The bottom line is that, to have a chance to benefit from positive tracking error, investors must accept the virtual certainty that negative tracking error will appear from time to time. Emotions associated with negative tracking error can lead investors to abandon carefully developed investment plans. Only investors willing and able to accept the risk of tracking error regret should consider diversifying across other risk factors.
In the next chapter, we will show you how you can utilize what you have learned to build more efficient portfolios by combining Fama and French’s work with insights from Harry Markowitz’s work that won a Nobel Prize. We will explain how you can add risky, but non-perfectly correlating, assets to a portfolio and generate higher returns without a commensurate increase in the portfolio’s volatility.
Chapter 3:
Building a More Efficient Portfolio
We will begin with a portfolio that has a conventional asset allocation of 60 percent stocks and 40 percent bonds. In this case, the stock allocation is to the S&P 500 Index and the bond allocation is to five-year Treasury notes (the highest quality intermediate-term bond). The time frame will be the 42-year period from 1975 through 2016. We chose this period because it is the longest for which we have data on the indices we need. While maintaining the same 60 percent stock/40 percent bond allocation, we will then expand our investment universe to include equity asset classes other than U.S. large-cap stocks. We will see how the portfolio performed if one had the patience to stay with this allocation for the duration and rebalanced annually. We will then demonstrate how the portfolio’s performance could have been made more efficient by increasing its diversification across asset classes. We do so in four simple steps. (Indices are not available for direct investment.)
Portfolio 1
1975–2016
*Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
By changing the composition of the control portfolio, we will see how we can improve its efficiency. To avoid being accused of data mining, we will alter our allocations by arbitrarily “cutting things in half.”
Step 1: The first step is to diversify our stock holdings to include an allocation to U.S. small-cap stocks. Therefore, we reduce our allocation to the S&P 500 Index from 60 percent to 30 percent and allocate 30 percent to the Fama/French US Small Cap Index. (The Fama-French indices use the academic definitions of asset classes. Note that regulated utilities have been excluded from the data.)
Portfolio 2
1975–2016
*Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
Step 2: Our next step is to diversify our domestic stock holdings to include value stocks. We shift half of our 30 percent allocation to the S&P 500 Index to a large-cap value index and half of our 30 percent allocation to small-cap stocks to a small-cap value index.
Portfolio 3
1975–2016
*Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
Step 3: Our next step is to shift half of our equity allocation to international stocks. For exposure to international value and international small-cap stocks, we will add a 15 percent allocation to both the MSCI EAFE Value Index and the Dimensional International Small Cap Index.
Portfolio 4
1975–2016
*Data source: MSCI
**Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
One effect of the changes has been to increase the return on the portfolio from 10.4 percent to 11.8 percent. This outcome is what we should have expected to see as we added riskier small-cap and value stocks to our portfolio. Thus, we also need to consider how our changes impacted the risk of the portfolio. The standard deviation (a measure of volatility, or risk) of the portfolio increased from 10.3 percent to 11.4 percent. Returns increased by a relative 13.5 percent while the relative increase in volatility was 10.7 percent.
You have now observed the power of modern portfolio theory at work. You saw how you can add risky (and, therefore, higher expected returning) assets to a portfolio and increase its returns more than its risk rose. That is the benefit of diversification across asset classes that are not perfectly correlated. While most investors and advisors with this knowledge have used it in the preceding manner, there is another way to consider employing it. Instead of trying to increase returns without proportionally increasing risk, we can try to achieve the same return while lowering the risk of the portfolio. To achieve this goal, we increase the bond allocation from 40 percent to 60 percent and proportionally decrease the allocations to each of the equity asset classes.
Portfolio 5
1975–2016
*Data source: MSCI
**Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
Compared with Portfolio 1, Portfolio 5 achieved the same return with far less risk. Specifically, Portfolio 5 returned the exact same 10.4 percent per year while experiencing volatility 2.1 percentage points lower (8.2 percent versus 10.3 percent). In relative terms, its volatility was 20.4 percent lower.
Now that you have a good understanding of how modern portfolio theory can be used to build more efficient portfolios, we will move to our last step. We will show you how, by concentrating your equity allocation in only the highest expected returning asset classes, you can improve a portfolio’s risk profile even further, making it look more like Portfolio B (the one you preferred) than Portfolio A from the illustration in Chapter 1.
Just as the equity premium is compensation for taking risk, so are the size and value premiums. Thus, we add the usual disclaimer that the future may look different from the past. There are no guarantees in investing.
Due to data limitations, the period we will now consider is the 35 years from 1982 through 2016. We will look at two portfolios, A and B. Portfolio A is again allocated 60 percent to the S&P 500 Index and 40 percent to five-year Treasury notes. Portfolio B will hold 25 percent stocks and 75 percent five-year Treasury notes. With U.S. stocks representing roughly half of the global equity market capitalization, we will split the equity allocation equally between U.S. small value stocks (using the Fama/French US Small Value Index) and international small value stocks (using the Dimensional International Small Cap Value Index).
