Property and casualty insurance companies which combine disciplined underwriting with solid investing can generate wealth. The good ones produce what has been called “structural alpha” because their float gives them low-cost – or no-cost – leverage. The best ones actually generate a profit on their float. Returns are typically lumpy because the insurance industry is inherently subject to episodic events which generate large numbers of claims.

A good point to get greedy is when they trade at or below book value. Another metric to track is the ratio of investments per share to the share price. For example, consider a case where you could buy a good P&C company at $100 per share that holds $300 per share in investments. If the company has a history of generating long-term investing results of 6% it implies an 18% return on your initial carrying cost.

Here are a few names to track taken from Fairfax Financial’s 2010 Annual Slide Presentation. These results include a very difficult time in the stock market. I have also included three additional slides which show Fairfax Financial’s long-term performance. Although much less known than Warren Buffett, Prem Watsa of Fairfax Financial – sometimes called “the Warren Buffett of Canada” – and Tom Gayner of Markel are worth studying. By way of disclosure, I am long Fairfax, Berskhire and Markel.

*The author of this blog is NOT an investment, trading, legal, or tax advisor, and none of the information available through this blog is intended to provide tax, legal, investment or trading advice. Nothing provided through these posts constitutes a solicitation of the purchase or sale of securities/futures. The data and information presented in this blog entry is believed to be accurate but should not be relied upon by the user for any purpose. Any and all liability for the content or any omissions, including any inaccuracies, errors or misstatements in such data is expressly disclaimed.*

Ron TaylorHi Greg I was just wondering why Fairfax has dropped so much. I know they had a bad quarter and have replaced the Coo. But I see no justification for such a drop.

Any insight??? Thanks in advance. Ron

Greg SpeicherPost authorHi Ron. I do not have any real insight into why Fairfax has dropped recently. As you wrote, the market may be focused on short-term earnings. Also, the market may not like the way Prem has the portfolio hedged.

Prem has been very forthcoming that Fairfax’s performance will be lumpy which makes for a volatile stock. The soft insurance market puts additional pressure on near-term earnings and the acquisition of Zenith which is currently operating in California’s tough economy only adds to this.

Fairfax is in large part a bet on Prem and his team’s ability to follow a proven process which combines disciplined underwriting – even if the long-term cost of float exceeds 100% – with above-average investing results. The long-term results thus far have been very good.

As the adage goes “past performance is not a guarantee of future performance”. Nevertheless, in my view, this is a rational investment which over time will produce satisfactory results.

Newbie investorFor a first cut at stocks to look at in the space, wouldn’t you want to take the first slide – the one that shows 5 year BV growth and 5 year share price growth, and focus on the companies with high BV growth but low share price growth?

Greg SpeicherPost authorNewbie, not necessarily because ones with low share price growth may have been overvalued or fully-valued at the beginning of the five-year period. If you are interested in the industry, it might make sense to read all their most recent annual reports to learn about the industry.

Pingback: Sunday Link-Fest and Consuelo Marck Interview | ValueWalk.com

Giuseppe PiazzollaHi Greg, I think this 2 links could be helpful for your readers to understand this concept :

opalesque.tv/youtube/Joe_Taussig/1

and

ineichen-rm.com/images/stories/pdf/absolute%20returns%20revisited.pdf (from p. 54)

Greg SpeicherPost authorGiuseppe, thank you for passing along these links. I’ve seen the video which was very interesting. I look forward to digging into the .pdf which looks like it gives some detail on this important subject. I own Greenlight RE based largely on 1) the structural advantages of this business model (combined with disciplined underwriting) and 2) Einhorn’s investment skill.

value_123Based upon Joe Taussig’s e-mail, it seems that the formula for calculating LT ROE for an insurer is as follows:

Pre-tax ROE: IR + LR (IR + IOP)

IR = Investment portfolio return

LR = Leverage ratio (Investments per share / Float per share)

UP = Underwriting profit (100 – combined ratio)

If this is the case, we only need three variables to determine an insurer’s ROE (assuming 30% tax rate).

Ex. Average P&C insurer

IR = 5% (100% bond portfolio)

LR = 5x

UP = Combined ratio of 103 (UP = -3%)

Pre-tax ROE: IR + LR (IR + IOP)

= 5% + 5 (5% – 3%) = 15$

After-tax ROE: 15% * (1 – 0.3) = 10.5%

Can you please walk us through your math on Fairfax. Do you have assumptions for LT investment portfolio returns, combined ratio and leverage ratio? You mention Fairfax’s goal of 15% growth in BV. In your opinion, how does he derive this figure using the equation above?

Greg SpeicherPost authorFairfax has approximately $1,072 of investments per share and $379 in book value for a leverage ratio of 2.8x. If they earn 6.5% after-tax (income, realized and unrealized capital gains) that is 18.2%. Subtract Fairfax’s average cost of float of 2.3% (Tausig’s UP) and you get about 16%.

