The Steps of Monte Carlo Simulation
Suppose you come up with a plan for trading a certain commodity. You notice a certain level of autocorrelation in the price movements, and your plan is to simply purchase the commodity after a previous daily close of 0.1% or greater, and short the commodity following a previous daily close of -0.1% or less.
You can better understand the results of this strategy using __Monte Carlo simulation__. Monte Carlo simulation is a sort of "stress test" for a model or investment strategy.
What is the quantity of interest in this example?
Exactly! This is really what you are working to investigate.
No, this is incidental to your research. You are interested in making money from your trading strategy.
No, that's the trigger for your strategy, but it's not what really interests you the most. What interests you the most is making money!
After this, you're ready to let the computer create 250 observations. What would these observations be centered around a mean of?
No, using annual returns in a daily simulation gives you some odd results.
That's right!
To simulate daily returns on the commodity, just use the average daily returns for the commodity.
No, there isn't any reason to force the simulation to return a mean of zero.
Since you want to purchase the commodity following a 0.1% increase and short the commodity following a -0.1% price change, then you can calculate the daily returns earned using this strategy on each day following these price changes. How many returns will this give you?
No, this isn't possible. The random variable will generate 250 returns on the underlying commodity, but not all of these will trigger a trade.
No, this is extremely unlikely. The random variable will generate 250 returns on the underlying commodity, but not all of these will trigger a trade.
Exactly!
Since your trading strategy is triggered by prior daily returns outside of the -0.1% to +0.1% band, it is quite reasonable to assume that there are many days where the daily returns are close to zero, and so you will not have a position. This will result in fewer than 250 returns for your strategy.
With these simulated trading strategy returns throughout the year, you can now calculate a geometric average of returns to see how your strategy might have fared.
Is this good enough? Do you want to put real money into a trading strategy after this single trial? Probably not, and this is where Step 7 comes in: go back to the computer simulation and run a number of trials. Computing power is very cheap, and the information is valuable. Run this simulated year over and over to see how often you end up beating your return objective. Then you'll have your answer as to whether or not you have really come up with something useful.
To summarize this discussion:
[[summary]]
This involves several steps:
1. Specify the quantities of interest
2. Specify a time grid
3. Specify distributional assumptions for risk factors
4. Use a computer program to generate random values
5. Calculate the underlying values using the random values
6. Compute the quantities of interest
7. Go back to Step 4 until a number of trials are completed.
So, now you specify a time grid. This will be daily returns, and you might choose to look at these for a year, or even multiple years. Assume that you choose one trading year, for 250 daily returns.
Next, you'll need the distributional assumptions for these daily returns. You might measure them to find that daily returns for this commodity are approximately normal, with a little excess kurtosis. That's the distribution you'll build into your simulation. Each trading day a return is generated which, over your time grid, has this same leptokurtic (but almost normal) distribution.
At this point, take a look at the list of steps again:
1. Specify the quantities of interest
2. Specify a time grid
3. Specify distributional assumptions for risk factors
4. Use a computer program to generate random values
5. Calculate the underlying values using the random values
6. Compute the quantities of interest
7. Go back to Step 4 until a number of trials are completed.
You specified your interest in learning what returns you would generate with this strategy, specified a time of daily returns for a year, chose a distribution for your commodity's daily returns, and ran 250 random observations with your computer. Now you're ready for Step 5, where you'll use these generated random variables to test your trading strategy.
The return you would obtain over a period of time with this strategy
The price of the underlying commodity
The previous daily price change
Zero
Whatever average daily returns the commodity earns
Whatever annual returns the commodity earns
Fewer than 250 returns
250 returns
Greater than 250 returns
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