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John Emerson
John Emerson
Articles (106) 

Investing Sabermetrics: A Formula for Financials and Holding Companies

June 20, 2012 | About:

"There's a way to do it better — find it." — Thomas Edison

Open any Berkshire Hathaway (NYSE:BRK.A)(BRK.B) annual letter and the first thing you see will be a listing of the yearly gains in the book value per share of BRK.A from 1965 to the present year. At the bottom of the year-by-year synopsis lies the compounded annual growth rate (CAGR) of those gains in equity. Later in the article I will show the mathematical formula for calculating those compound gains.

Buffett believes that gains in book value per share are a better reflection of the growth in value of BRK.A as opposed to gains in the price per share of the company. Buffett uses book value as opposed to price per share since he feels that the market does not always assign a fair valuation to his company. He then compares changes in the equity of BRK.A to changes in the value of the S&P index while adding back in dividends.

This is Buffett's acid test for evaluating his efficiency in allocating capital at Berkshire Hathaway. After all, if the gains in the equity of his company were not significantly superior to gains in the S&P plus the dividends which they accrue, why would any sane individual choose to invest in BRK.A instead of an S&P index fund?

Rest assured that Buffett has passed the acid test with flying colors. Since 1965 Berkshire's book value has compounded at an annual rate of 19.8%, while the S&P with dividends included has compounded at an annual rate of only 9.2%. That means that Buffett has outperformed the S&P at a compounded rate of 10.6% since the inception of the current Berkshire Hathaway holding company in 1965. That translates into a gain in excess of 500,000% for the original stockholders. Alas, if only I had invested a double sawbuck of my grade school allowance in 1965.

All that said, today's article is not about singing the praises of "The Oracle." Rather, it is about introducing a better investing sabermetric in evaluating the efficiency of the management of a company. For reasons which I discuss later, today's analysis is best suited for evaluating financial stocks and holding companies.

The thesis of today's article is that investors should focus on businesses which have a 10-year annual compounded growth rate of book value per share in excess of 15 percent. Further, investors should only purchase these companies when they are trading at a 25 percent discount to their 10-year cyclically- adjusted price to book value ratio.

The idea is simple: Buy stocks with high quality management when they are inexpensive in relative terms.

Incidentally, GuruFocus has all the information you need to access this information — and you thought you knew everything about GuruFocus. More on that later.

Book Value as the Key Metric for Financial Stocks and Holding Companies

Traditional earnings multiples do not supply investors with relevant evaluation tools in the case of many financial stocks or holding companies. When looking at holding companies the reason is clear. Take the example of BRK.A: The only earnings which are derived from their extensive investment portfolio are the dividends or interest payments they receive from the various securities.

The reason is not so clear to investors when evaluating financial companies; however, asset-based evaluation metrics are generally superior to earning-based metrics in evaluating such companies for the following reason:

Many financial companies have extensive investment portfolios which only record earnings gains on dividends, interest payments or capital gains if a security is sold. Therefore, the value of the these investment portfolios, particularly the unleveraged portions of the investments, is not reflected by the earnings power of the business. For my purposes, the unleveraged portion is defined as total invested assets less the float (prepaid premiums and other money held in investment accounts that does not belong to the company).

Allow me to illustrate the point since I am sure that many readers are confused by the previous paragraph. Let's compare two mythical insurance companies. Assume that both companies have earned $1 in investment earnings for the last five years. Suppose Company A has $50 million in equity on their balance sheet whereas Company B has equity of $100 million.

Let's further assume that both companies possess equal float which is invested in government agencies and treasuries which supply exactly the same interest yield for the two stocks. However, Company B is also an unleveraged equity portfolio which is valued at $50 million. For the sake of simplicity, say it contains stocks that pay no dividends. Company A has no unleveraged capital to utilize for investment purposes; it merely invests the amount of its float in fixed-income investments.

According to an earnings-based metric such as a price to earnings ratio, the companies are equivalent in value in terms of investment earnings (of course their operating earnings are a different matter). However, what if Company B decides to sell its equity holdings tomorrow and distribute the after-tax proceeds to its shareholders in the form of a special dividend? In such cases, the intrinsic value of Company B is much better reflected by its price to book ratio rather than its price to earnings ratio.

To reiterate, price to book ratios offer a better measurement of the value of a company's investment holdings, particularly the unleveraged portion of a financial company's investments. Thus, investors are generally better served by estimating a financial company's intrinsic value by using asset-based metrics rather than earnings-based metrics.

Gains in Equity per Share as the Key Metric in Financial Stocks and Holding Companies

I will now return to our previous discussion involving Company B and its unleveraged equity portfolio. As we discussed earlier, Company B is definitely cheaper than Company A in terms of its price to book ratio. But is it necessarily a better investment merely because it is cheaper? The answer lies in evaluating the long-term CAGR of the book value per share of Company B vs. Company A.

Let's journey back ten years and examine the two companies. Ten years ago, Company A had $20 million in equity and Company B had had $40 million, so both companies have grown their equity by 150 percent. Therefore, are they roughly equivalent? Hardly. Further examination reveals that Company B had $40 million shares outstanding ten years ago. Now they have 100 million shares outstanding. The extra shares were created by a secondary offering and stock options which were granted to management.

