“Contradictions do not exist. Whenever you think you are facing a contradiction, check your premises. You will find that one of them is wrong.” – Ayn Rand

**Traditional Planning Model**

Imagine a 65 year old couple, Jack and Diane, about to retire with no private pension, and $1 million in RRSPs. Jack worked outside the home for over 40 years in Canada, and so he qualifies for full CPP and OAS. Diane never worked for income outside the home.

When we first arrive at the site, we must enter Jack’s month and year of birth so that the system can consult lifespan tables and produce his Median Remaining Lifespan (MRL). This important number is simply the age at which Jack has a 50% chance of mortality. For a 65 year old male non-smoker, this age is about 82, which suggests a 50% chance that he will live for at least another 17 years.

We then enter CPP and OAS information for Jack, assuming maximum 2010 monthly numbers of $934 for CPP. This is factored into total annual income later in the exercise. Like so many practicing healthcare professionals, Jack and Diane have no private pension income.

Source: Canadian Retirement Income Calculator

The next step is to enter the total value of RRSP savings ($1 million), as well as Jack’s preferred age of retirement (65). We then have an opportunity to adjust Jack’s expected lifespan, which we leave at age 82. Finally, we choose an expected return for the portfolio, which Service Canada defaults to 7%, and an inflation rate of 3.5% (again, the default). The image below summarizes these inputs. Note that we are contributing $0 to Jack’s RRSP because he is retiring imminently.

Source: Canadian Retirement Income Calculator

Let’s zero-in on the number that the calculator computed as the estimated annual retirement income from Jack and Diane’s RRSPs. The calculator suggests the couple can withdraw $75,421 per year from their RRSPs (eventually RRIFs) according to the inputs we provided. This amounts to a withdrawal rate of approximately 7.5% from their RRSP portfolios.

We can replicate this calculated number using a simple Excel spreadsheet, such as the one captured below. It is also computable via a standard Future Value calculation, but the spreadsheet below better illustrates cash-flows and portfolio ending values. Note that the calculator below solves for a slightly different portfolio income of $75,744, which is slightly higher than the $75,421 derived from Services Canada. This small deviation is probably due to the fact that the Median Remaining Lifespan used by the Services Canada calculator wasn’t exactly 17 years. In fact, it is 17.14 years according to the Statistics Canada tables.

- constant returns to the portfolio of 7%, and with no variability
- constant inflation of 3.5%
- a fixed lifespan of 82 years.

The use of averages in the models without accounting for the variability around the averages implies a great deal of ambiguity about the model’s likelihood of success. For example, if expected AVERAGE returns are to be 7% per year, one must acknowledge a 50% possibility of experiencing returns below this average, which would result in a failed retirement plan. Further, if the average expected lifespan is 82 years, there is a 50% chance of living beyond this age, which would again result in a failed retirement.

**Actuarial Model**

The next step in our case study is to contrast the results from the standard planning exercise above with an actuarial approach, such as the model advocated by Dr. Moshe Milevsky in his paper ‘Sustainability and Ruin‘. The actuarial approach allows us to tailor the inputs in ways that account for the random nature of lifespan, inflation, and market returns. Further, this approach captures the influence of year-to-year variability in portfolio value as a result of bull and bear markets. We call this variability in portfolio value ‘Sequence of Returns Risk’.

Let’s walk Jack and Diane through the process of modeling safe retirement income using this actuarial approach. We will assume the same age and savings numbers, and use a precise MRL number from StatsCan tables. In addition, we will include a number which captures the variability of returns that Jack and Diane might expect in order to achieve a 7% annualized return on their investments.

The actuarial approach recommended by the most qualified experts in the retirement planning and pension community requires 4 inputs, in contrast with the two inputs to the traditional model.

Source: Butler|Philbrick & Associates

**Expected Return: **the average annual return that the portfolio is expected to return over a person’s retirement horizon, adjusted for inflation

**Portfolio Volatility: **the degree to which the portfolio experiences ups and downs in value as markets rise and fall

**Median Remaining Lifespan: **the number of years between a person’s current age, and the age at which the person has a 50% chance of mortality.

**Confidence Interval:** the degree to which a retiree wants to be certain of success. For example a more conservative retiree may want to be 85% confident of outliving his or her portfolio. In contrast, a more adventurous retiree may wish to have a higher retirement income, and thus settle for a lower confidence interval, say 70%. Note that a traditional plan, by definition, provides for a maximum of 50% confidence.

**Safe Extraction Rate:**the portion of a retiree’s portfolio that can be safely withdrawn each year for income while maintaining an appropriate level of confidence in the future success of the plan. For the traditional plan, the extraction rate reflects a median outcome: 50% of future outcomes will cause the plan to fail.The purpose of an actuarial approach is to tailor plans to accommodate the level of safety needed by each individual retiree. This approach also facilitates annual reviews which quantify whether a plan is on track based on whether current portfolio values fall into a certain confidence interval range. For example, a plan can be reviewed each year, and incomes can be adjusted if confidence intervals rise above, or fall below, certain confidence threshold, say 90% or 70% respectively.

**Reverse Engineering the Traditional Model**

What happens when we plug the output from the traditional model into our actuarial model? What is the actual probability of a successful retirement if we apply the assumptions and extraction rate arrived at in the Service Canada exercise above?

Let’s review the assumptions:

Expected Return: 7% returns minus 3.5% inflation = 3.5%

Median Remaining Lifespan = 17.14 years

Extraction rate = 7.5% ($75,421 income from $1 million portfolio)

Our actuarial analysis also requires a ‘Portfolio Volatility’ assumption to account for ‘Sequence of Returns’ risk. This number is not without some controversy, and is dependent on an individual’s allocation to stocks, bonds and other assets. However, we can work backward from the Expected Return assumption above to find a portfolio of stocks and bonds that, based on simple long-term historical stock returns and current bond yields, would lead to an Expected Return of 7% (before inflation). It turns out that a portfolio consisting of 30% bonds and 70% stocks provides for a 7% return. Such a portfolio has a Portfolio Volatility of about 13.25%.

New assumption:

Portfolio Volatility: 13.25%

Now that we have all of our inputs we can run our actuarial analysis. The table and chart below summarize our assumptions and the results of our analysis.