

When I drive home, I take the most efficient route, knowing for sure that I'll get there. But when I give somebody directions to my house, I suggest a route that is easier to navigate successfully, even if it's longer. I want people to maintain the hope that the road they're taking will lead to where they want to go. That way they are much less likely to lose their confidence and make counterproductive decisions.

For the same reason, subjective risk really matters to investors. For a client with a long-term goal, I could easily prescribe an all-equity portfolio. If the past is any indication, that will produce the highest return.

But if the client loses confidence along the way, that client will never make it to the desired destination.

I'd rather have a client invest successfully in an imperfect portfolio than choose a theoretically more advantageous portfolio, only to fail in carrying it through.

Remember this when you are thinking about where you belong on the scale of security (mostly fixed income) vs. high returns (mostly or all equities).

Part of my role as an advisor is to be the devil's advocate, the person who questions preconceived notions and unexamined assumptions. Without that, I would be doing our clients no favors.

The data we have, of course, is from the past. But investors can buy only the future, not the past. Although we know future returns won't be the same as those of the past, we can be pretty sure certain patterns will continue.

Here are three very important correlations:

• Premium returns come from investing in stocks instead of T-bills or bonds.
• Premium returns come from investing in value stocks instead of growth stocks.
• Premium returns come from investing in small-cap stocks instead of large-cap stocks.

Those relationships have been true over long periods of time, and we have no reason to think they will change. But over shorter periods, they don't always hold up. There will always be periods when T-bills and bonds outperform stocks (think 2000 through 2002) and other periods when large companies outperform small ones. Likewise, at times growth companies will outperform value companies.

The most important questions for savvy investors are these: How big are these premiums and how reliable are they? The answers are shown in Figures 8 and 9.

Figure 8 shows the results of thousands of computer trials designed to find out how likely investors were to receive the premiums from 1926 through 2002.

Figure 8: Equity Premiums from 1926 to June 30, 2003
Market Premium	1-Year	5-Years	10-Years	15-Years	20-Years	25-Years
Best	154.6%	346.6%	439.2%	978.5%	1565.1%	3208.0%
Average	8.3%	47.3%	121.3%	241.4%	412.8%	634.5%
Worst	-66.2%	-69.5%	-44.7%	-21.6%	15.8%	62.9%
Reliability	67.6%	80.7%	95.9%	95.7%	100.0%	100.0%
Size Premium	1-Year	5-Years	10-Years	15-Years	20-Years	25-Years
Best	66.1%	138.5%	180.2%	359.3%	291.2%	223.3%
Average	3.0%	17.7%	35.3%	55.0%	72.2%	84.6%
Worst	-33.0%	-45.7%	-34.4%	-44.3%	-25.2%	-10.2%
Reliability	55.5%	58.8%	65.7%	77.8%	85.2%	98.1%
Value Premium	1-Year	5-Years	10-Years	15-Years	20-Years	25-Years
Best	89.3%	127.6%	203.1%	266.1%	304.6%	394.4%
Average	4.3%	22.4%	53.4%	96.6%	146.4%	206.1%
Worst	-42.8%	-53.8%	-49.0%	-40.7%	-17.1%	10.6%
Reliability	62.1%	78.3%	91.1%	94.6%	99.6%	100.0%

Market Premium is market returns minus Treasury-bill returns. Size Premium is small stock returns minus large stock returns. Value Premium is High BTM returns minus low BTM returns. Reliability is the percentage of advantageous periods.

To illustrate what the numbers mean, let's start at the upper left corner, measuring the market premium (the stock market vs. T-bills) for one-year periods. The figures are derived from measuring returns during every possible one-year period (for example March 1933 through February 1934) from 1926 through 2002.

The "reliability" figure indicates that in 67.6 percent of all those one-year periods, stocks outperformed T-bills. On average, stocks had total returns of 8.3 percentage points higher than T-bills. In the best of those one-year periods, stocks' return was 154.6 percent better than that of T-bills. In the worst one-year period, stocks did only about one-third as well as T-bills.

The reliability number is the most important. It tells you that over this time, you had roughly two chances out of three of beating T-bills by investing in the S&P 500 Index. Measuring longer periods, the odds improved to more than 80 percent in five-year periods, to 96 percent in 10-year periods and to 100 percent in 20-year and 25-year periods.

The size premium and value premium parts of that table work the same way.

Once understood, this table becomes an excellent tool for investors. In each case, you can determine how much certainty you require in order to feel confident that you'll get the expected premium. And in each case, the more certainty you require, the longer you may have to wait to achieve the desired result.

If your certainty threshold is 90 percent, then you would have achieved it in 10 years for the market premium and the value premium - but not until 25 years for the size premium.

The information in Figure 8 can also be used by short-term investors. Often people wonder what's the best way to invest money earmarked for a down payment on a home, college tuition or some other major need that may be a few months or a few years away.

