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The New Effective Frontier

By Craig Israelsen

February 24, 2014

The basic premise underlying diversification and portfolio design (i.e., asset allocation) can be summarized in a

simple sentence by Harry Markowitz: To reduce risk it is necessary to avoid a portfolio whose securities are all

highly correlated with each other.1

The efficient frontier, popularized by Harry Markowitz, is a graph that demonstrates the risk/return attributes of a

portfolio that uses varying allocations of cash (the risk-free asset) and stock (the return of the market). These

two assets have demonstrated low correlation with each other over multiple decades; hence, the combination of

these two asset classes have long been used in the depiction of the efficient frontier. In general, the efficient frontier

assumes a shape as illustrated in Figure 1 (see blue dotted line).

The left-most blue dot represents a 100 percent cash investment. The return of cash is represented by theperformance of three-month U.S. Treasury bills. The next blue dot to the right represents an annually rebalanced

portfolio consisting of 90 percent cash/10 percent stock (stock is represented by the performance of the Standard &

Poors 500 Index). The blue dot furthest to the right in the graph represents a 100 percent stock portfolio. Thus, the

efficient frontier in this example is the various combinations of cash and stock ranging from all cash, 90 percent

cash/10 percent stock, 80 percent cash/20 percent stock to 100 percent stock. The performance of each asset class

(cash and bonds) covers the 44-year period from Jan. 1, 1970 to Dec. 31, 2013.

Also shown in Figure 1 (as depicted by red triangles) is what I will refer to as the effective frontieras

represented by various combinations of cash and a low-correlation, multiple-asset portfolio. The multi-asset

portfolio comprises large U.S. stock, small U.S. stock, non-U.S. stock, REITs, commodities, U.S. bonds and U.S.

casheach equally weighted at 14.3 percent and rebalanced annually. The average correlation among all seven of

these portfolio ingredients over the past 44 years was 0.20.

The actual indexes represented by these seven asset classes include the S&P 500 Index; the Ibbotson Small

Companies Index from 1970-1978 and the Russell 2000 Index from 1979-2013; the Morgan Stanley Capital

International EAFE Index (Europe, Australasia, Far East) Index; the Ibbotson Intermediate Term Bond Index from

1970-1975 and the Barclays Capital Aggregate Bond Index from 1976-2013; three-month Treasury bills; the

NAREIT Index (National Association of Real Estate Investment Trusts) from 1970-1977 and the Dow Jones US

Select REIT Index from 1978-2013; and the Goldman Sachs Commodities Index (GSCI). As of Feb. 6, 2007, the

GSCI became known as the S&P GSCI.

As can be seen in Figure 1, the effective frontier (representing various combinations of cash and a multi-asset

portfolio) is located above and to the left of the cash/stock efficient frontier. The effective frontier is more

diversified and, as a result, offers a superior risk/return trade-off than the efficient frontier. Very simply, more

diversification is better than less diversification in achieving superior risk-adjusted returns.

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For example, at a standard deviation level of 8 percent, the asset combination on the effective frontier was a 30

percent cash/70 percent multi-asset portfolio, which produced an 8.9 percent annualized return over the 44-year

period. By comparison, at 8 percent standard deviation, the efficient frontier was 60 percent cash/40 percent large

U.S. stock, which produced a 7.7 percent annualized return over the 44-year period. Thus, the effective frontier

produced a return that was 120 basis points higher than the efficient frontier at the same risk level (8 percent

annualized standard deviation).

Lets now consider the development (i.e., risk/return shape) of the effective frontier as assets are combined

sequentially in order of their individual standard deviation of return (from lowest to highest), as shown in Figure 2.

The first asset, of course, is cash. The all-cash portfolio is represented by the left-most red triangle. A 100 percent

cash portfolio had a 44-year annualized return of 5.22 percent and a standard deviation of annual returns of 3.4

percent. The next asset added (in the red graph) was U.S. bonds. Now we have a 50 percent cash/50 percent bond

portfolio that was rebalanced annually over the 44-year period from 1970-2013. The two-asset cash/bond portfolioreturn improved to 6.63 percent and the standard deviation increased slightly to 4.2 percent. The next red triangle

represents a three-asset portfolio (33.33 percent cash, 33.33 percent bonds and 33.33 percent large U.S. stock). This

three-asset portfolio had a 44-year annualized return of 8.22 percent and a standard deviation of return of 6.9

percent.

As the next three assets are sequentially added (REITs, small U.S. stock, non-U.S. stock), the return of the

increasingly diversified portfolio increases as does the standard deviation of return. Finally, commodities are added

as the seventh asset. The 44-year annualized return increases to 10.22 percent, but interestingly, the standard

deviation of return decreases (that is, moves to the left). This is a manifestation of the low correlation between

commodities and all six other asset classes over the past 44 years.

As seen before in Figure 1, theeffective frontier in Figure 2 is above and to the left of the efficient frontier.

If the investment objective was to produce a portfolio that produced (more or less) a 10 percent standard deviation of

annual returns, the required asset mix on the efficient frontier would have been approximately 60 percent stock/40

percent cash. The annualized return of a 60 percent large U.S. stock/40 percent cash mix over this 44-year period

was 8.72 percent with a standard deviation of 10.7 percent.

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By comparison, the 44-year standard deviation of the fully deployed seven-asset model (highest red triangle) was

10.2 percent, but also produced an annualized return of 10.29 percent. Thus, at a standard deviation level of

approximately 10 percent, the effective frontier multi -asset portfolio produced a performance premium of more

than 157 bps compared with an efficient frontier two-asset model.

Moving from the efficient frontier to the effective frontier is achieve d by genuine diversification. By genuine, I

mean to imply that if one is willing to diversify, one needs to do so in a material way. Trivial allocation (under 2

percent) to real estate or commodities, for example, does not represent genuine diversification. Rather, such minute

allocations might be better described as dabbling in diversification. Also important in building diversified

portfolios is implementing a protocol of systematic rebalancing. Rebalancing a multi-asset portfolio once per year

typically produces better results than rebalancing monthly.

Building an investment portfolio that resides on the effectivefrontier is now easier than ever, thanks to a rich array

of investable asset classes at our disposal in the form of mutual funds, index-based funds and exchange-traded funds.

Endnote

1 Markowitz, H., 1991, "Portfolio Selection," Blackwell Publishing.