1982–2016
Portfolio A: 60 percent S&P 500 Index/40 percent five-year Treasury notes*
Portfolio B: 12.5 percent Fama/French US Small Value Index (ex utilities)/12.5 percent Dimensional International Small Cap Value Index/75 percent five-year Treasury notes*
*Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
As you can see, while Portfolio A produced an annualized return 0.6 percentage points higher than Portfolio B (10.3 percent versus 9.7 percent), it did so while experiencing volatility 3.1 percentage points greater (10.3 percent versus 7.2 percent). In relative terms, Portfolio A’s annualized return was only 6 percent greater than Portfolio B’s while the volatility it experienced was 43 percent higher. In addition, Portfolio B had fewer events in the tails of the return distribution (said another way, it had both fewer extremely good and fewer extremely bad years). While Portfolio A had 11 years with returns greater than 15 percent, Portfolio B had nine. And while Portfolio A had one year with a loss greater than 15 percent, Portfolio B never experienced one that large. Moving the hurdle to years with 20 percent gains or losses, we see that Portfolio A had seven years with returns greater than that level and no years with losses of that size while Portfolio B had just two years of gains that large. Moving the hurdle to the 25 percent level, both Portfolio A and Portfolio B had two years with returns in excess of that amount and no years with losses that great. The best single year for Portfolio A was 1995, when it returned 29.3 percent. The best single year for Portfolio B was 1985, when it returned 28.0 percent. Note that while Portfolio B has just 25 percent in equities, its bes
t year was almost as good as the best year for Portfolio A, which has 60 percent in equities. On the other hand, Portfolio A’s worst single year was 2008, when it lost 17.0 percent. The worst single year for Portfolio B was 1994, when it lost just 1.2 percent. In addition, while Portfolio A experienced five years of negative returns, Portfolio B posted just three.
Portfolio B—the low-market-beta/high-tilt portfolio—with its shorter tails looks more like our original Portfolio B. While its best year was not as good as Portfolio A’s best year, and it had fewer years in the good right tail, its worst year was much less painful than Portfolio A’s worst year, and it had fewer years in the bad right tail.
There is another important point to cover, and to help make it we have reproduced the original illustration of the potential dispersion of returns for Portfolios A and B.
Recall your preference for Portfolio B was based on your aversion to risk—your willingness to give up the opportunity for the extreme good returns in the right tail of Portfolio A in return for minimizing the risks of the extreme bad returns in its left tail. The illustration shows that, if you choose Portfolio B, both the good and bad tails of Portfolio A are reduced equally. However, using actual returns, we saw that while Portfolio A did produce more good years than Portfolio B, and had a higher best returning year than Portfolio B, the difference in returns between their best years was just 1 percentage point while the difference in returns between their worst years was almost 16 percentage points. In other words, bad tail risk was curtailed much more than good tail risk. If you preferred Portfolio B to Portfolio A, you should have a strong preference for a low-market-beta/high-tilt portfolio.
Before moving on, we must admit there is no way that, in 1982, we could have predicted the allocation for Portfolio B would have produced returns so similar to the allocation for Portfolio A. We might have guessed at a similar allocation, but we cannot predict the future with anything close to that kind of accuracy.
We have one final example to take you through. On December 23, 2011, Ron Lieber, financial columnist for The New York Times, wrote an article titled “Taking a Chance on the Larry Portfolio”—and the “Larry Portfolio” (LP) was born. The LP is the “technical” term for a portfolio that basically limits its stock holdings to the highest returning equity asset classes available to individual investors in low-cost, passively managed investment vehicles, specifically U.S. small value stocks, developed markets small value stocks and emerging market value stocks. Limiting stock holdings to the highest expected returning asset classes allows you to maintain a lower overall allocation to stocks and achieve the same expected return in your portfolio.
Due to data limitations, we now will consider the 28-year period from 1989 through 2016. We will again look at two portfolios, A and B. Portfolio A is once again allocated 60 percent to the S&P 500 Index and 40 percent to five-year Treasury notes. Portfolio B will hold 28 percent stocks and 72 percent five-year Treasury notes. (Note the change from the previous example, which used 25 percent stocks, and recall our disclaimer that we cannot predict with perfect accuracy what allocation will produce the same returns.) Again we split our equity holdings, with domestic and international stocks each receiving a 14 percent allocation. Emerging market stocks make up about 25 percent of international equity capitalization, so our international allocation becomes 10.5 percent international small value stocks and 3.5 percent emerging markets value stocks (using the Fama/French Emerging Markets Value Index).