The big decision with such money is whether to invest any of it in equities. This table shows that it all depends on how long before you need the money - and how much uncertainty (another word for risk) you are willing to tolerate.

These relationships are shown graphically in Figure 9. In every time period, you can see that the market premium has been the most reliable and the size premium the least reliable.

With this information, it's possible to draw some interesting conclusions. Over the past three quarters of a century, for instance, stocks beat T-bills in every 20-year period you can measure. And on average, stocks yielded more than five times the return of T-bills (up 412 percent) over 20-year periods.

For another example, you can conclude that if you had to choose between weighting an equity portfolio toward value stocks or toward small-cap stocks, your choice should be value. In 10-year periods, the value premium averaged an additional return of 53 percent, compared with only 35 percent for the size premium. Further, you had a 91 percent chance of getting a value premium in 10 years, vs. only a 66 percent chance of getting a size premium in 10 years.

Fortunately, investors don't have to choose between value and size. Optimum combinations can be put together to take advantage of diversification by geography, size and value orientation.

And here is where a lot of investors, including mutual fund managers and other professionals, get into trouble.

If you look carefully at the curves in Figures 4, 5 and 6, you can find a point on each curved line that is closest to the upper left-hand corner of the graph. That is the theoretically "ideal" allocation to get the best combination of high return at low risk. For example, in Figure 4, the ideal point appears to be about 60 percent S&P 500 Index and 40 percent EAFE.

If the curves (and the results from which they are drawn) never changed, this might be a valid method of fine-tuning an asset allocation. But guess what: If the underlying results never changed and we could rely on the future to mimic the past, investors would be fools to diversify. A rational investor would simply choose the top-performing asset.

But because the future won't be a mirror image of the past, diversification is necessary. Likewise, the curves shown in these graphs won't be the same in the coming years as they were in the past.

What I am sure of is this: The curves in Figures 4, 5 and 6 will continue to bend to the left, meaning that diversification will continue to add value. I'm also sure that the shapes of those curves will change. And if that is true, then the "ideal" point on each curve can't be predicted accurately.

It is tempting to optimize an asset allocation based on past data. Many investors, including professionals, do this. It's not hard to use tables and charts like these to show how well an investor could have done in the past by getting everything perfectly "right."

Fundamentally, this is similar to looking back at the stock market of the last 10 or 20 years and showing exactly which stocks an investor should have owned to maximize a return.

Though this technique is impressive, it leads to mischief. For example, based on some measurement of the past, a manager can carefully allocate a portfolio with some precise percentage of its assets in value stocks. But after a few years when the curve of Figure 6 changes, what is that manager going to do?

To continue the hypothetical example, assume value stocks perform very well for several years. At that point the updated curve might indicate that the ideal past allocation would have been a higher percentage of value stocks.

To remain competitive, the manager may reallocate the portfolio accordingly.

Essentially, that is just another form of chasing recent performance. And when you chase recent performance, you tend to buy high and sell low - exactly the opposite of what most investors believe they should be doing.

The way out of this trap is to diversify without trying to achieve precision.

My approach begins with the assumption that an investor's equity assets should be equally divided between U.S. and international, equally divided once again between value and a blend of value and growth, and equally divided once again between large and small.

With an equity portfolio that well diversified, an investor is not likely to miss out on any major market trends.

However, that diversification has another effect that investors must understand: It makes a portfolio behave differently from the broad market indexes.

I don't make many absolute promises to clients about the returns they will receive, but here's one I can make without any qualms: If you are properly diversified, your returns will be different from those of the S&P 500 Index.

You'll see this in Figure 10, which compares year-by-year returns of a fully diversified equity portfolio with the returns of the index.

Figure 10
Year	S&P 500	DFA Equity	Difference
1970	4.03	-2.67	-6.70
1971	14.32	36.32	22.00
1972	18.98	31.44	12.46
1973	-14.67	-20.11	-5.44
1974	-26.46	-27.77	-1.31
1975	37.21	52.39	15.18
1976	23.85	23.96	0.11
1977	-7.18	29.61	36.79
1978	6.57	32.12	25.55
1979	18.42	14.11	-4.32
1980	32.41	29.97	-2.44
1981	-4.91	1.69	6.60
1982	21.41	14.06	-7.35
1983	22.51	30. 27	7.76
1984	6.27	6.32	0.05
1985	32.17	43.10	10.92
1986	18.47	34.53	16.06
1987	5.23	21.79	16.56
1988	16.81	26.15	9.34
1989	31.49	30.87	-0.62
1990	-3.17	-14.57	-11.40
1991	30.55	26.94	-3.61
1992	7.67	3.73	-3.94
1993	9.99	30.89	20.90
1994	1.31	2.66	1.35
1995	37.43	18.41	-19.02
1996	23.05	12.75	-10.30
1997	33.21	5.28	-27.93
1998	28.57	6.05	-22.52
1999	21.03	22.63	1.59
2000	-9.10	-4.86	4.24
2001	-11.92	-2.74	9.17
2002	-22.11	-10.82	11.29
Average	12.20	14.65	3.06
Std. Dev.	18.29	19.05	13.86
Maximum	37.43	52.39	36.79
Minimum	-26.46	-27.77	-27.93

As you can see in that table, the calendar-year returns of the two portfolios were very similar (within two percentage points of each other, in only six of the 30 years from 1973 through 2002.