On the other hand, Company A still has the same amount of shares outstanding as they did ten years ago — 20 million. So the book value per share of Company A has increased from $1 per share to $2.50 per share in the past ten years. For Company B, the book value per share has remained at a $1 per share, although their equity has risen 150 percent. Furthermore, the equity portfolio still has the same market value as it did ten years prior. Additionally, the combined ratio for Company B is inferior to that of Company A, indicating the company writes inferior business. All these factors have played a part in the divergence of the growth of equity per share between the two companies.

In this illustration, the management of Company A has clearly performed in a superior manner when compared to the management of Company B. Their superiority is reflected in the equity growth per share in the business. It would seem that the discount to book that the market is offering on Company B is really no bargain after all.

Gains in equity per share reflect the effectiveness of management decisions in terms of capital allocation as well as revealing the operating efficiencies of a business. For instance, if stock options are issued and exercised they show up in the figure. The same is true for all stock buy-backs and secondary offerings as well as increases or decreases in the retained earnings of a company.

So long as the management exercises veracity in their accounting practices, evaluating the CAGR of equity per share is an excellent measurement of business efficiency and the effectiveness of management.

Calculating CAGR

As promised earlier, I will now unveil the mathematical formula used to calculate the compound annual growth rate (CAGR). The following example calculates the CAGR of the S&P 500 from 1986 through 2005, brought to you courtesy of allfinancialmatters.com.

CAGR = [(Ending Value ÷ Beginning Value)1/n] – 1

Where “n” is the number of time periods (20 years for this example)

Substituting the numbers from the example, the equation looks like this:

CAGR = [($95,421.19 ÷ $10,000)1/20] – 1

CAGR = [9.542119.05] – 1

CAGR = 1.119392 – 1

CAGR = .119392 or 11.94%


Finding CAGR of Book Value and Tangible Book Value per Share on GuruFocus

GuruFocus provides CAGR per share in its 10-year financial section. Just go to the 10-year financials section and click on book value per share and you will be transported to a page that shows the following information:

Everest Re Ltd Annual Data











Total Equity











Preferred Stock











Total Shares Outstanding











Book Value per Share











The yearly price to book value range for a stock can also be accessed in the 10-year financials section. The price of the stock appears directly under Book Value Per Share listed as Month End Stock Price. One can easily calculate the average price to 10-year book ratio of a stock by performing the simple mathematics.

A Formula for Success in Purchasing Financials and Holding Companies

Our goal is to purchase outstanding companies at discounted prices based on their 10-year CAGR of book value per share and their 10-year average price to book multiple. It is imperative that we add back dividends into the formula since they represent equity which was distributed to shareholders.

We are looking for financial stocks or holding companies which have grown the highest CAGR of BV per share, including dividends, trading at a minimum of a 25% discount to their 10-year average price to book multiple.

Thus our revised formula for CAGR of BV now reads as follows:

CAGR of BV per share = [(Ending Value + dividends ÷ Beginning Value)1/n] – 1


CAGR of BV per share is > 15%


The stock price is< .75 its 10-year average price to book ratio

If investors prefer to eliminate intangibles from the equation they should feel free to do so. I have decided to include goodwill and other intangible assets in my price to book ratios due to accounting changes enacted in 2002.

Goodwill is now impaired rather than amortized; therefore, theoretically, it will disappear from the balance sheet if it contains no real economic value. That said, I fully understand the subjective nature of goodwill impairments. Fortunately, many financial stocks show little in the way of goodwill and other intangible assets on their balance sheets, unless they engage in serial acquisitions. In the case of holding companies that is another story.

RE a Perfect Example of Value Uncovered by the Formula

Last August, I purchased Everest Re (NYSE:RE) when it fell within the value parameters outlined in today's article. I wrote an article about the stock titled: Everest Re: Low Risk High Reward http://www.gurufocus.com/news/143388/everest-re-low-risk-high-reward

At that time RE had generated 10-year CAGR of BV per share with dividends included was 26.8%. The stock qualified under the investing sabermetric since it was trading at approximately .7x its book value in August with a 10-year average price to book value of 1.115; therefore it was trading at approximately 63% of its mean price to book ratio.

Currently RE has reached a 52-week high and is trading at about .89x book value. It would qualify as a buy under the investing sabermetric if the price the price dropped below $89 per share using the latest financials to determine its current book value per share.


1) Warren Buffett uses CAGR of book value to track the progress of Berkshire Hathaway and his management efficiency.

2) A similar method which tracks CAGR of book value plus dividends can be use to identify high quality financial stocks and holding companies.

3) It is imperative that investors purchase these high quality companies at favorable prices; I suggest buying the companies at less than 75% of their ten-year average price to book ratio.

4) The formula is as follows:

CAGR of BV per share = [(Ending Value + dividends ÷ Beginning Value)1/n] – 1


CAGR of BV per share is > 15%


The stock price is < .75 its 10-year average price to book ratio

5) The formula is best suited in evaluating financial stocks and holding companies.

About the author:

John Emerson
I have been of student of value investing since the mid 1990s. I have continued to read and study value theory on an ongoing basis. My investment philosophy most closely resembles Walter Schloss although I employ considerably less diversification. I also pattern my style after Buffett's early investment career when he was able to purchase shares of tiny companies.

Rating: 3.6/5 (16 votes)


Rdj1234 - 5 years ago    Report SPAM

Hi John,

I've enjoyed your articles here on gurufocus and look forward to more sabermetrics. any chance you'll be doing one on evaluating the interplay between retained earnings and book value when a company has been buying back large amounts of stock?

thank you

John Emerson
John Emerson - 5 years ago    Report SPAM

Thank you for the kind words Roger,

I had not thought of your idea; however I will take it under advisement.


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