Use of Monte Carlo Simulation and Scenario Analysis

Use of Monte Carlo Simulation and Scenario Analysis

Shortcomings of Mean-Variance Optimization

As discussed, mean-variance analysis can help investors and advisors begin to zero in on an asset allocation while considering asset correlations, total return, and total risk. Effectively use of MVO will result in a specific set of output for current asset allocations, e.g.:

  • 60% equity.
  • 30% fixed income.
  • 5% real estate.
  • 5% cash.

One of the main criticisms of this result is that it is a single-period output. In real-world applications, investors want to know how their portfolios will behave over time, given various allocations, interest rates, tax rates, etc. In other words, building, properly managing, and utilizing wealth is an ongoing, life-long process—Monte Carlo simulation steps in at this point to bridge the gap.

Monte Carlo Simulation (“MCS”)

Monte Carlo Simulation is essentially a random-number generator. The user will define realistic limits on variables such as expected asset class returns, volatility, and correlation. The generator will go through thousands of iterations, creating a random yet realistic set of outcomes for a portfolio over the specified time horizon.

This randomly generated path allows the analyst to view realistic outcomes of a plan, as pictured below, to decide whether the chosen asset allocation results in acceptable portfolio outcomes as predicted by MCS.

Monte Carlo SimulationMonte Carlo simulations enable investment advisers to deal with practical issues that are difficult or impossible to analyze analytically. It may be appropriate for a taxable investor to rebalance their assets into a strategic asset allocation. It is easy to calculate the tax impact during a single period. MVO assumes that rebalancing is irrelevant in single-period settings.

In most multi-period investment problems, however, capital gains and losses will be realized when the portfolio is rebalanced. Tax payments (and transaction costs) will vary depending on a specific rebalancing rule. Mathematically formulating the multi-period problem would be difficult. A Monte Carlo simulation would more efficiently incorporate the interaction between rebalancing and taxes.

Choosing among asset allocations can be determined by an investor’s wealth at the end of their time horizon. Risk and return interact to determine future wealth. An asset allocation needs to be evaluated using Monte Carlo simulation based on whether or not cash flows are coming into or going out of the portfolio. When an asset allocation does not generate cash flows, the sequence of returns is irrelevant; ending wealth is path-independent (unaffected by the trajectory of returns). Simulated returns are also independent and identically distributed if cash flows are simulated. The analysis could find terminal wealth expected and percentiles. Typically, terminal wealth depends on the sequence of returns (the interaction between cash flows and returns) since investors save/deposit money and spend money from their portfolios. 

Question

Monte Carlo Simulation can most likely remedy which of the following shortcomings of mean-variance analysis?

  1. Sources of risk may not be diversified.
  2. Allocations are not ideal for valuing liabilities.
  3. Single-period framework.

Solution

The correct answer is C:

MVO is a single-period framework that does not consider trading/rebalancing costs and taxes. In other words, MVO is a recommendation for an asset allocation, a single snapshot in time. Investors are commonly more worried about how the portfolio will likely behave over its lifetime and what kind of outcomes are realistic for similar portfolios. This is where the Monte-Carlo simulation shines.

A is incorrect. Diversification of risk is a fundamental concept in portfolio theory and is addressed by mean-variance analysis. Mean-variance analysis seeks to construct portfolios with the highest expected return for a given level of risk, where risk is measured by the variance (or standard deviation) of the portfolio’s returns. Diversification is achieved by combining assets to reduce the overall portfolio risk.

B is incorrect. Mean-variance analysis is used to construct efficient portfolios, not value liabilities. Valuing liabilities involves estimating the present value of future cash flows, which is a separate issue from constructing an efficient portfolio.

Asset Allocation: Learning Module 4: Principles of Asset Allocation; Los 4(e) Discuss the use of Monte Carlo simulation and scenario analysis to evaluate the robustness of an asset allocation

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.