One argument from **Amazon**'s (NASDAQ:AMZN) bulls is that its hefty P/E ratio is supported by its stellar growth prospects. Our calculations showed that at Amazon, $1 new investment generates only 6¢ additional return. For sure there is growth and it is better than the yield of Treasuries, but certainly not stellar.

In summary, we found that:

- It took Amazon an average six quarters for its investment to start generate revenue
- $1 new investment generates only 6¢ additional return
- Even worse, its growth saw a steady down trend over time

Below we brief our approach. All the data and results are in ** Appendix **(below).

It's natural that investment has a lagging effect. A new plant or a new store may take quarters to build and will not generate sales immediately. Amazon is not (yet) a brick-and-mortal retailer, but investment in high-tech components also takes time. Usually a high-tech component needs to undergo steps, including development, verification and validation, and deployment. And it may go through iterations of those steps to finally work.

We use correlation analysis to quantify the lagging. If the correlation between two series of data points A and B is X%, it means that X% of A's variation can be explained (linearly) by B's, and *vice versa*. If revenue growth has the highest correlation with investment *n* quarters ago, it means that the growth is best explained by new investment *n* quarters ago. Hence we know the lagging is about *n* quarter.

We use revenue growth instead of earning growth because earnings are notoriously polluted by one time items, but revenue is not.

Both Amazon's revenue and investment numbers demonstrated strong seasonality, which would have skewed correlation analysis. We calculated four-quarter moving average to eliminate seasonal effects. The revenue growth is calculated to be the quarterly increase of the smoothed revenue.

Calculation showed that the correlation is the highest between growth of smoothed revenue and smoothed investment six quarters ago. Thus our first finding.

Next, we used regression analysis to estimate additional revenue that $1 investment would generate. We want to find a linear relationship such that:

Revenue Growth = *k* x Investment

Calculations showed that *k* is 1.50, meaning that $1 investment generates on average $1.50 additional revenue. Because Amazon's profit margin has always been less than 4% in the past five years, it would extract no more than 6¢ profit from the $1.50 revenue. Thus our second finding. The profit would be only 4.5¢ if we used the average profit margin at about 3%.

We also want to know whether $1 investment would generate more or less revenue the next year than it did this year. To quantify this increasing or diminishing return, we introduced a linear term into the regression analysis. The new relationship is:

Revenue Growth = *k* x Investment + *j* x Number of Quarters

Calculations showed that *j* is -$18.5 million, meaning revenue growth would in fact decrease $18.5 million each quarter, thus our third finding.

Amazon's investment increased every quarter. But our calculation showed it only generated a mediocre return of 4.5% to 6.0%. Even worse, the growth was diminishing. Maybe it's time that Amazon's senior management team clarifies its growth strategy. Or it can return the cash back to investors who can seek better growth elsewhere.

**Appendix**

*Click to enlarge*

The first table contains all the raw data: revenue of each quarter, investment of each quarter, smoothed revenue, growth of smoothed revenue, smoothed investment and that with lagging of one quarter, two quarters, three quarters, etc. All numbers in million.

The second table is the correlation between growth of smoothed revenue and smoothed investment with different lagging. The highest correlation is reached at "6Q Ago". The number at 82.13% showed strong correlation. It also justified the viability of the correlation analysis.

The third table is the regression analysis to find a linear function. The output of the linear function is growth of smoothed revenue. The input has two components: investment six quarters ago and number of quarters that is used to quantify the diminishing growth.

In the linear regression, we forced to have a zero interception.

The coefficients is the *k* = 1.50 and *j* = -18.5. The multiple R is 95.77%, meaning that the function we calculated can explain 95.77% of growth of smoothed revenue. The P values describe the probability if there is no linear relation. Both are less than 5%, thus the probability is ignorable. The high multiple R and low P values justified the viability of the regression analysis.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.