Of course these results will be lumpy and are not guaranteed. Therefore, it will take patience and conviction to hold Fairfax. By the way, Fairfax’s historic returns are very strong (see Prem’s 2011 letter to shareholders, page 14 – http://www.fairfax.ca/Assets/Downloads/110304ceo.pdf: Common stocks – 17.2% over past 15 years, bonds – 10% over the past 15 years.

value_123Thanks you for your response Greg. Very interesting to hear your thoughts on this. I find your discussions on ROE, capital structure, re-investment of retained earnings, etc. to be some of the most interesting commentaries on the web.

Further more, if Taussig’s framework is theoretically correct, this seems to be a very useful way to evaluate the sustainable ROE of any insurance company (i.e. playing with the assumptions for leverage, underwriting profit, investment returns, etc.).

However, I’m not sure if I exactly understand how Taussig derived some of his figures. To clarify, if I understand Taussig’s paper, there are 4 variables that are used in the ROE formula:

Investment portfolio returns

Underwriting profit

Leverage ratio

Tax rate

How is the leverage ratio calculated? Joe Taussig provided the following quote:

“In terms of ROEs, the key is the ratio of reserves to equity(leverage), which runs around 5x in the industry.”

What exactly is the formula? In your response, I believe you used investments per share in the numerator and book value in the denominator for Fairfax to calculate the leverage ratio? Why did you choose to use book value as the denominator?

Also, can you please clarify your calculation for Fairfax? I believe you refered to after-tax investment income and pre-tax underwriting profit? Do these 2 figures need to be both pre-tax or after-tax? If I gross-up your 6.5% investment returns (6.5 / 0.7), I get the following calculation:

Pre-tax ROE = 9.3 + 2.8(9.3-2.3)

= 28.9%

After-tax ROE = 28.9 * 0.7

= 20.2%

Is this correct or am I missing something in the calculation?

Thank you for your response.

Greg SpeicherPost authorvalue_123, I’ll try to answer your questions:

1) How is Tuassig’s leverage ratio calculated? It is the ratio of debt to equity. (see discussion and chart starting page 54 of doc).

2) My figure of 6.5% is the net after tax. It does not equate to 9.3% (6.5/0.7) because the 6.5% is a blend of income (some tax exempt, such as munis), realized cap gains (taxable) and unrealized cap gains (not taxed). The mix will vary from year to year. I simply inverted what it would take net of taxes – understanding that all items were not taxable – to achieve 15% plus growth in book value. I picked a conservative figure that is far less than Fairfax’s historic rate of return.

Your 9.3 + 2.8 (9.3-2.3) assumes an extra turn in leverage. Fairfax has 2.8x (not 3.8x) investments to equity.

I prefer to use investment – not assets – in the numerator, because they produce the returns. The other assets – net of investment assets – are arguably captured in the cost of insurance or combined ratio.

3) I chose to use book value as the denominator because you asked how Prem could get to a target of 15%. By creating a ratio of investments to book value and calculatingly the earnings power (including cap gains) we can project how fast book value will grow.

The stock price may grow more if the market recognizes Fairfax’s investment skill and affords it a higher price-to-book multiple.

value_123Thank you Greg. That is very helpful. I am enjoying your commentary on this and find the discussion to be quite informative. I just have a few follow-up questions to hopefully clarify any outstanding questions. Perhaps if you have some time, I’d love to see you walk through Taussig’s ROE formula with an insurer to illustrate the approach in action?

1) Tuassig seems to be calculating leverage as defined by Total liabilities/Shareholders’ Equity. However, I can’t reconcile the figures with his report (pg. 56). He refers to Berkshire’s capital structure in 2002 as $210B in assets, $140B in liabilities, $70 billion in SE (D/E of 2x). When I look at Berkshire’s 2002 B/S, I get $169.5B in assets, $104B in liabilities, $64B in SE (D/E of 1.6x). Both the absolute figures and the D/E figure seem to be different from Tussig’s report. What am I missing?

2) I agree re: the taxes and I understand that you used 6.5% after-tax investment returns as a plug to arrive at a 15% ROE as opposed to this being your expectation going forward for Fairfax. However, just to clarify, you seemed to use a different formula than Tuassig to calculate sustainable ROE. Your formula seems to be as follows:

ROE = (ATIR * LR ) – UP

ATIR = After-tax investment returns

LR = Investments per share / BV per share

UP = 100 – combined ratio (LT cost of float)

ROE = (6.5% * 2.8x) – 2.3% = 15.9%

You note that I use an extra turn in leverage. This seems to make sense. However, isn’t the same thing being applied when Taussig looks at Berkshire. He calculates pre-tax ROE as “Investing the equity at 12% and adding 10% for each increment of reserve(investment returns of 12% minus the 2% COI), the total was a pre-tax 32% (12% + 2×10%).” Doesn’t this approach count the 12% returns 3x instead of twice when Berkshire only uses 2x leverage?

