To a lot of people the mention of Monte Carlo will automatically refer to the resort town in Monaco but in actual fact it is a technique developed by scientists while working on nuclear weapons which requires simulations.It invented during the 1940s by a Mathematician named Stanislaw Ulam, while he was working on nuclear weapons project at Los Amos Laboratory. The Monte Carlo Method is often used for simulating systems or projects that have many uncertain or random inputs. In finance it is used to create different models to solve different problem arising from finance such as simulating the stability of the financial system, how much money a company will lose in a given amount of time (VaR) and so on. Since then it has been used in various industries such as Finance (risk control), manufacturing (soap to semiconductor), operational research, project management, engineering, oil & gas, transportation (traffic lights), environmental control and many more.
Common users of the Monte Carlo Method in the financial industry can be found in insurance companies where it is used for calculating the risk of the company going insolvent. The solvency of any company depends on whether its assets are bigger than its liabilities. Since the assets and liabilities of insurance companies depended on the claim, inflation rates, returns on investment from fixed income, income from both renew and new policies the outcome can be considered uncertain.
So in order to know what are the scenarios on the solvency of the company in the next few months or up to a few years they need to simulate a model whereby they can estimate the assets and liabilities in advance. With the given number of random inputs, The Monte Carlo Method will produce simulations that will generate tens if not hundreds of thousands of outcome or different scenarios or probabilistic distribution as is known in Mathematics. This can be summarized and then plotted into graphs and histograms and will help produce better answers.
Is Cash Better than Stocks?
To illustrate the use of the Monte Carlo Method in helping us in our everyday investing decisions we shall use the following model which is a result of the research done by the York University of Ontario.
Case Study:
 You re given a $10,000 inheritance
 What will be your choice? Invest everything in Stocks or deposit it into Certificate of Deposits.
 Currently the CD is paying an interest rate of 5%
 Your problem is whether your Portfolio of U.S securities will outperform the 5% interest from the CD in 1,5,10,20 years?
The researchers have constructed the following table with the aid of the Monte Carlo Method in simulating different scenarios on whether the Portfolio of U.S securities will outperform the 5% yield from the CD.
Table 1. Probability of Underperformance
Time in Years

Underperform in %

1

34.83

2

29.06

3

24.97

4

21.77

5

19.16

10

10.87

20

4.06

25

2.56

30

1.63

35

1.05

Source : Professor Moshe, York University
From the above we can deduce that there is a 34.83% chance that the Portfolio of securities will underperform the 5% yield from the CD. Further to that you should notice that the percentage gone down to 10.87% after 10 years. Put it another way there is a 89.13% chance that your Portfolio will beat the performance of your CD. The longer the time horizon the better the chance your portfolio beating the 5% return from the CD. If you can wait another 10 years the chances of your portfolio outperforming is 95.94%. In other words the longer the timespan the safer will be your portfolio and hence the risk.
The above table also offers you the choice of different time period of risk and return to your portfolio. If you think that you need the money within 5years time to finance your child’s education, then you know that your chance of beating the return from the CD is 80.84%. Or put it another way your chance of underperforming is only 19.16%.
So basically the above table can help you in making your investing decisions based on the risk and time interval. It also shows you that the longer the time interval the safer will be your investments and hence produce a better than expected return than the CDs.
In the next few articles we will touch on how to use the Monte Carlo Method in helping you make decisions in Asset Allocation, Trading with margin, Diversification and etc.
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