Some sources advise that after applying Modern Portfolio Theory to reveal the efficient frontier curve of best-diversified portfolios, long-term investors use this graph to compare the portfolios and make the portfolio choice. They label the vertical axis “return” and the horizontal axis “risk”, and advise making the choice based on “risk tolerance”.

For example, the red-dot portfolio would be said to have “risk” of 18% while the blue has “risk” of only 6%. It appears that by choosing the blue instead of the red, we are reducing “return” by only 6% while reducing “risk” by twice as much, by 12%

“Risk”

Compounding is the key to long-term investment growth. For longer terms, it produces disproportionally larger gains. For example, at a rate of 10%, compared to the gain over ten years, the gain over twenty years is over 3.5 times as great.

Over longer terms, compounding also makes higher return rates produce disproportionally larger gains. Over twenty years, compared to the gain at an 8% rate, the gain at a 16% rate is over 5 times as great.

For this reason, increases in expected return rate that appear very small on the single-year efficient frontier produce far larger increases in expected long-term return. To see this advantage, you have to move beyond the efficient frontier’s single-year view, to compare the portfolios in long-term compound return.  

The graph at right is a compound frontier graph. It’s just like the efficient frontier graph, except that the vertical expected-return axis compares the portfolios in compound long-term return instead of return for the single year.

This graph shows that for longer-term investment, as you move to left along the curve to reduce the return-rate standard deviation, the reductions in expected return are vastly greater than shown on the single-year efficient frontier.

On the single-year efficient frontier, it appears that as you move from the red portfolio to the blue, the reduction in expected return is only about 6%. But that’s for the single investment year. The compound frontier graph shows that for a twenty-year investment, the reduction in expected return would be from 1100% down to under 300% -- a reduction of over 800%.

Along with compounding, there’s another long-term effect that makes portfolio comparison very different for longer investment terms: standard deviation shrinkage.

On the graph at right, two asset classes are compared in return-rate average for various lengths of investment. For each asset class, the horizontal line represents expected rate, and the vertical ribs represent one standard deviation above and below the expected rate.

This graph shows that for the return-rate average, for longer investment terms the standard deviation shrinks.

The reason for this is logical. With more investment years, it is more likely that while some years will have low deviations, other years will have high deviations, and  the deviations willl tend to balance out and produce an average return rate closer to the expected rate.

The graph at right shows long-term effects of both compounding and standard deviation shrinkage, by comparing long-term returns for the two asset classes at various constant rates

For each asset class, the curve shows growth of total return at the expected return rate. For each number of years, the vertical ribs show how much higher or lower total return would be if the return-rate average were one standard deviation above or below the expected rate.

For longer investment terms, the asset class with higher expected rate and larger standard deviation becomes better and better.

This illustrates the long-term investor’s advantage: For longer investment periods, the advantage of higher expected return rate increasingly outweighs the disadvantage of larger return-rate standard deviation. Investments with higher expected rates become far more favorable in prospects and even more favorable in risk.

To compare the frontier portfolios for long-term goals, the comparison must be advanced from the single-year efficient frontier to prospects and risks for long-term results -- the kind of comparison shown on Goal Frontier graphs.

This graph reveals that for long-term goals, portfolio comparisons are very different from what the efficient frontier graph shows. The efficient frontier graph shows that compared to the red portfolio, the blue has much less “risk”. But that is for the single year. The Goal Frontier graph shows that for the long term goal, the red is vastly better than the blue in both prospects and risk.

The red’s expected result is $1.2 million, vs. less than $400,000 for the blue. And the red’s probability of meeting the goal is more than 80%, compared to less than 30% for the blue.

For almost every individual and family, the principal purpose of investment is (or should be) meeting long-term needs and goals. With the combination of Modern Portfolio Theory and Monte Carlo simulation reflected in Goal Frontier graphs, investors and financial advisors can now zero in on best portfolios in prospects and risks for long-term plans and goals.

Unfortunately, most tools and sources of guidance in use of Modern Portfolio Theory advise that long-term investors’ portfolios be selected based on the single-year comparison shown on the efficient frontier, and label its dimensions of comparison simply “return” and “risk”, concealing the single-year focus and limitation of these measures and comparisons. This approach amounts to comparing and choosing portfolios based on short-term fears instead of long-term goals.

Clients’ short-term fears must certainly be dealt with -- but the most responsible way to do so is to provide best education on the importance of looking beyond the short-term ups and downs and focusing on the long-term goals. The approach of selecting portfolios on the single-year efficient frontier amounts to instead endorsing short-term fears as the logical basis for portfolio selection, and never even showing the clients how the frontier portfolios compare in prospects and risks for their long-term goals.

As the preceding graphs show, this approach can lead to choice of portfolios much worse than the best, offering much lower long-term prospects and much greater risk of falling short of long-term needs and goals.

All who are concerned with shaping or providing investment advice to individuals and families should be most concerned that the combined application of Modern Portfolio Theory and Monte Carlo simulation represented by Goal Frontier graphs be adopted and applied -- to replace the dangerous current misuse of single-year portfolio comparisons, as well as to provide investors the new power of optimizing for long-term goals.