Page 61 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 10.a: Describe steps in running a simulation.
LOS 10.b: Explain three ways to define the probability distributions for a READING 10: PROBABILISTIC APPROACHES: SCENARIO ANALYSIS, DECISION TREES, AND SIMULATIONS
simulation’s variables.
LOS 10.c: Describe how to treat correlation across variables in a simulation.
MODULE 10.1: PROBABILISTIC APPROACHES

Step 1: Determine the probabilistic variables: uncertain input variables that influence the value of an investment. Some are either
predictable –and hence can be derived, or have an insignificant influence -and hence assumed to be constant.

Step 2: Define probability distributions for these variables: Set the appropriate distribution (e.g. uniform or normal to characterize this
uncertain variable (e.g. cash flows), and then specify the parameters (e.g. mean, variance): 3 Approaches (almost mutually exclusive):
1. Historical data: Assumes that the future values of the variable will be similar to its past
2. Cross-sectional data: Using values of peers (similar-sized companies);
3. Pick a distribution and estimate the parameters: Subjective specification (based on insights into the industry).

Step 3: Check for correlations among variables (based on historical data). If so:
1) allow only one of the variables to vary (the other variable could then be algorithmically computed), or
2) build the rules of correlation into the simulation (this necessitates more sophisticated simulation packages).
Step 4: Run the simulation: Randomly input variables to generate estimated values. Do so repeated to yield thousands of estimates of
value, giving a distribution of the investment’s value. The number of simulations needed for a good output is driven by:
1. The no. of uncertain variables: The higher the number of probabilistic inputs, the greater the number of simulations needed;
2. The types of distributions: The greater the variability in types of distributions, the greater the number of simulations needed; and
3. The range of outcomes: The wider the range of outcomes of the uncertain variables, the higher the number of simulations needed.

LOS 10.d: Describe advantages of using simulations in decision making.

1. Better input quality: As analyst goes through the process of selecting a proper distribution for critical inputs, rather than relying on single
best estimates. The distribution selected can additionally be checked for conformity with historical or cross-sectional data.

2. Provides a distribution of expected value rather than a point estimate. Note that simulations do not provide better estimates of
expected value (These should be close to the expected value obtained using point estimates of individual inputs.)

Overall, they provide more complete but still imperfect picture of the risk in an investment. For example, the distribution of NPVs of a capital budgeting
project gives an indication of the risk of the project. However, if the required rate of return already incorporates the underlying risk, then the risk proxy
from the distribution of NPVs should not be used to evaluate competing capital budgeting projects. Avoid double counting risk!