In 13 of those 30 years, the difference was more than 10 percentage points, and in five years it was more than 20 percentage points.

A big positive difference is easy to accept, when (as in 1977) a diversified portfolio is up 29.6 percent while the index loses 7.2 percent. But when diversification trails the index by 27.9 percentage points, as it did in 1997 (with the index up 33.2 percent and the diversified portfolio up only 5.3 percent), that can be tough.

The differences in return can persist for years. A fully diversified equity portfolio underperformed the S&P 500 Index for four consecutive years in 1989 through 1992, then beat the index in 1993 and 1994, only to underperform for another four straight years, 1995 through 1998.

That second four-year period coincided with the greatest bull market of the 20th century in large U.S. stocks. While the diversified portfolio was profitable in each of those four underperforming years, many investors would have lost patience with it.

Those who became frustrated and "defected" to the S&P 500 Index probably regretted doing so, as the diversified portfolio trounced the index in every year from 1999 through 2002.

I spend plenty of time on this with clients, telling them that unless they are prepared, they may "fire" us and move their money elsewhere just before our diversified approach regains its advantage.

Figure 11 shows the same comparisons for balanced portfolios. In one case the portfolio is divided equally between Treasury notes and the Standard & Poor's 500 Index; in the other case, it's divided equally between the equity portfolio used in Figure 10 and a fixed-income portfolio with an average maturity of 2.5 years.

Figure 11
Year	50/50 S&P 500 T-notes	50/50 DFA Equity DFA Bonds	Difference
1970	10.63	4.41	-6.22
1971	11.76	21.27	9.51
1972	11.94	16.49	4.55
1973	-5.21	-7.73	-2.52
1974	-11.11	-10.86	0.25
1975	22.11	28.42	6.32
1976	18.52	17.07	-1.45
1977	-2.91	15.38	18.30
1978	5.30	18.22	12.91
1979	11.18	12.20	1.02
1980	18.08	19.43	1.35
1981	2.17	10.71	8.54
1982	25.54	18.50	-7.04
1983	14.82	18.41	3.59
1984	10.32	7.90	-2.42
1985	26.29	28.81	2.52
1986	17.14	22.91	5.77
1987	5.47	14.52	9.05
1988	11.39	16.35	4.96
1989	22.28	18.66	-3.62
1990	3.38	-4.76	-8.14
1991	23.02	18.26	-4.76
1992	7.51	4.34	-3.17
1993	10.66	18.42	7.75
1994	-1.90	0.43	2.33
1995	26.40	14.65	-11.75
1996	12.24	10.41	-1.83
1997	20.47	5.84	-14.63
1998	19.89	6.88	-13.00
1999	9.27	12.68	3.41
2000	1.51	0.39	-1.12
2001	-1.99	1.51	3.50
2002	-5.33	-1.95	3.38
Average	10.55	11.20	0.83
Std. Dev.	10.59	10.06	7.30
Maximum	26.40	28.81	18.30
Minimum	-11.11	-10.86	-14.63

As you might expect, the yearly differences were less extreme with the balanced portfolios. But there were still five years when the difference was in double digits. And the two four-year periods when diversification under-performed were still there.

Even with half your money in bond funds, you can gain return and reduce risk through proper diversification. And with the experience of the past few years still fresh in their minds, conservative investors might be quite happy with the comparative results for 1999 through 2002. In that four-year span, an initial investment of $100,000 would have grown to $102,918 in the S&P 500 Index/Treasury notes combination; in the properly diversified balanced portfolio, it would have grown to $112,588.

The additional total return of the diversified portfolio is nearly 10 percent of the original portfolio value - something most investors would be very happy to have.

This comparison is a good example of the potential rewards that some investors forfeit because they want things to be simple and easy to understand.

If you want your money to work as hard as possible for you, you have to go beyond simplicity. Fortunately, diversification does not have to be daunting, and it doesn't demand perfection.

Our goal, as my father stated succinctly some years ago, is to give investors a piece of the action along with peace of mind.

In the end, investors need strategies with enough power on the upside to generate favorable returns, along with enough protection on the downside to keep them from bailing out in discouragement.

This is one of the hardest parts of investing. But it's well worth whatever time it takes to do it right.

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