Practice vs Theory: Account for Model Error In Your Investments

If you recall the article about transaction costs, you will remember that we compared the intangible and tangible costs associated with analyzing any decision. However, these costs, however accurate they may be, are still theoretical. In theory, we can estimate opportunity cost or even calculate out taxable income, but these estimates (and even the actuals that are recorded) are still only estimates…when it comes to decisions about your investments.

For example, imagine you buy a computer for $1000. You record this with a 10 year, straight-lined depreciation to $0 salvage. Therefore, its $100/yr depreciation. This is your accounting so far. Then, in year 3, the computer dies. Suddenly, you have $700 of “utility” still left for this computer on your financial statement, but the actual asset is at salvage value already. So you can decide to write-off the asset from your system for that year as -$700 (and subsequently adjust the capital portion of the balance sheet by throwing out the computer), you could re-adjust the depreciation to a 3-yr straight-line depreciation, or could keep the computer and continue to account for the asset’s value according to your original linear depreciation model. Either of the three ways are legitimate for accounting and investment purposes (technically, you probably wouldn’t keep the added $700 on your balance sheet).

Now according to that accounting balance sheet, we have accounted for the depreciation and utility of the asset. But have we really? For instance, do we consider the “work performed” on the computer asset as compared to a faster or slower model? Furthermore, can we really predict such a cost/benefit to any degree? We could by estimating added value for particular tasks, but it would still just be an estimate. Furthermore, all of these transactions don’t translate to real-life utility. The best we can do to emulate a real-life scenario is by using stochastic processes. These processes (whether linear or non-linear) focus on explaining a system’s variability to some degree of significance, and then optimizing that system based upon either maximizing efficiency for certain parameters and/or minimizing residual errors.

This brings me to my point. It’s extremely important that you understand that models have errors (residual errors), whether accounting, trading or algorithmic. Some model errors are intrinsic to the system (non-diversifiable), and others are extrinsic to the system (diversifiable). ¬†While most extrinisic errors (random errors) can be diversified away within portfolios, regressions, etc; systematic (intrinsic) errors are not.

Just remember the next time that you read a balance sheet, learn a new trading technique, or perhaps analyze an option’s spread, be sure to account for your own execution error as well as the inherent assumptions and errors within the model. Using safety margins, limit stops, hedging techniques, or maybe just reading a little bit more about the situation, company or event that you are about to trade, can do wonders for improving your PnLs, and save you from some un-deserved heartache. It never hurts to err on the side of caution.

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