As a computer engineer, I simply can't keep myself from looking at stock prices as just mere numeric data series.

In my first article, I tried to spot some 3 correlated values suggesting a potential upside for Annaly Capital (NYSE:NLY) stock.

In this article, I'll try to take a step forward and share with the readers a formula I found to estimate Annaly stock value from the current interest rate environment.

I can preview that not only the accuracy of this formula is in the +/-6% range for almost all Annaly quotes from 2013 to August 21st, 2014, but that it can also suggest which yields are the most relevant drivers for the stock price.

**A first attempt**

My first attempt was to consider the whole history of Annaly stock on the market (from October 8th, 1997 to August 21st, 2014) and try to assess its statistical correlation to:

- All the official Daily Treasury Yield Curve Rates recorded on the official website of the U.S. Department of the Treasury: 1 month, 3 months, 6 months, 1 year, 2 years, 3 years, 5 years, 7 years, 10 years, 20 years and 30 years
- The S&P 500 index value (Source: Yahoo Finance)

I then applied a Linear Regression machine learning algorithm and found out the following formula to estimate the value of Annaly stock on any given day, based on the yields environment and market index of the same day:

Where:

- 1MO is the official yield of 1-month Treasuries
- 3MO is the official yield of 3-month Treasuries
- 6MO is the official yield of 6-month Treasuries
- 1Y is the official yield of 1-year Treasuries
- 2Y is the official yield of 2-year Treasuries
- 3Y is the official yield of 3-year Treasuries
- 5Y is the official yield of 5-year Treasuries
- 7Y is the official yield of 7-year Treasuries
- 10Y is the official yield of 10-year Treasuries
- 20Y is the official yield of 20-year Treasuries
- 30Y is the official yield of 30-year Treasuries
- SP500 is the S&P 500 index value

I assessed the accuracy of this draft formula against the real NLY prices, and found out that unfortunately, it was pretty poor, as shown in the two charts below (one for the absolute error, and one for error as a percent of the real stock price).

The error range is (-53.20%; +59.83%), which simply renders the formula useless for any practical use.

**A second, more focused (and fruitful) attempt**

The widely different economic situations and context that occurred from late 1997 to present days can be the reason behind the failure of my naive attempt of reducing the complexity of stock and market fluctuations to a simple linear combination of a few economic data.

Still, the modeling results are way better if we focus on a homogeneous time frame, in which the underlying economic context (e.g. central banks policies) can be considered as constant.

In fact, if we narrow the considered time frame to 2013 to present, and apply again the previous linear regression algorithm, we get much more interesting results:

This time, the accuracy is quite surprising: the error range is (-6.05%; +11.08%), and if we discard just the worst 4 days, it gets as high as (-6%;+7%).

This level of accuracy for the formula can be reasonably thought to last as long as the current economic context will, or in other words, until the tapering by Fed will continue within a still accommodative monetary policy framework.

The two charts below give evidence of the improved accuracy of this second formula over the current time frame.

**An interesting result**

Not only can the second formula predict the value of Annaly stock with a surprising accuracy, it can also tell what the drivers of the stock price really are, all backed by statistic correlation.

Looking again at the formula...

... we can deduce the following, useful considerations:

- The shortest-term yields, from 1 month to 1 year, are not relevant at all for the stock price.
- While in almost all the articles available on the web, Annaly's earnings are reported to depend on the spread between 2-year and 10-year yields, the single-most important driver for Annaly's price (in other words: the single factor with the heaviest weight) is the 3-year yield, and not the 2-year yield.
- The 10-year yield is confirmed to be the second-most important factor.
- The behavior of the general market (S&P 500) is almost irrelevant. This is just another way to confirm the low "beta" of the stock (0.16, Source: Google Finance), whose statistical correlation to the general market index is almost nonexistent.

Finally, and most important, the above formula will be a helpful tool for all Annaly investors who tried at least once to figure out an answer to the popular question: "*How would Annaly react to the most-awaited increase in the interest rates when it will finally come?*"

The reaction depends, of course, on the shape of the yield curve, and the formula is a practical tool to simulate scenarios.

For example, given a hypothetical scenario, where on August 21st next year:

- Short-term yields (<5 years) increase 10%
- Medium-term yields (5 to 7 years) increase 20%
- Long-term yields (>=10 years) increase 30%
- S&P 500 stands at current

Under these hypotheses, the stock would be estimated to quote 10.03 USD, which confirms a great sensitiveness of the stock to interest rates increase.

In case it might be of interest, you can download the complete spreadsheet I used from this link.

**My bottom line**

Being a computer engineer, I must admit I am biased toward machine learning (and I really love the subject).

In this case, I think that the application of a simple linear regression model greatly helped to envision a better knowledge about Annaly Capital in two ways:

- Spotting the most relevant yields for the stock price.
- Providing a practical formula to estimate the stock value in a given yields environment.

I hope you enjoyed this article, and I'm looking forward to your comments and ideas.

**Disclosure:** The author is long NLY.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.