In my previous article "Your Retirement Income Calculator Might Be Lying To You" (seekingalpha.com/article/4014217-retirem...), I outlined some of the reasons why I chose to develop my own retirement income calculator called Cu Parachute (itunes.apple.com/WebObjects/MZStore.woa/...). Part of the philosophy behind the app is that a good software tool should be simple to use, perform highly complex operations, and provide the user with actionable intelligence.

For a retirement calculator, "actionable intelligence" should include things like: how withdrawal rates affect retirement success probability, how retirement success changes if you live longer, how asset allocation affects success probability, etc. Based on the results of personalized simulations, the user can take action to increase their savings rate, change their asset allocation, put off retirement a few years, etc. In this article, I have used Cu Parachute to perform 14.1 million complete retirement scenarios in order to reveal the links between withdrawal rate, longevity, and asset allocation.

Early retirement (or financial independence) is becoming more and more in vogue. Many rules of thumb, like the 4% withdrawal rate, are based on a 30-year retirement. Someone who retires early at the age of 45 may expect to have a retirement as long as 50 years.

**1. Simulation Inputs**

Many simulations were performed to fill out the tables below. Each simulation used an estimated inflation rate in retirement of 3%, and 100,000 Monte Carlo iterations of complete retirement scenarios in order to determine success probability. For the purposes of this article, no Social Security, pension, taxes, or continued accumulation of retirement assets were used. For each simulation, the stock and bond values (asset allocation) were changed, as were the years in retirement, and the starting annual retirement income. The starting portfolio value stayed constant at $1,000,000, and the annual retirement income was increased by the inflation rate in each successive year (see Figure 1).

Figure 1 - Simulation Inputs: Left- Inputs That Change, Center- Constants, Right- Simulation Results

**2. It's Just Math**

The success probability goal used in this article was ≥ 85.0%. If you are less risk averse, you may be comfortable with a lower success probability for your own retirement plan. Because Monte Carlo simulations are probabilistic and not deterministic, the success probability can change slightly with each successive run using the same inputs. Using 100,000 iterations, Cu Parachute simulations will only change by a few tenths of one percent (+/- 0.002). Each simulation was run a single time.

An 85% success probability leads to a starting withdrawal rate of 3% for a 30-year retirement, 2.4% for a 40-year retirement, and 2.0% for a 50-year retirement in this series of scenarios. I am not trying to claim that these are hard and fast rules to govern your retirement planning. Your personal risk tolerance will determine what you consider a "safe" withdrawal rate. Please use this tool to personalize your own retirement plan, and determine for yourself what constitutes success. After that you can perform quick sensitivity analyses to show you how different inputs change your success probability. In the end, it's all just math.

**3. 4% Versus 3% Starting Withdrawal Rate**

The first series of simulations was performed to look at 4% and 3% withdrawal rate success probabilities over a 30-year retirement. A 4% withdrawal rate could not meet the 85% success probability threshold, regardless of asset allocation. For the 3% withdrawal scenarios, the successful simulations were centered near a 50% stock/50% bond asset allocation and peaked at 85.9% (See Figure 2).

Figure 2 - Success Probability Of 4% Versus 3% Starting Withdrawal Rate For A 30-Year Retirement

The simulations show that the highest success probability for the 4% scenario occurs with an asset allocation of 100% stocks.

**4. 2.4% Starting Withdrawal Rate For A 40-Year Retirement**

A 40-year retirement comes very close to success using a starting withdrawal rate of 2.4%. The success probability peaks around 84.4% with an allocation to stocks of between 65%-80%. The reason I chose to call this success is that a 2.3% starting withdrawal rate is well over the threshold of 85% while including the +/- 0.002 uncertainty. The actual maximum starting withdrawal rate would be somewhere between 2.3% and 2.4%. For the purposes of this article 2.4% is close enough. In order to perform a check of this result, the portfolio value was increased in order to make the starting annual retirement income the same as in the 3% withdrawal scenario ($30,000/year). The results using different starting portfolio values compare very well to each other (see Figure 3).

Figure 3 - Left: 2.4% Starting Withdrawal Rate For $1M Portfolio, Right: 2.4% Starting Withdrawal Rate For $30,000/Year Income

Note that the highest success probability (highlighted in green) is very close in each table, as is the lowest success probability (highlighted in red). The asset allocation is also very close in each table.

**5. 2.0% Starting Withdrawal Rate For A 50-Year Retirement**

A 50-year retirement succeeds (within the +/- 0.002 uncertainty estimate) using a starting withdrawal rate of 2.0%. The success probability peaks around 84.9% with an allocation to stocks of between 80%-95%. In order to perform a check of this result, the portfolio value was increased in order to make the starting annual retirement income the same as in the 3% withdrawal scenario ($30,000/year). The results using different starting portfolio values compare very well to each other (see Figure 4).

Figure 4 - Left: 2.0% Starting Withdrawal Rate For $1M Portfolio, Right: 2.0% Starting Withdrawal Rate For $30,000/Year Income

Note that the highest success probability (highlighted in green) is very close in each table, as is the lowest success probability (highlighted in red). The asset allocation is also very close in each table.

**6. Conclusions**

Using the success probability threshold of 85.0%, a successful starting withdrawal rate was found to be 3% for a 30-year retirement using an asset allocation of 50% stocks and 50% bonds. For a 40-year retirement, a successful starting withdrawal rate was found to be 2.4% using an asset allocation of 65%-80% stocks. For a 50-year retirement, a successful starting withdrawal rate was found to be 2.0% using an asset allocation of 80%-95% stocks. It is interesting that the shorter retirement benefited more by having half of the portfolio in bonds. That allowed for downside protection against the half of the portfolio in stocks that experienced higher volatility. As the length of retirement increased, the usefulness of the downside protection of bonds diminished and the higher real return of stocks became more important.

If you plan on taking a fixed starting withdrawal from your retirement, it may need to be smaller if you retire early (and are in retirement longer). Early retirees may also need to allocate a larger percentage of their retirement portfolio to stocks in order to meet their retirement income goals. A variable withdrawal rate is also something that early retirees (or any retirees for that matter) can use to help improve retirement income success probability (i.e. take a lower withdrawal rate in years with low retirement portfolio returns).

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

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I am trained as an engineer, and am not a financial professional. This article reflects my own opinions and should not be considered financial advice.