Any investment portfolio has two engines of growth: the contributions made by the investor, and the rate of return generated by the portfolio. But which has the greater impact?

A detailed analysis designed to isolate the impact of changing the savings rate versus changes in the portfolio return revealed that the answer depends greatly on a client's age.

The Savings Matrix chart below shows various ending account values at age 65 based on four different starting ages of an investor. The example assumes a \$35,000 starting salary at age 25 and a 3% annual increase in pay. The baseline figures in the first column assume an annual savings rate of 6% of income and an annualized portfolio return of 6%. The other two columns show how the results would vary if the savings rate were to jump to 10% or if the portfolio return were to increase to 10%, while holding the other variable constant.

For an investor who begins contributing to an investment portfolio at 25, the baseline terminal value at 65 is \$528,007. If the annual portfolio return increases to 10% and the savings rate stays at 6%, the portfolio value at 65 soars to nearly \$1.4 million. On the other hand, if the savings rate increases to 10% a year and the portfolio return stays at 6%, the ending portfolio value at 65 is \$880,012.

Of course, one might suggest that the best of all worlds for a 25-year-old client is to save 10% of income each year and have a portfolio return of 10%. No question about that - the ending portfolio value would be a sweet \$2,321,264.

But clearly, for a young client, the portfolio rate of return has more impact on the ultimate account value than the annual savings rate.

Next, consider an investor just getting started at 35 years old. Assuming a 6% savings rate and a 6% annualized portfolio return, the baseline portfolio value at 65 is \$337,540 (assuming a salary of \$47,000 at age 35 and a 3% annual increase in pay). If the portfolio's annual rate of return increases to 10% while the savings rate is constant at 6%, the ending account value at 65 is \$673,071, compared with \$562,567 if the savings rate is increased to 10% while holding the portfolio return at 6% annually. Once again, for a younger client, an increase in the portfolio return provides greater impact than the same increase in the savings rate.

THE NEW MATH

But at age 45, the math gets interesting. A person who starts investing at that point benefits more from increasing his savings rate to 10% than from attempting to increase his portfolio return to 10%.

This may be counterintuitive; the conventional wisdom might suggest that if a person is late to the retirement game, he needs to make up for lost time by trying to build a portfolio that can crank out returns of 10% to 12% a year. This research suggests otherwise. In fact, the older investor needs to save more each year rather than build an overly aggressive, high-risk/high-return portfolio.

Think of it this way: If the time frame of a client is reduced to 20 years from 40 years, the beneficial impact of compounding is drastically reduced. Since the dramatic compounding-based growth in a portfolio really starts to pick up steam after 20 to 25 years, within shorter time frames, a portfolio benefits more from direct contributions.

PERILS OF 'JUICING'

In addition to the limited upside benefit, "juicing" a portfolio in hopes of cranking out higher returns increased the downside risk in any given year significantly.

Over the past 43 years (1970-2012), for example, one portfolio design generating a 6% annualized return had an asset allocation of 85% cash or 3-month T-bills, 10% bonds and 5% large-cap U.S. stocks. Over those years, its worst one-year return was a loss of 0.04%. (Yet the past few years, the average return for such a portfolio hasn't been much higher than that.)

By contrast, a different portfolio design that generated a 10% annualized return had an asset allocation of 35% large-cap U.S. stocks, 20% small-cap U.S. stocks, 10% non-U.S. stocks, 25% bonds and 10% cash or 3-month T-bills. Its worst-case one-year return was a loss of 22.6%.

You could construct other portfolios to try to generate similar returns, but the point is that a higher-return portfolio is also a higher-risk portfolio, and older clients have fewer years in which to hope to recover from such losses.

For an investor who starts saving at age 55, raising the savings rate to 10% of income produces an ending account value that is nearly \$40,000 higher than if the portfolio return is raised to 10%. Clearly, this is an investor who is very late to the game - and, of course, unlikely to be one of your clients. Such investors need to do all they can to prepare for retirement. These results clearly indicate that saving as much of their income as they can has a greater impact than cranking up the portfolio risk to try to generate higher returns.

