This is in response to an article published by Sivaram Velauthapillai who was citing a Globe and Mail article on the art of calculating returns.
The calculation and interpretation of “return on investment” is not as easy as one might think. The two most important and basic formulas in calculating return I will illustrate. They do not factor in the removal or addition of cash in an account.
The simple method of calculating the return, in very non-technical terminology, the following:
(simple return) = [(value today) – (value invested)] / (value invested)
To convert this into a percentage return, multiply by 100 and append a “%” to it.
You can see by this formula that if the “value today” is less than the “value invested”, you will have a negative return.
This formula should be in the arsenal of everybody investing. If you cannot calculate it on your own, there is really no point in investing in the markets at all since you will have no idea how to measure your own performance. Online sites have tools to measure performance, but without understanding the underlying formulas, the numbers will be meaningless.
The next parameter to get thrown into the equation is “return over time” – for example, making a simple return of 40% over one year is different than making a simple return of 40% over four years. Most people take 40% and divide by 4 and say they made “10% per year”, which is an incorrect calculation since it ignores the effects of compounding.
If you make 10% a year, your actual return would be 1.1^4-1 = 46.4%, not 40%.
To factor in compounding when calculating an annual return, you must engage in some mathematical finagling, which is a test of how much you remembered in high school math:
(annual compounded return) = exp[ln[1+(simple return)] / (time in years)]-1
For those not mathematically oriented, exp[…] and ln[…] refer to the exponential function.
When plugging in a 40% simple return over 4 years, you end up with an annual compounded return of 8.78% a year, which is the correct answer – verify by doing (1.0878^4)-1 = 40%.
The calculations become more complicated when you try to measure them for cash, time, and simple return. This will wait for a future post.
Hi Sacha,
I agree, it’s very important to keep track of your performance as an investor. That’s the only way to review and improve.
I’ve been wondering if I’m calculating and tracking my portfolio accurately. I’m curious as to how you’re calculating your returns and if there is a consensus methodology of calculating returns. (ex. whether to keep track of positions under FIFO and the right metrics to keep track of actual returns, based on the fluctuating contributions throughout the year)
Advice would be appreciated.
Thanks,
Michael
There are no right methods to calculating returns, only wrong ones.
In terms of your FIFO question, for tax purposes, Canada uses weighted average for the adjusted cost base.
This post does not get into adjusting for contributions, but I will get into that in a future date.