Page 95 - Mumme Booklet

DRAFT

The Probability Analysis in this plan uses Monte Carlo simulation, a problem-solving technique that
approximates the probability of certain outcomes by running multiple simulations, called trials, using random
variables. The Probability Analysis runs multiple trials (500) of a hypothetical portfolio or investment strategy
to determine how it performs over the time available to attain a goal. The Probability Analysis considers your
goal to be what you have identified as your objectives on the Objectives page(s) of this plan, and considers
the resources that you have stated are and will be available over time to meet your goal as described on the
Resources page(s) in your plan. The Probability Analysis will consider assumptions as to contributions and
withdrawals made over time as well as the taxation of any investment income or gains. Assumptions about
expected returns and inflation that are disclosed below will be used for this Probability Analysis. Assumptions
you have made about rates of return and annual increase rates shown for income or expenses on the
Objectives, Resources, and Assumptions pages will not be used for this simulation.

Each trial examines the cumulative simulated annual returns of the portfolio or investment strategy for the
given period. Each trial also determines the dollars needed to fund the goal given the cumulative effect of
varying rates of inflation over time, and compares the dollars needed to the resources available to determine
a level of goal coverage. Because this Probability Analysis uses randomly generated return rates and inflation
rates, each trial has a different outcome.
The Monte Carlo simulation used for this Probability Analysis was developed by the Investment Risk
Management division of Northwestern Mutual. The hypothetical, randomized annual investment returns and
inflation rates used in the 500 trials were determined using a model of asset class returns and inflation. The
resulting returns, standard deviations and correlation coefficients from that model over a 30-year time horizon
are disclosed in the Asset Class Assumptions and Asset Class Correlations listed below.

The model which we use for simulating asset class returns and inflation assumes that risk factors in the
economy such as inflation, unemployment, and gross domestic product (“economic risk factors”) are the
drivers of asset class returns. We studied the historical correlation between these risk factors and the prices
and performance of asset classes, and constructed a statistical model that could explain the prices of asset
classes over time based on the risk factors. We also consider current valuation levels of asset classes. In
each of the 500 trials, we randomized the economic risk factors to create a possible future path of the
economy, and each year calculated the asset prices and returns based on the randomized risk factors. For
example, if in a trial in a given simulated year the risk factors show the economy in a recession, negative
GDP would negatively impact the price of stocks. We randomize the risk factors using a time series model
with mean reversion, meaning that the values in one year are the starting point for determining the values in
the next year, and that over time risk factors revert to historical averages. We assume that asset prices and
asset returns have different components (such as growth versus dividends or income) and determine each of
those components independently, based on the risk factors.

The models we use to randomize risk factors consider present asset prices and current economic conditions
as the starting point for simulations. The mean reversion within the model means that each year the average
risk factors are different and the returns of asset classes are different, and shift over time. After 30 years, real
U.S. GDP is assumed to average 1.99% and inflation is assumed to average 1.84%.

The simulation considers present asset values and interest rates as its starting point. The average expected
geometric return for U.S. Equity - Large Cap is 6.51% after 30 years. The model also considers current
interest rates, which are low by historical standards. The simulations assume that over time real interest rates
will increase as they revert to historical averages. Cash and Fixed Income have lower short-term rates of
return, due to current interest rates, but average returns increase with the assumption that real interest rates
will increase as well. The average geometric return for Fixed Income is 4.32% after 30 years. The average
geometric return for Cash is 2.65% after 30 years.
The simulations used are the same simulations used to derive the capital markets assumptions used
elsewhere in the plan. For example, the rates used in Asset Allocation, and as the default rates of return for
purposes of deterministic planning are based on the average rates from these simulations over a 30-year time
horizon.

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This plan is not complete without the Assumptions and Disclosures pages appearing at the end.
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