1989–2016
Portfolio A: 60 percent S&P 500 Index/40 percent five-year Treasury notes*
Portfolio B: 14 percent Fama/French US Small Value Index (ex utilities)/10.5 percent Dimensional International Small Cap Value Index/3.5 percent Fama/French Emerging Markets Value Index /72 percent five-year Treasury notes*
*Data source: © 2017 Morningstar, Inc. All rights reserved. Reproduced with permission.
Portfolio A produced an annualized return 0.6 percentage points higher than Portfolio B (8.9 percent versus 8.3 percent), but it did so with volatility 3.8 percentage points greater (10.5 percent versus 6.7 percent). In relative terms, Portfolio A’s annualized return was only 7 percent greater than Portfolio B’s, while the volatility it experienced was 57 percent greater higher. In addition, Portfolio B generally had fewer events in the tails (fewer extremely good and fewer extremely bad years). Portfolio A had seven years with returns greater than 15 percent while Portfolio B had six. However, while Portfolio A had one year with a loss greater than 15 percent, Portfolio B never experienced one that large. Moving the hurdle to years with 20 percent gains or losses, we see that Portfolio A had five years with returns greater than that level and no years with losses of that size while Portfolio B had just one year of returns that large. Moving the hurdle to the 25 percent level, Portfolio A had one year with a return in excess of that amount and no years with losses that great. Portfolio B did not experience a single year with a loss or gain of 25 percent or greater. The best single year for Portfolio A was 1995, when it returned 29.3 percent. The best single year for Portfolio B was 2003, when it returned 22.2 percent. Note that while Portfolio B has just 28 percent in equities, its best year’s return was only 7.1 percentage points lower than Portfolio A’s best year. On the other hand, in 2008, the worst year for both portfolios, Portfolio B lost just 3.3 percent, 13.7 percentage points less than Portfolio A’s loss of 17.0 percent. In addition, while Portfolio A experienced five years of negative returns, Portfolio B recorded just three. If you are like most investors, you would have slept much better with Portfolio B than with Portfolio A.
Experience has taught us that limiting the risk of large losses increases the odds that you will be able to maintain discipline during bear markets, thereby avoiding the panicked selling that destroys the odds of achieving your financial goals.
The next chapter addresses a question we are often asked: Is the “Larry Portfolio” well diversified?
Chapter 4:
Is the “Larry Portfolio” Well Diversified?
While the “Larry Portfolio” (LP) has earned superior risk-adjusted returns (producing a higher Sharpe ratio than a market-like portfolio, with much smaller worst-case losses) over the 28-year period we examined, one concern investors have expressed is that the portfolio “is not well diversified.”1 In one sense that is a true statement. The LP does limit its stock holdings in both the U.S. and developed international markets to small value stocks, and in emerging markets to value stocks. That means it holds no small-cap, mid-cap and large-cap growth companies in the U.S. and developed international markets, as well as no mid-cap and large-cap value companies. In emerging markets, there are no growth stocks, just value stocks.
To answer the question of whether the LP is well diversified, we need to have you think about diversification differently from the way you probably are used to. The conventional way of addressing how well a portfolio is diversified is to think in terms of the number and weighting of individual stocks, asset classes and geographic regions. We want you to also think about diversification in terms of exposure to the factors that determine the risk and return of a portfolio.
As we have discussed, to understand how markets work, financial economists have developed what are called asset pricing (factor) models. Until recently, the “workhorse” model was the Fama-French three-factor model. Again, the model’s three factors are market beta (exposure to the risk of the stock market), size (exposure to the risk of small-cap stocks) and value (exposure to the risk of value stocks). To determine how well a highly tilted portfolio is diversified, we will begin by looking at the exposure a total stock market fund (portfolio) has to the three Fama-French factors.
A total stock market (TSM) fund has, by definition, an exposure to market beta of 1. However, while a TSM fund holds small stocks, it has no exposure at all to the size factor. This seeming contradiction confuses many investors. The confusion arises because factors are long/short portfolios. The size factor is the return of small-cap stocks
minus the return of large-cap stocks. In other words, small-cap stocks provide a positive exposure to the size effect and large-cap stocks provide a negative exposure to it. Thus, while the small-cap stocks in a TSM fund provide positive exposure to the size factor, the large-cap stocks in the fund provide an exactly offsetting amount of negative exposure. That puts the net exposure to the size factor at 0. The same is true for value stocks. The value factor is the return of value stocks minus the return of growth stocks. Value stocks provide a positive exposure to the value effect and growth stocks a negative exposure. While the value stocks in a TSM fund provide positive exposure to the value factor, the growth stocks in the fund provide an exactly offsetting amount of negative exposure. That puts the net exposure to the value factor at 0.
Reducing the Risk of Black Swans Page 4