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Monte Carlo Simulation

The term "Monte Carlo" was introduced during World War II as a code name for simulation of problems associated with development of the atomic bomb. Algorithms were used to generate random samples from different kinds of probability distributions. Using this simulation, a whole range of possible outcomes could be determined in advance. Then by altering the inputs, the probability of achieving the desired outcome was increased. The same technique can be used to control investment risk. Now, however, there are more probability distributions, more sampling techniques, and much faster calculation speeds than were possible 55 years ago.

To find the probability of a total loss of your retirement funds, we must simulate a large number of possible and potential futures. Specifically, we must identify the range of futures that could happen given your personal circumstances. In some future scenarios, your assets will rise in value, in others they will hold their value, while in others still, they may fall in value. The purpose of simulation is to find out what the odds are of achieving any potential rate of return. This step allows us to create a mix of assets in your portfolio such that the combination of risk level and withdrawal rate is most likely to keep your balance positive or growing indefinitely given the market's volatility and the probable inflation rate.

With MCS, we do not assume a static future. Rather we assess the range of possibilities.  We let market returns fluctuate as wildly in the simulated future as they have in the real past, and in proportion to their occurrence.  We simulate the impact of a changing inflation rate.  Importantly, we do all these things simultaneously in one evaluation.


SIMULATION EXAMPLE

INPUT DATA:

  • Age: 65
  • Needed Income: $250,000 initially, increasing annually with inflation
  • Type of Portfolio: Diversified
  • Portfolio Balance: $3,000,000
  • Expected Annual Rate of Return: 9%
  • Volatility (standard deviation): +/- 10%
  • Inflation Range: 2.5 to 5.0%
  • Projection Period: 30 years

OUTPUT DATA:

  • Sampling: Monte Carlo
  • Number of Iterations: 5,000
  • Output Distribution: Normal
  • Probability of exhausting all funds before 30 years: 39%

This output shows us a range of possible outcomes with probabilities attached to each outcome. To be sure, we do not know which outcome will occur. But we can alter your investment portfolio to reduce its risk or raise its return to change the probability of a bad outcome and increase the likelihood of a good outcome. As cumbersome as all of this sounds, with today's computers, appropriate software, and experience with the procedures, the simulations can be done quickly.

Discussion

The preceding example is typical for an affluent retiree. It also seems reasonable that this person's retirement account should grow over a 30-year time period. But will it? Our simulation shows there is a 61 percent chance that this person will be able to draw down the desired income from his/her investment accumulation over the next 30 years without going broke. But there is also a 39 percent chance that he/she will go broke. The $3,000,000 question is this: Are you (the retiree) willing to risk a 39 percent chance of going broke?

Assuming you are not, we can suggest several things. First, we can develop a hypothetical new portfolio by changing the mix of assets to reduce the volatility, and rerun the simulation. We will optimize the risk/return tradeoff so that the new portfolio is efficient from a risk reduction standpoint.  We can also alter the income level assumption and repeat the procedures until we have achieved an acceptable probability that you will realize a satisfactory income level during all your retirement years.

Portfolio optimization and risk reduction via covariance analysis are techniques of Modern Portfolio Theory, the same techniques that the Nobel Prize committee found so compelling for the recipients mentioned in the introduction. Although a detailed discussion of these techniques is beyond the intent of this article, readers should not take them lightly. They are part of the new tools of investment management.

Conclusion

Uncertainty about the financial markets coupled with greater longevity and higher expectations about our standards of living have given rise to the need for most of us to plan for our retirement years with greater care than was necessary in the past. In particular, we all need to start early, build up higher levels of wealth, and understand our own comfort levels for investment risk. Equally important, we need to select our investment and risk managers with much greater care. Managers who do not use state-of-the-art tools put you at a great disadvantage. They simply cannot answer the critical questions about your investment planning needs.

In summary, MCS shows the odds of reaching a retirement goal and how much to safely withdraw from savings during retirement. MPT provides the tool to help make it happen. At Tisch Investment Advisory we simulate a large number of potential futures, determine the probability of their occurrences, and build safeguards into investment portfolios to assure with higher degrees of certainty that your retirement future is secure.

Please call us at 734/994-1188 to arrange an appointment.