Are you planning an early retirement? We urge you to check out our retirement income arithmetic before you hurry off into the sunset. Let’s look at the arithmetic of a financially secure and comfortable retirement.

First, we start with a portfolio balance of 50/50 stocks and bonds. A 50/50 mix offers a nice defense against down years and dampens your overall portfolio volatility.

Next we make some return assumptions. Our long-term return expectation for stocks is 8.8%. If you’re still using historical returns of 10%+ you’re going to be sorely disappointed. Our stock return assumption is based on an adjusted earnings and dividend yield on the Dow Jones Industrial Average. We adjusted the earnings of the Dow for GM’s big loss over the last year and made an adjustment for the level of buyback activity. Our adjustments result in an earnings yield of 5.8% and a dividend yield of 3%. Adding the two together gets you to 8.8%.

For our bond return assumption we assume a 50% investment in Vanguard GNMA and a 50% investment in preferred securities. This combination yields 5.9% in today’s environment.

Using the last 60 years of market activity on a 50/50 portfolio we come up with a standard deviation assumption of 9.1%. We further build in a 0.8% annual allowance for a registered investment advisor fee. If your portfolio is valued at $1 million or more, the tax-deductible value of a registered investment advisor is a low-impact cost for the order, discipline and attention to detail a professional investment staff can bring to the table for you.

To account for the corrosive effects of inflation we built in a modest purchasing power deflator. We assume your initial income draw increases by 3% for the first 15 years, 2% for the next 10 years, and 1% thereafter. As an investor ages, we assume that spending will naturally decline. Let’s look at an example to see how your annual income draw will change based on our purchasing power deflator. We’ll start with an initial portfolio value of $1,000,000 and a 4% draw. That means in year one we’ll take $40,000. In year two we’ll take $40,000 plus 3% of $40,000 which is $41,200. In year three we’ll increase our draw by another 3% which comes out to $42,436. By year 20 our draw will be upwards of $68,000 per year.

Using these assumptions we ran a number of simulations to establish the probability that an investor will not outlive his money. We tested various withdrawal rates over an array of time periods. A summary of our results is presented in Table 1 below. The column headers in Table 1 present three scenarios – one where you maintain principal throughout retirement, one where you maintain 20% of your principal, and a final one where you are only concerned with maintaining a retirement income. In the last scenario it is assumed you will draw down your entire principal. The row headings indicate your initial withdrawal rate. The percentages in each table are the probability that you will meet your goal selected in the column head.

You want your probability of success to be greater than 85%, and the higher the better. For example, if you plan your retirement for 25 years and you want to maintain your principal, there is a 91% chance you will be successful with a 3% draw, but only a 74% chance if you take a 4% draw. If you want to maintain principal you better stick with a 3% draw in this case. If on the other hand you’re willing to draw down your entire portfolio, there is 97% chance that you will be able to maintain a 4% draw throughout retirement. At a 97% probability you can be pretty comfortable that your portfolio will meet your objectives.

**Table 1**

Asset Allocation: 50% Stocks, 50% Bonds

Stock Return: 8.80%

Bond Return: 5.90%

Standard Deviation: 9.1%

Management Fees: 0.8%

Purchasing Power Deflator: 3% for first 15 years, 2% for next 10 years, and 1% thereafter

#### Jeremy Jones, CFA

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