### Use of Monte Carlo Simulation in Financial Planning

Monte Carlo Simulation: What is it? It is a technique used to understand the impact of risk on the  outcome of any project, wherein the impact of the risks can't be forecasted using traditional techniques. The source of risk is mainly the uncertainties related to the various inputs.

The uncertainties of input would generally follow a probability distribution. For example, the market returns tend to follow the normal distribution and inflation tends to follow the lognormal distribution.

The Monte Carlo Simulation (MCS) converts the uncertainties of the inputs into probability distributions, chooses values randomly from the distributions of each of the inputs, feeds them into the model of the project, and generates the output. MCS repeats this process thousands of times to produce a range of possible outcomes with the probability of their occurrences.

MCS: Use in Financial Planning We take a simple example to illustrate the use of MCS in financial planning. Suppose a client needs to have INR 10 lakh 10 years from now. Based on his risk tolerance level and income stream, his financial advisor suggests him to invest INR53,875 each year in a mix of equities and bonds for ten years, investment to be made at the beginning of each year, with asset mix expected to yield a CAGR of 11%.

The inputs in this investment model are:

i) The asset class weights, the returns on each of equity investments or simply the equity component of portfolio,

ii) Returns on each of debt investments or only the debt component of portfolio,

iii) Number of years, and

iv) Amounts of the investments made at the beginning of each year. We assume that returns on debt and equity components of the portfolio are variable while rest all is constant. Now, the MCS is applied in following steps:

1. Each of the variables is assigned a probability distribution as per their statistical characteristics.
2. Then, the possible range of values of those variables, i.e. the probable returns with their probability of occurrences is generated.
3. One value is chosen randomly from the corresponding range of likely values of each input variable.
4. Those values are then used in the investment model to calculate the output, i.e. the value of the investment at the end of 10 years from now.
5. The processes 3 & 4 are repeated thousands of times to give all possible values of output based on all possible values of variable inputs and the constant values of rest of the inputs.
6. This gives the possible values of the investment at the end of 10 years from now with their probability of occurrences.

Therefore, by using the MCS, the financial advisor can see the probability of his recommended investment model meeting the financial goal of his client. In this way, MCS would improve the investment model he would be recommending to this client.

Similarly, the financial advisor can use the MCS to advise the retirement planning to a client based upon his income stream, risk tolerance, post-retirement expenses, and expected years of life post-retirement.

Characteristics of MCS

• MCS allows several inputs to be variable at the same time to generate a probability distribution of one or more outputs.
• MCS supports a range of probability distributions of the inputs
• MCS takes into consideration all possible values of the inputs instead of relying on the average expected values.
• MCS gives a range of output values with their probabilities of occurrences. Limitations of MCS
• MCS cannot take into account the infrequent but radical market movements like the market downturn during 2008 financial crisis.
• Sometimes, MCS gives an unrealistic picture of returns for some asset classes in particular situations. For example, in US context, when the return on cash is almost zero, MCS can show the return of 2%.
• Wrong selection of probability distribution regarding inputs would provide misleading results.
• Its process is complicated.

Conclusion

MCS is an e cient tool for risk containment which incorporates all uncertainties of the inputs along with their probabilities of occurrences. A financial plan incorporating the MCS has better probability of achieving the financial target than the one based upon deterministic tools like expected average future value and simple spreadsheet functions.

Therefore, despite some limitations, it is increasingly being used by the financial planners the world over for making financial plans for their clients.

About tre Author: Swarn Saurabh, is a research analyst at Pulse Labs Research and Technology Solutions Private Limited. He primarily focuses on the domestic and global macroeconomic events and portfolio performance metrics. He holds master's degree in Science (Mathematics) and Business Administration and has cleared Level 1 of the CFA program from the CFA Institute.