Asset Allocation Part 2: Constructing an Efficient Portfolio
[Editor’s Note: This article first appeared as part of our series on Advanced Asset Allocation Strategies. To read the rest of this series, check out: Asset Allocation Part 1: What It Is and Why You Need It, Asset Allocation Part 3: Your Stock and Bond Portfolio Mix and Asset Allocation Part 4: Model Portfolios and PostRetirement Planning]
Last week, in part 1 of my series on asset allocation, I emphasized the importance of diversifying one’s investments so that some zig up while others are zagging down. Minimizing downside volatility by canceling out the inevitable down moves is critical to generating wealth in the long term.
Investing Only in Stocks May Be Hazardous to Your Wealth
I just read a 2009 paper by University of Colorado finance professor Michael Stutzer that gives a great illustration of this point. He assumes that the stock market will appreciate at a 6% average annual real return, but do so with 40% annual volatility. A 40% volatility level means that chances are two out of three that the actual stock market return in any given year will not exceed –34% on the downside (6% minus 40%) or 46% on the upside (6% plus 40%).
It turns out that the high volatility – i.e., allowing your portfolio return to decline by 34% in a given year — wreaks havoc on the probability of making money in the long run (30 years in this example):
The statistical expected future value of the stock market is the familiar calculation that compounds the market’s initial value at 6% per year. But this statistic is extremely misleading. The median future cumulative return, i.e. the number which has a 5050 chance of being exceeded after 30 years, will be much lower. In fact, the median cumulative return after 30 years is a loss of around 43% of the initial investment. Thus there is a greater chance of losing money than there is of making anything, much less 6% per year!
Cash May Be Trash, But Not As Part of a Portfolio
Stutzer demonstrates that by changing the portfolio mix from 100% stocks to 50% stocks and 50% U.S. Treasury bills, volatility is reduced sufficiently that the median return becomes a 34% gain.
Here’s the kicker: he assumes that the treasury bills actually lose 0.1% per year. The benefit of adding the treasury bills is that they safeguard 50% of the portfolio from those dreaded 34% declines. Then, through annual rebalancing to maintain a 5050 portfolio split, 17% of the treasury bills are sold and converted into stock at the lower stock prices caused by the 34% decline. In essence, the combination of adding treasury bills and rebalancing not only reduces volatility but forces you to buy stocks when they are cheap and sell stocks when they are expensive, which turns a probable loss into a gain.
You heard right – reducing volatility is so important to wealth generation that you can actually increase your probability of making money by adding an asset class that loses money on average! Wow.
Roll Up Your Sleeves and Construct a Portfolio!
With that story as a backdrop, let’s get into the nuts and bolts of how to construct an efficient investment portfolio. In this context, “efficient” means the portfolio with the lowest annual volatility for each level of expected annual return. A portfolio that will generate a 10% annual return with 20% volatility is not efficient if there is another portfolio that will generate a 10% annual return with only 15% volatility.
So, the first step is to find the portfolio of “risky” assets (i.e., assets that can go down in price) that produces the highest return for each level of risk (i.e., volatility). The universe of risky assets theoretically should include all investable assets in the economy (e.g., common stocks, longterm bonds, real estate, private equity) and I provided a percentage breakdown of the total investable capital market Part 1.
Portfolio Efficiency: The Final Frontier
Take a look at this link, which provides a chart of an efficient frontier. Individual stocks are represented by the yellow dots and are all below the curved line. This is because individual stocks never by themselves constitute the minimum volatility — it is always beneficial to combine different stocks together to get the volatilityreducing zigzag effect going. With the volatility (a.k.a. standard deviation) on the xaxis and expected return on the yaxis, the goal is to find the portfolio located furthest towards the Northwest corner of the chart. The Northwest quadrant maximizes return and minimizes volatility.
Sharpe Ratios Are Cool
The optimal portfolio is the one with the highest Sharpe Ratio, which is defined as excess return (portfolio return minus riskfree rate) divided by standard deviation. Theoretically, the optimal portfolio is equivalent to the market portfolio because the market portfolio includes every investable risky asset, which maximizes zigzag and minimizes volatility. If the optimal portfolio of risky assets is too volatile for an individual, he can reduce volatility by adding riskfree U.S. treasuries to the mix. On the other hand, if the optimal portfolio does not provide enough return, he can borrow on margin to purchase more of the risky portfolio. Any mixture of the optimal risky portfolio with riskfree cash (the straight capital allocation line seen in the chart) is more efficient (i.e., more Northwest) than any point on the efficient frontier.
In reality, investing in the entire capital market is not practical (although the introduction of ETFs is making it easier than before) and borrowing on margin can be costly and dangerous. Consequently, most people’s optimal portfolio will consist of a subset of all investable assets (probably limited to stocks, bonds, and REITs). This means that you can’t just buy a single prepackaged solution, but will need to do some work selecting which asset classes and individual securites to include in the investment portfolio that is best for you.
Low Correlations Are the Holy Grail of Asset Allocation
The key to finding asset classes that complement each other with zigzag returns is to know how their returns correlate with each other. Correlation ranges from +1 (moving in lockstep with each other) to –1 (moving in diametrically opposite directions). Mixing assets with a +1 correlation together provides no diversification benefits, whereas adding assets with a –1 correlation together provide perfect diversification. It’s pretty rare to find assets with a negative correlation (in some studies, commodities and stocks have negative correlation), so the best you can reasonably hope for is a low positive correlation under 0.5.
For example, stocks and longterm government bonds usually have a low correlation with each other. In strong economic times, stock prices tend to go up because of increasing earnings whereas bonds tend to decline out of fear of increasing inflation. In economic recessions like 2008, stock prices go down because of declining earnings but bonds go up as inflationary fears recede and there is a flight to safety. If you take a look at a chart from 2008 comparing the returns of the S&P 500 with 20year U.S. Treasury bonds, you will see as close to a nearperfect 1 correlation as you’re ever going to find:
Source: Bloomberg
A typical correlation matrix of asset classes looks like the following:
Asset Class 
U.S. Equity 
Emerging Market Equity 
U.S. Investment Grade Bonds 
Real Estate 
NonU.S. Bonds 
Commodities 
U.S. Equity 
1.00 

