Many of us have been searching for ways to enhance the quality and accuracy of the financial plans we create for clients. The use of Monte Carlo simulation (MCS) is one example, but there’s still plenty of room for improvement. In the past few posts, we’ve discussed three different distributions (normal, uniform and triangular) that can be used with MCS in financial planning applications. In this post, we’ll discuss why the lognormal distribution is the best choice for the inflation assumption.
Inflation is clearly one of the more important assumptions in financial planning. However, beyond the consumer price index (CPI), as planners we should also consider using a separate inflation rate for Medicare, other health insurance premiums and college tuition, as these have risen faster than CPI. This should produce a more accurate expense assumption and hence, financial plan. However, we’ll focus our attention on the CPI data from January 1947 to the end of 2013 (66 years).
The annual rate of change in the CPI during this period was approximately 3.7%. Three of the years were negative and the rest were positive. The table below contains the CPI data by tranches.
Here’s how I determined that the lognormal distribution is the best choice. First, I selected the annual CPI data (i.e. percentage change) using a program called Batch Fit which is included in Crystal Ball. (Crystal Ball is a Monte Carlo application which is an add-in for Microsoft Excel). Batch Fit analyzed the data and determined the lognormal distribution was the best fit.
Normally, we think of a lognormal distribution as always positive. Therefore, if inflation is sometimes negative, how can the lognormal be the best fit? Here’s how. The lognormal distribution requires three parameters, the mean, the standard deviation, and the location. You know the first two parameters, but location may not be as familiar. Location is simply the lower end of the boundary or parameter. If you refer to the following exhibit you’ll notice that the location for the CPI data is negative 2.88 and the mean and standard deviation are 3.66 and 2.81 respectively.
The characteristics of a lognormal distribution are as follows: it is always positively skewed and the majority of the data is closer to the lower boundary. As you can see, CPI meets these criteria well.
Expenses are one of the two most important assumptions in a financial plan. Therefore, if we can improve its accuracy, we should be able to improve the quality of the financial plan when using MCS.
Have a great week and thanks for reading!