Another, related issue: Contributions are a variable that is more in the control of the investor, while portfolio performance, particularly in the short run, is far less controllable. As a result, investors who rely upon portfolio performance to do their heavy lifting will usually fall into the trap of having too much equity exposure and, therefore, too much risk.

Particularly for clients who are in or near retirement, the performance of an investment portfolio should accomplish two primary goals: preserve and protect principal and provide a modest rate of return.

PAY NOW, OR PAY LATER

Understandably, in an era of supersize meals, vehicles, houses and egos, the notion of a "modest" rate of return may sound rather unsophisticated. But what the analysis suggests is that the performance of a portfolio should never be expected to make up for under-saving. Here's a clear message for your clients' young adult children: A contribution rate of 1% to 2% of income into a 401(k) or IRA is simply inadequate.

That advise is hardly groundbreaking. But Americans often allow their list of wants to put the squeeze on their retirement savings rate. (It brings to mind the Fram oil filter commercial from 30 years ago: You can pay now, or pay later.) An inadequate savings rate now will inflict a heavy price later, when a family's total savings is only a fraction of what it needs to be.

If younger investors are willing to take more risk, there is a distinct payoff in the long run - and they have the crucial benefit of time on their side. But for older investors, taking on more risk exposes them to losses that they have neither the time to recoup nor the emotional stamina to endure.

Consider a simplistic example that illustrates the importance of not deferring saving. Once again, assume that a 25-year-old worker begins her career earning \$35,000 per year, and that her salary increases 3% annually over the next 40 years. If she invests 10% of her income each year in a 401(k) - with, say, her own 6% savings and a 4% match from her employer - she will have a nominal balance of \$275,000 accumulated by the time she's 65 if the portfolio earns a rate of return of 0%. That is, she will have more than a quarter of a million dollars entirely as a result of her own contributions, the first engine of growth.

Now, let's consider the second engine of growth, portfolio performance. If her 401(k) account averages an annualized return of 6% per year, her account value when she's 65 will be \$880,000 (of which \$275,000 will be her contributions). Clearly, the "return" of the portfolio is a significant part of the ending account value, along with her contributions.

Now assume the 25-year-old invests only 2% of her salary each year until she retires at 65. Assuming a 0% return in her retirement portfolio, she would have an account balance of \$55,000. And with a 6% average annualized return over 40 years, her balance would be only \$176,000.

To achieve an ending balance of \$880,000 by the time she's 65 while maintaining her low 2% contribution rate, her retirement portfolio would need to generate an average annualized return of 12.4%. In other words, her inadequate contributions force the portfolio to (try to) do the heavy lifting. Can a portfolio reasonably be expected to produce an average annualized return of 12.4% over a 40-year period?

Over the past 87 years, there have been 48 rolling 40-year periods. The S&P 500 has produced a 40-year annualized return in excess of 12.4% on only two occasions out of 48 possibilities, and a 60% stock/40% bond portfolio has never once achieved a 40-year annualized return of 12.4% or higher.

In fact, the average 40-year return (over the 48 periods since 1926) for a 60/40 portfolio was 9.2%. If our 25-year-old wants to accumulate \$880,000 by the time she's 65 and earns an average return of 9.2%, she would need to increase her annual savings rate to 4.25% from 2%.

This type of hypothetical analysis can go on forever, but the reality is glaring: A 2% savings rate is not adequate preparation for retirement. For that matter, not even a 4% savings rate is adequate.

The most important step that can be taken to help Americans be better prepared financially for retirement would be to increase the annual savings rate to at least 6% of income. A rate of 10% would be that much better. For investors older than 45, this is even more vitally important.

Craig L. Israelsen, Ph.D., is a Financial Planning contributing writer in Springville, Utah, and an associate professor at Brigham Young University. He is the author of 7Twelve: A Diversified Investment Portfolio With a Plan.