Emerging Market Equity 
0.52 
1.00 

U.S. Investment Grade Bonds 
0.19 
0.04 
1.00 

Real Estate 
0.44 
0.34 
0.16 
1.00 

NonU.S. Bonds 
0.01 
0.03 
0.45 
0.00 
1.00 

Commodities 
0.12 
0.20 
0.11 
0.16 
0.08 
1.00 
Source: Morningstar
Other online examples of correlation matrices are here, here, and here.
Magical Asset Combinations
A reallife illustration of how portfolio performance is improved by adding together assets with low correlations is shown below. Portfolios are ranked in descending order from best to worst based on three criteria: (1) annual return, (2) volatility, and (3) Sharpe Ratio.
Portfolio Performance: 1972 to 2005 

Portfolio 
Annual Return (%) 
Portfolio 
Volatility (%) 
Portfolio 
Sharpe Ratio 
CD 
13.89 
ACD 
10.76 
ACD 
0.71 
BCD 
13.66 
ABCD 
11.29 
BCD 
0.67 
ACD 
13.48 
BCD 
11.80 
ABCD 
0.66 
C 
13.40 
ABD 
12.78 
CD 
0.63 
ABCD 
13.29 
AD 
12.96 
AD 
0.58 
BD 
13.02 
CD 
13.28 
ABD 
0.57 
BC 
12.95 
AC 
14.60 
AC 
0.51 
AD 
12.90 
ABC 
14.90 
BD 
0.51 
ABD 
12.85 
BD 
15.41 
C 
0.50 
AC 
12.64 
BC 
15.60 
BC 
0.50 
ABC 
12.53 
C 
16.72 
ABC 
0.49 
D 
12.03 
A 
17.46 
AB 
0.39 
AB 
11.58 
AB 
17.67 
A 
0.37 
B 
11.34 
B 
22.19 
D 
0.35 
A 
11.16 
D 
24.58 
B 
0.33 
Source: Roger C. Gibson, Asset Allocation
A = U.S. Stocks, B = NonU.S. Stocks, C = Real Estate, D = Commodities
The first thing that strikes me from the table is that all of the singleasset portfolios are near the bottom of the lists. They exhibit relatively high volatilities and low Sharpe Ratios. But magical things start to happen when you add them together. For example, U.S. stocks (A) has annual volatility of 17.46%. If someone suggested that you add commodities (D) to your stock portfolio, you’d probably hesitate because the table says that commodities are the most risky asset class with an annual volatility of 24.58%. Yet, if you did add commodities (thus creating portfolio AD), your overall portfolio volatility would actually decline by 4.5 percentage points to 12.96%!
Similarly, if you owned a real estate portfolio (C) that returns 13.4% per year, you probably wouldn’t think it logical to add commodities (D) to the mix because commodities only return 12.03% per year. Yet, adding lowerreturn commodities to your real estate portfolio actually increases your overall portfolio return (CD) by half a percentage point to 13.89%!
Portfolio Optimizer Software Is a Must
Don’t take my word for it. You can play around with portfolio optimizer software and see the benefits of diversified asset allocation for yourself. For example, Bill Sharpe (who developed the Sharpe Ratio) has a website with a free portfolio optimizer calculator. In the calculator, input the annual return, volatility, and correlation numbers from the charts above for up to three asset classes. Then click the “process” tab. You’ll get a result that shows you the optimal percentage of each asset class to own. The suggested portfolio is the one with the highest Sharpe Ratio. You’ll see that the portfolio’s volatility is lower than the volatility of any of the individual asset classes.
Next: Asset Allocation Part 3: Your Stock and Bond Portfolio Mix.
Editor’s Note: For more information on this topic, check out our FREE special report on Asset Allocation Strategies!
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