Efficient Frontier

by Tim Isbell  (Posted March 2013; revised 2/14 to repair 2 broken links.)

Yes, I know, "efficient frontier" sounds esoteric. But it is a core concept in Asset Allocation, which is the strategy that drives all investing. So it's worth the time to get acquainted with the principles of the efficient frontier.

First we will unpack the meanings hidden in the curve. (By the way, as you read this page you may need a bigger version of this curve. To get one, just double-click it.) Then I'll point you to resources where you can learn more. In another section of Investments, this background will help us understand Asset Allocation, a core strategy in Personal Investing. 


Ok, here we go.

Take a look at the horizontal and vertical axes in the above graph, and ignore everything else. The vertical axis is your investment's compounded annual return, over a defined period. The horizontal axis, labeled Standard Deviation, is how finance people quantify risk. So this graph provides a way to indicate an investment's risk/reward tradeoff.

For example, If you buy a stock for $10, and its nominal return is 9%/year over 10 years you'd feel great! But what if some of those years your investment lost 15% and other years it gained 17%? Your investment provided an excellent 10-year return, but it was a perilous ride. 

Of course, there is another kind of investment. Suppose you bought a CD at the local bank that promises to pay 1%/year. That's pretty small, but for such investments, the standard deviation from year to year on that CD's interest is virtually zero. So you can't make much money from this investment, but at least, it's safe.

Next, notice the dots A and B (but continue ignoring the line/curves connecting A and B). The lowest dot is labeled 100% A, and it marks the risk/return for Investment A. The highest dot is labeled 100% B, and it marks the risk/return of Investment B. Stop here for a moment and think what this means. Our graph has two investments. Investment A provides lower risk; investment B provides a higher return. So, is there a way we can mix investments A and B into an investment C and come up with a better result?

Yes, there is.

Let's pretend that we have $1000 to invest, and we put $500 in A and the other $500 in B. Together these two investments become investment C. Furthermore, let's assume that every time A increases 5%, so does B (and when A drops 5%, so does B). Mathematicians call this "perfect correlation." They give it a number: +1.0 because two investments vary in the ratio of 1/1. If one goes up and the other goes down by the same percentage, the two investments would have a correlation of -1.0.

Now let's look at the straight line connecting A and B; it's labeled Correlation +1.0. It shows the risk/return for our combined investment C, as we shift our money from being 100% in A to 100% in B, at 10% intervals. Every small dot along this line represents the change of another 10% of our investment from A to B. In our example, we've split our total investment C equally between A and B, so our risk/reward point for Investment C is 5 dots away from A (or 5 dots away from B). With a little math, you can convince yourself that everything is proportional. Every time we move one dot from A towards B we get a higher return, but at a proportionally greater risk. That's okay, but all it returns is the average of A and B. Wouldn't it be nice if there were something better? 

There is.

Take a look at the other three curves connecting A and B. The one most interesting to us is labeled Non-Correlation (square dots). At point A we have all of our $1000 in A. If we move $100 to B, we move up the line one dot. Notice a very striking thing: our overall investment (C) got less risky while our overall return rose fast! Stop and think about that for a minute. That's remarkable! We mixed in a riskier investment, and the combined investment got less risky!

Now follow the Non-Correlation curve to the 4th dot. At this point we've moved $400 from A to B. The return is higher than at point A, and the risk is the same as it was when 100% of our investment was the low-risk investment A! Think about that long enough for it to sink in: We mixed a riskier investment with a less risky investment, got a disproportionately bigger return, without any increase in risk! Amazing. But true. It's just math.

Now let's connect this understanding to the real world of investments. Investment A is very much like Bonds. Investment B is very much like stocks. When the time window is large enough, say ten years, you can be pretty confident that stocks and bonds are pretty close to the large square markers.

This is the engine behind Asset Allocation (one page above this one on the site).

What this means in actual numbers

Ok, now let's combine the concepts in this Efficient Frontier page with the actual annual returns from the Asset Allocation page.

The efficient frontier predicts that the lowest risk portfolio is NOT a portfolio with 100% bonds. It is a portfolio of 25% stocks and 75% bonds. Beyond that, if we increase our percentage of stocks to 40% we get a higher overall return, at a risk no larger than a 100% bond portfolio! 

The Asset Allocation page reports historical data saying that the average annual real (inflation-adjusted) return for stocks is about 7%, and for bonds is about 3.5%.  

Combining the above two paragraphs results in a reasonable expectation that over 10+ years: 

  • a 25/75% stock/bond portfolio should result in about 4.375% real annual return. This lowest risk portfolio returns 0.875% more than a pure bond portfolio, so for the most conservative investor, shifting 25% of the portfolio to stocks is a no-brainer!
  • a 40/60% stock/bond portfolio should result in about 4.9% real annual return. This portfolio is the same risk as a 100% bond portfolio, but it returns 1.4% higher real return! 
Coupling these two bullets with the table on Portfolio Expectations webpage results in a sensible target asset allocation.

What you can do next

Check out this page from Investopedia on the Efficient Frontier. Be sure to watch the great video clip at the bottom of that web page!

For some real data on how stocks/bonds fared during the 2008 and 2001 stock market crashes, check out Mike Piper's What Happens to Bonds in a Stock Market Crash? Don't just look at the two charts, be sure to read the article!

Jeremy Siegel describes the efficient frontier in his book: Stocks for the Long RunThis is a classic personal finance "textbook." It includes a chart showing the correlation coefficients between monthly stock and bond returns from 1926 to 2006 (Figure 2-4). There is also a graph of the risk/return trade-offs for investment holding periods of from 1 to 30 years, covering the periods from 1802 to 2006 (Figure 2-5). 

You can Google "efficient frontier" and find lots of additional material.


For a larger list of resources that I use for personal finances, check out Resources/Links.

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All the best,

Tim Isbell

Edited with Grammarly