3) I am trying to understand the major differences between Tuassig’s approach and your calculation to get a sense for how to look at LT ROE for an insurer? Do you prefer using the approach you described above for Fairfax as opposed to Tuassig’s framework? The major differences seem to be:

1. You start with after-tax investment returns

2. You calculate Leverage as Investments / BV vs. Liabilities / BV. Which did you prefer – using investments or liabilities in the numerator?

3. You use underwriting profit pre-tax

4) One final posint re: historical investment returns. You note that 6.5% after-tax returns are far less than Fairfax’s historic return which seems correct. Any suggestions as to how I could calculate their historic returns? They provide 15 yr equity returns of 17.2% and 10% bond returns. However, I assume these are pre-tax returns. Also, based upon the asset mix over the past few years, it seems that 70%+ of portfolio is fixed income? How do you arrive at an approximation of their historical after-tax investment returns?

Greg SpeicherPost authorvalue_123, here’s my attempt to answer.

Q#1: It appears Taussig is using a very simplified balance sheet to show how BRK works. He is not trying to replicate its balance sheet at a set point in time. At least that’s my best guess.

Q#2: When you have a debt/equity ratio of 2x, you have a asset/equity ratio of 3x. Taussig, because he is showing a very simplified balance sheet to make a point, loosely equates assets with BRK’s investment portfolio. If you make that assumption, which I don’t really like because not all assets are investments, you get a 3x leverage of investments to equity.

Q#3. I prefer the framework I use (which I got from Bruce Berkowitz). I don’t like that Taussig implicitly equates assets with the investments, although his purpose is to make a point about capital structure not provide a specific valuation of BRK. The asset approach works better when valuing a bank.

Q#4. What we do know is that Fairfax has compounded book value at a rate of 25% for 25 years. We could extract the embedded investment return if we knew the leverage (investments to book value) in each of those years and the average cost of float (which we do). Unfortunately, the leverage ratio is a variable that I expect has changed over time as Fairfax built up its float and made changes to its balance sheet. You would need to study its historical financials to make a reasoned determination.

value_123Great! That is very informative. Thank you again for sharing your thoughts on this. This has been very helpful in providing me with some more context on how to analyze an insurer. I find your approach and Berkowtiz’s to be quite compelling.

I find Berkowitz’s approach to be very intuitive: “the key concept for insurance companies is to take a look at the investments per share. And you can find companies where the investments per share are significantly higher than the stock price. Markel has roughly $400 per share of investments. If they can break even on their underwriting and only make a 5% after-tax investment return, that’s $20 per share. Not bad for a company at $140 per share (in market price). So the trick is to have that investment leverage and at the same time break even or make an underwriting profit.”

The problem I have it applying it to other insurers is that Berkowitz was assuming that Markel would break-even on their insurance operations over time. However, for most P&C insurers, they tend to lose money on their core underwriting (i.e. operating with an average combined ratio below 100). I am trying to understand how to use the Berkowitz approach and apply it to insurers that have a negative underwriting margin?

Can you put it all together using the Fairfax (or any other insurer) example describe earlier?

Investments/share: $1,139 (pg. 12 of annual report)

BV/share: $379

Leverage: Investments/BV or 3x

Cost of float: -2.3% (average since inception)

Investment returns (plug): 6.5% after-tax

ROE = (After-tax inv. return * Leverage) – Cost of float

= (6.5 * 3) – 2.3

= 17.2%

Is this a correct interpretation of after-tax ROE for Fairfax if we assume that my assumptions are accurate? I am not sure how to reconcile the fact that we used after-tax investment returns and pre-tax cost of float? Also, we applied a 3x multiple to investment returns which makes sense. Do I need to put a multiple on cost of float or just substract it at the end of the calculation?

Thank you again for sharing your thoughts on this. I feel I have a much better graps of analyzing an insurance co. and trying to value the business.

Greg SpeicherPost authorI think you could adjust the equation to take taxes into account for the cost of float, i.e. – (2.3 * .7).

One final thought. Even though this formula\model is useful in evaluating insurance stocks, it is not a substitute for deeply studying the business and its management.

cogitoI have a clarification on the formula

ROE = (After-tax inv. return * Leverage) – Cost of float

Isn’t

ROE = [after-tax Investment earnings (income, realized, unrealized) – after-tax underwriting loss] / Equity

= (after-tax investment earnings / total investments) x (total investments / equity) – (after-tax underwriting loss / float) x (float / equity)

= after-tax inv return x leverage – after-tax cost of float x (float / equity)

I’m missing a factor of float/equity for the last term. Thanks!