*This is a guest post from Dylan Ross, a certified financial planner and owner of Swan Financial Planning, LLC, a registered investment adviser in New Jersey.*

**How much money must you save each year to have the equivalent of $1 million today, 30 years from now?**

At first glance, this sounds like an easy enough question to answer by calculating a simple annual savings amount; however, a couple of very real variables can create an enormous range of possible answers. Two of the more influential variables are (1) how the money is invested (asset allocation) and (2) what the investments return year-to-year (timing of returns). The investor can control one of these variables, asset allocation, but the timing of returns is beyond anyoneâ€™s control.

The timing of returns is important because, although an allocation may ultimately live up to average returns, the sequence of the returns that make up the average play a greater roll than the final average will. If you are saving each year, future returns will have a greater impact on your savings because they will be on larger balances. If the more favorable returns that contribute to an average happen early on when your balances are smaller, you may end up with less than you anticipate.

If you are wondering how much impact the timing of returns can have on your savings, the table below illustrates the answer to a savings question using probabilities for success. To arrive at the savings amounts, each asset allocation was subjected to 1, 000 trials wherein each yearâ€™s return was randomly generated based on the allocationâ€™s risk and reward characteristics (see Assumptions below).

Savings targets are shown at 70%, 80% and 90% probabilities for success because those are numbers that may seem reasonable to plan for. A 50% target is coin-flip odds and generally too low to plan your future on, and 100% certainty may be overboard and can lead to unnecessary sacrifices. Keep in mind that success is defined, in this case, as having at least $1 million at the end of 30 years of saving, so at 80%, there is a 20% chance of either having something less than $1 million or needing to save even more each year.

Asset Allocation |
70% |
80% |
90% |

100% Cash | $32, 150/year | $33, 435/year | $35, 415/year |

60% Stocks/40% Bonds | $17, 500/year | $19, 725/year | $23, 850/year |

100% Stocks | $13, 815/year | $16, 610/year | $21, 310/year |

**Assumptions:**

» Inflation will be 3% per year.

» Investment fees are 0.20% per year.

» Savings will increase each year with inflation.

» Risk and return assumptions:

— Cash: 4.29% average return, 4.52% standard deviation

— 60% Stocks/40% Bonds: 9.71% average return, 12.45% standard deviation

— 100% Stocks: 12.32% % average return, 18.38% standard deviation

» Taxes were not included.

The first thing you may notice is that the more risk you take, the less youâ€™ll need to plan on saving each year. You may also notice that the lower risk, cash allocation savings amounts do not increase as drastically in order to achieve a greater probability than the higher risk, 100% stock allocation does. This is because higher risk investments have a wider range of potential outcomes that will impact your chances of reaching your investing goals. The risk is also mitigated by time. As the time horizon is shortened the gap between the 100% stock and 60% stock allocations will narrow and eventually the savings amounts for the 100% stock portfolio will be more than the 60% stock portfolio at higher probability targets.

This is not intended to promote one asset allocation over another but rather to illustrate the effect riskier investments can have on your savings, both positive and negative.

** nickel’s thoughts:** This is a great illustration of the risks that you take when you adopt a seemingly ‘low-risk’ investment strategy. Even after accounting for the inherent volatility of the stock market, incorporating stocks into your investment portfolio greatly increases the likelihood that you’ll be able to meet your long-term financial goals.

FYI: I invited Dylan to write this as a followup to an article by JLP of AllFinancialMatters which considered the costs of meeting your financial goals without stocks. Thanks Dylan!

J, the standard deviation for cash is based a composite of historical periods from short-term Treasury indices. The methodology was developed by the creators of the Monte Carlo engine I used to serve as a proxy for cash and equivalents. A standard deviation as low as youâ€™re referring to would mean that Treasuries would almost never lose value or achieve double-digit returns, neither of which is accurate. I suspect that you are thinking in terms of simply buying T-bills, holding them to maturity, and then reinvesting instead of maintaining a portfolio with a 90-day maturity, which is what was modeled.

Dylan, the T-Bill sd is greater than the mean, which indicates that T-Bills will give a negative return fairly often. I do not have a number in my pocket but my recollection is that the sd would be closer to 33% of the mean rather than over 100% of the mean so I was wondering where you obtained the data. Thank you.

Dylan,

Thanks for the explanation. I would hate to have a 30 year average return of 1.71%!!!

I guess there is a chance that this can happen if we are extremely unlucky.

J, the standard deviation used for cash does not imply a loss of principal. Standard deviation represents the frequency and extent to which values deviate from a statistical mean. Is there a different figure that you feel would be more appropriate?

When have T-Bills lost principal (as the deviation implies they can)?

MoneyNing, this does not assume the same return year-over-year. Yes, that would be way too optimistic using these numbers, which are just statistical averages. This was based on a simulation of the ups and downs that similar portfolios may experience over 30 years. Those average return numbers help to create the simulated returns but will not necessarily be the resulting average of the simulated returns.

For example, the 60/40 portfolio that resulted in an 80% probability for success had 800 out of 1,000 separate simulations result in $1,000,000 or more, and the 30 year average returns for those 800 simulations ranged from 5.86% to 14.63%. Of the 200 that missed the target, returns ranged from 1.71% to 7.41%.

Can we really safely assume that we can get 12% return year over year for stocks and even 10% return if we have 60% in stocks and 40% in bonds? Isn’t this being too optimistic?

Walt: I certainly agree that real-life would be much more complex. These numbers were used to illustrate risk and return as it relates to saving. To keep it simple, the standard deviations are based only on large cap stocks, long-term govâ€™t bonds, and T-Bills. This wasnâ€™t meant to make a case for or diversification but rather to contrast a higher risk/higher return investment with a lower risk/lower return investment. You are correct in your observation that these may not represent the most efficient investment portfolios.

The problem with the deviation numbers is that there is quite a bit of other information not included… Things that an advisor or analytial service must disclose in calculating these numbers. For example, are international positions used to reduce volatility and if so how much? Is the term stock just representative of a broad index or does it more appropriatly follow the size and styles suggested by MPT (modern portfolio theory)? Were bonds just investment grade corporates or is a diversified portfolio used, including agencys, governments, corportate bank loans, munis and higher yeild debt? All this can improve up capture and reduce volatility. Things that may cost more than 20 basis points but be well worth a reasonable additional fee…

This is an area that many of those who know little about the stock market understand. They think that the low risk solution is perfect and they can’t afford to invest in the stock market. In reality, the numbers show you can’t afford to stay out of the stock market over the long run.

Interesting article. The key in my opinion is that no matter which allocation you choose, you must be willing to stick with it. The extra return potential with a higher risk allocation can be a detriment to a portfolio if you are prone to panic and would sell into a falling market.

I follow a riskier allocation myself but am comfortable with the fluctuations.

The Dividend Guy

J, the cash standard deviation is based on the 90 day T-Bill and the distribution is lognormal.

Hello. How did you get the standard deviations so that, assuming normal distributions, cash has about a 15-20% chance of negative nominal returns but there is almost no chance of a bear market in the next 30 years?