In Part 1 of this series I suggested that there are indications that the global markets are behaving in a manner consistent with the PIMCO "New Normal."

In this article I want to attempt to illustrate both *why* this should matter to retirees, as well as *how much* it could potentially impact portfolio drawdown rates during retirement.

In his book "Are You A Stock or A Bond" author Moshe Milevsky states that one of the achievements he is most proud of is a one-line formula he and some colleagues developed that can, in many cases, eliminate the need for expensive and cumbersome retirement simulation software.

Moreover, Dr. Milevsky (an Associate Professor of Finance at York University's Schulich School of Business and Executive Director of the IFID Centre) has generously made his formula available to the general public as an Excel workbook.

This workbook is an excellent adjunct for retirement planning, not so much from the standpoint of the *accuracy* of its results, but from its ability to illustrate the *sensitivity* of changes in investment return, volatility, and life span on drawdown rates.

Here's a screenshot of the original spreadsheet from Milevsky's 2004 paper (click the image to enlarge):*(Click to enlarge)*

In the interests of preserving the integrity of Milevsky's spreadsheet, I have not changed, altered, or removed any of the original structure (even though some of it is not relevant for my purposes in this article).

Accordingly, some explanation about the spreadsheet is necessary before using it to illustrate possible scenarios:

- Milevsky's spreadsheet was designed to evaluate both the uncertainty related to investment outcomes and the uncertainty related to the retiree's remaining lifespan. The MRL column shows that, according to the longevity tables Milevsky used in 2004, a 50 year old had a median remaining lifespan of 27 years, a 55 year old had a MRL of 26 years, etc. For our use, we can think of the MRL column as simply the "investment time horizon" and could, for example, replace any number in the MRL column with, say, 35 years to illustrate the impact of return and volatility over a 35-year retirement period.
- The Lambda values next to the MRL column are used for internal calculations within the spreadsheet and key off of the numbers in the MRL column; we can ignore them for our purposes.
- Milevsky developed the chart to determine the probability of "ruin"; that is, the probability that one will run out of money over the investment time horizon in the MRL column. To get the probability of "success" (or that one will
*not*run out of money), simply subtract the percentages in the green area from 1. - The spending rates in Milevsky's spreadsheet are on a
*real*basis, meaning that inflation effects have been removed from the calculations. To get an idea of the spending rates in*nominal*terms, simply add your outlook for annual inflation to the spending rate numbers expressed as percentages. (In other words, $4.00 real spend rate per $100 = 4% real drawdown or 5.5% nominal drawdown if one assumes inflation at 1.5%).

To interpret the example value circled in red in Figure 1, we first note that Milevsky assumed (in 2004) an average annual investment portfolio return of 7% with volatility of 20% (lower left corner). A 50 year old having a median remaining lifespan (or investment horizon) of 27 years could remove $4 for every $100 in his portfolio (4% drawdown) and have only a 17.4% probability that he would run out of money by the end of the 27 year period ... or an 82.6% chance of *not* running out of money (probability of success).

Now let's use the tool to evaluate some different scenarios.

In Part 1 (see link at the beginning of this article) I suggested that a 5% return and 25% volatility might be consistent with the muted returns and greater market uncertainty associated with PIMCO's "New Normal" concept.

If we substitute these values into Milevsky's spreadsheet the probabilities now change to those in Figure 2:*(Click to enlarge)*

In this circumstance, a 4% spending rate for our 50 year old with a 27 year retirement period results in a 46.7% probability of ruin (or 53.3% probability of success). Stated differently, if these "New Normal" conditions were to prevail throughout his MRL of 27 years, he has only slightly better than a 50/50 chance of making it to the end without running out of money. Worse yet, even reducing the drawdown to 3% does not sufficiently increase the probability of success.

To determine the spending rate that yields a lower "probability of ruin" in the range of 10-20%, it is necessary to change (reduce) the spending rate numbers. In Figure 2a the spending rates have been reduced to the range of $1.00 - $5.00.

Under these "New Normal" conditions of return and volatility our retiree is now faced with a truly disheartening drawdown rate of only 1.5% to achieve the same probability of success shown in Figure 2.

Of course, skeptics might point out that 25% volatility over such a long time period is unduly harsh; after all, since the beginning of 2012 we've enjoyed uncharacteristically *low* volatility in the U.S. markets. Perhaps the higher volatilities suggested by PIMCO's "multi-speed" global recovery are largely behind us, and 15% volatility is more likely going forward?

To accommodate this scenario, let's change the volatility to 15% in Figure 3:*(Click to enlarge)*

This certainly looks more encouraging; in fact, the probability of success at a 4% drawdown over 27 years assuming a 5% average portfolio return is now roughly the same as Figure 2 in which a **7%** average return (with higher volatility) was assumed.

Thus, in these three scenarios we have begun to get a sense of the trade-offs between *return* and *volatility* assumptions going forward.

Now, before relying too heavily on this tool for planning purposes, you should know that Milevsky does not claim that his model will accurately reproduce those generated by more sophisticated Monte Carlo simulators.

But the numbers generated by Milevsky's simplified model are close enough given the uncertainty surrounding anyone's best guess as to the input values (return, volatility, and investment horizon).

The real benefits of Milevsky's model (at least for the purposes of this series of articles) are:

- it clearly illustrates that a long-term shift in volatility can have a
*very*significant impact on retirement outcomes, and - it allows one to get a sense of the trade-offs associated with changes in return assumptions relative to changes in volatility assumptions.

But is such knowledge more than just a theoretical exercise? That is, can anything actually be *done* in an investment portfolio to give the retiree better confidence in selecting an appropriate (hopefully on the higher end) drawdown rate when faced with uncertain forward volatility?

In the 3rd and final part of this series I'll be discussing another intriguing academic effort. It illustrates how investors can potentially mitigate the effects of volatility without necessarily experiencing a commensurate reduction in return over the investment horizon.

I hope you'll continue to follow the series.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.