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Inputs for a Two-Stock Monte Carlo Price Simulation

Article Quant Q&A · Author: Victor123
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Summary

The document considers what is needed to simulate the year-end prices and portfolio variance of two stocks. It challenges the idea that historical means and standard deviations alone can be used to draw independent lognormal prices and average them. The response points to a Brownian-motion Monte Carlo walkthrough, noting that variance is also needed to calculate drift and that the simulation requires additional setup choices.

The answer is only a brief pointer and does not specify the full model, parameter estimation method, time step, or how to represent correlation between assets. The question states zero correlation for the example, but a general two-asset simulation should encode the assumed dependence structure. The reference to historical observations also leaves open whether those estimates are appropriate for the future horizon. This document is useful as an introduction to required inputs, but not as a complete recipe for a reliable portfolio forecast.

Key ideas

  • A Monte Carlo forecast needs a defined price evolution model, not just starting prices and historical averages.
  • Variance is used to determine drift in the cited Brownian-motion setup.
  • A multi-asset simulation must represent the assumed dependence between stock returns.
  • Historical means and standard deviations may not fully describe future price behavior.

Tags

EquitiesStatisticsBacktestingPortfolio construction
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# How can I conduct a basic Monte carlo simulation on 2 stocks?


# How can I conduct a basic Monte carlo simulation on 2 stocks?












I have 2 stocks in my portfolio A and B.A is currently at 50 dollars and B at 40 dollars. Correlation between A and B is 0. Let us say I bought the stocks today at 50 and 40 dollars. If I wish to use a Monte Carlo simulation to estimate the individual stock prices of my portfolio and the variance at the end of 1 year, what other info do I need?

If the mean of the stock A was 50, that of B was 40 , the SD of A was 5, that of B was 4(all measured over last 5 years), does that give me enough info to proceed? Do I just draw random prices from 2 log normal distributions(meanA=50,meanB=40,sigmaA=5,sigmaB=4) ,take the average of the prices and call it done?

What else do I need to consider for a basic simulation? This is for education, not profit.

## Answer by MonteCarloSims (score 1)

https://quant.stackexchange.com/a/44799

Here is an excellent example of a code walkthrough of a Brownian Motion Monte Carlo Simulation. (Even if you're not coding this in Python - its just really nicely spelled out here step by step.)

In the article you will see that in addition to Mean and Standard Deviation you will also need Variance in order to calculate Drift.

Also, there are some other considerations in the article as to how to actually set up the Monte Carlo Simulation.

Hope this helps!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.