Risk Manager

Using MCS on investment returns can give us a more meaningful analysis than linear assumptions alone. But what if there are more variables in our forecast? What if investment returns are only one of the many uncertainties in our forecast? Which variables should you place parameters on?

All About Variables

First, let’s define a variable. A variable is any assumption in your analysis in which there is uncertainty (risk). Usually, uncertainty increases as the time horizon lengthens. The first question to ask, then, is which variables could have the greatest impact on the forecast. The answer will, of course, depend on the specific variables you are facing. Ideally, you should use MCS on as many variables as is possible.

To explore this further, let’s look at an example. Assume we have a 42-year-old client who is a business owner, married with children, and plans to send his children to college. Furthermore, he and his wife want to know if they’ll have enough money to live comfortably in retirement with a high degree of certainty that their money won’t expire before they do. What are the questions to ask and the assumptions to make? Here are a just a few: How long will they live? Which college and how much will that cost in the future? Do they need to reduce their current expenses to save more each year? How much investment risk are they comfortable with and how much do they need to assume to reach their goals? How much will Social Security provide or will the system be insolvent then? Should they invest in a Roth IRA or traditional IRA in addition to their company retirement plan? How would their portfolio be affected if the market declines at the same time they retire and begin withdrawing from their assets? Each decision they make today will have an impact on their future. Then, are the variables highly predictable or very uncertain? Significant or insignificant? If an assumption is highly predictable or varies little, then MCS probably won’t add much. On the other hand, if the assumption is very unpredictable, then MCS could provide a great deal of insight.

Next, let’s make a list of possible assumptions for this case. Investment returns are the obvious one. Next, we have to consider cash flows. Let’s start with cash outflows. Assume the couple would like to receive $100,000 annually after taxes, which includes a mortgage of $20,000. If their mortgage is a fixed rate, it should be separated and only $80,000 of their expenses would be subject to inflation. If the mortgage is a variable rate, MCS can help model this, and can include a minimum and maximum rate. The rest of the expenses are subject to inflation (which will vary). There could also be medical cost such as health insurance premiums or ongoing expenses associated with a chronic condition. Since medical costs have been rising faster than the general inflation rate, we could separate these expenses and include a separate medical inflation rate. Current education costs with a separate education inflation rate could also be included. Other costs may include new car purchases every few years, support payments, and future savings. Cash inflows could include earnings until retirement, annual bonuses, net rental income, alimony, an inheritance, Social Security, and pensions, to name just a few. Some of these inflows may increase with inflation and some may not. For those that will increase, you could attach a separate inflation rate. To be more conservative with the analysis, you could use a higher inflation rate on expenses and a lower one on inflows. What if the couple plan to sell their rental property in the future? Then consideration should be given to the rate of growth on the property, its cost basis, their tax bracket, and the capital gains tax rates.

If you’re trying to forecast future estate values, you would need to include the value of their tangible assets such as their primary residence, vacation home, personal property, automobiles, business interests, or anything else they own, such as life insurance. There could easily be in excess of 20 different assumptions to be modeled using MCS. Remember, some of these variables will have a greater impact on the forecast than others.

With the changing federal estate exemption in the next few years–$2 million in 2006-08, then $3.5 million in 2009–MCS can help assess the probability of someone’s estate exceeding these amounts.

The Importance of Linear Forecasts

We’ve all seen linear forecasts. Let’s assume we start with a portfolio of $100,000 and expect it to grow at 6% for the next five years. If these assumptions held true, our ending balance would be $133,822. What if we don’t earn 6% each and every year? In the past, all financial projections were based on this methodology. What is the probability of achieving a number equal to or greater than the linear forecast? Is there a normal range of probability and why is this important? When a linear forecast is calculated and a final value is determined, its probability is dependent on the amount of risk or uncertainty in the forecast. When the risk is greater, the probability is lower. This type of comparison can assist in quantifying the risk in the forecast. For instance, using a normal distribution curve, the majority of outcomes occurs around the mean, or 50th percentile. If a high degree of risk is present, as there may be with a stock concentration, the probability of the linear outcome would be much less than 50%. This number could be 20-30% or lower, depending on the amount of risk and the time horizon analyzed.

To summarize our exploration of Monte Carlo simulation, we can argue that MCS can enhance our understanding of and ability to manage risk in a number of ways. You could focus on the probability of running out of money at different ages, probabilities within a specified range, probabilities of achieving a return greater than x, and more. This technique can improve our decision making by allowing us to achieve a better understanding of the ranges of outcomes. When used properly, the client wins, the practitioner wins, and the financial services industry wins.

Mike Patton, a CFP and AEP (accredited estate planner), is a senior financial planner with JP Morgan Private Client Services in Baton Rouge, Louisiana. He specializes in retirement and investment planning, and wealth transfer strategies, with an emphasis on probability analysis using Monte Carlo simulation. He can be reached at [email protected].

How Many Trials?

The number of trials you should run in Monte Carlo simulations is related to the number of variables and the number of occurrences per trial.

Let’s look at an example. Assume you’re trying to determine the future value of a portfolio you will hold for five years. Assume also that there are no cash inflows or outflows to consider. Furthermore, assume the only variable in the analysis is the return on the portfolio. In this case the number of variables = 1 (the return), and the number of occurrences per trial = 5 (1 variable x 5 years). If you ran 100 trials you would have 500 total occurrences (1 variable x 5 years x 100 trials). Each time a trial is run the variable changes (randomly), not just in the first year but in each year it occurs. Since MCS selects numbers at random, it may select bad returns in the early years and good returns later, or the reverse may be true. In any event, each time a trial is run the ending portfolio value is changed. You’ll need to run a sufficient number of trials to assure you are modeling as many outcomes as possible. There is a point of diminishing returns, however. You’ll know you’ve reached this point whenever the additional numbers of trials yields little or no effect on the outcome (probabilities). In the above example, 250 to 500 trials may suffice.

In the retirement example used earlier, let’s assume we identified 20 variables. If the time horizon we’re modeling is 30 years and we ran 1,000 trials, then there would be 600 occurrences per trial (20 variables x 30 years) and 600,000 total occurrences (600 occurrences per trial x 1,000 trials).

So how many trials should we run? Let’s say we increased our trials from 1,000 to 3,000 and the probabilities changed significantly, but at 5,000 trials there was little or no change. In this case, then, the ideal number of trials is probably somewhere between 3,000 and 5,000. It’s difficult to say with any certainty how many trials should be run. You’ll have to experiment with this on a case-by-case basis. A simple rule of thumb is that the more variables you include, the more trials you should run.