Reward metrics
1. Reward metrics
Now that you have a series of historical monthly returns, you can compute key metrics on the past performance of stock ABC.2. Return on investment
The first natural question you probably have is: "What is the overall return on this investment?"3. Effective rate of return
The answer to this question is obtained by computing the effective rate of return. Given a series of T periodic returns, R1, R2, to RT, and an amount of invested capital C, the effective rate of return of an investment is defined as the rate R_E that solves the following equation.4. Effective rate of return
After a bit of algebra, the effective rate of return can be written as the product of the realized returns, augmented by one, raised to the inverse of the number of returns, minus one. In this expression you recognize the geometric mean of the series 1+R1,1+R2,…,1+RT. If the frequency of the returns is monthly, the effective rate of return is the monthly rate at which your initial investment has appreciated (or depreciated) so far.5. Effective rate of return
Let's take an example: you invest $100 in the stock ABC. At the end of the first month, the stock appreciates by 50%, but the month after, its value decreases by 50%. The effective rate of return, in this case, is equal to -13.4%. We see that with two returns of -13.4% in a row, the initial $100 would be $75.6. Average return
Investors are not only concerned about past performance, but also care about the future. It is therefore natural to estimate expected returns. A popular metric to infer the expected reward is the average return. The average return is computed as the sum of the past returns divided by the number of returns.7. Average return
If we take the same example as before, the average return is equal to 0%.8. Difference between effective and average return
The difference between the effective rate of return and the average return is crucial. For an investment whose return is +50% in the first month, and -50% in the second month, the average return is equal to 0%, whereas the effective rate of return is -13.4%. Since the final value of your investment is $75, so $25 lower than the initial value, you can come up with the conclusion that the average return is simply wrong. Well, this is not the case. When computing the average, all the returns are considered as independent. As such, it does not take the compounding effect into account, like the effective rate of a return does.9. Function AVERAGE()
To compute the average return with spreadsheets, you can use the function AVERAGE(). You need to pass the series of historical returns as the main argument, and the function will return the value.10. Effective rate of return: first approach
For the effective rate of return, this is a bit more demanding. You can proceed in two steps. First, include one column in which you add 1 to every return.11. Effective rate of return: first approach
Then, in a single cell, apply the formula. To do so, you can use a combination of the functions PRODUCT() and COUNT(). Both receive the series of returns augmented by one as the sole argument.12. Function ARRAYFORMULA()
An alternative way to compute the effective rate of return is by using the function ARRAYFORMULA(), which allows you to perform calculations with a range of cells. This function makes the computation process more direct since you don't need anymore to add a column with the returns augmented by one. You can directly perform the operations within ARRAYFORMULA().13. Functions ARRAYFORMULA() and GEOMEAN()
Together with ARRAYFORMULA(), you can use the GEOMEAN() function. This function takes one argument, a range of positive values, and returns the geometric mean of those values.14. It's time to practice!
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