Quantitative Analysis is not Trivial — The Case of PB-ROE

I debated on whether to post on this topic or not. I try to be a gentleman, so I don’t want to be too rough on those I criticize. Let me start out by saying that those I criticize have honorable intentions. They want to make investing simple for investors. Noble and laudable; the trouble comes when one over-simplifies, and errors get introduced as a result.

I am both a quantitative and a qualitative analyst, which makes me a little unusual. It also means that I am not as good as the best qualitative or quantitative analysts. To be the best, it takes dedication that would squeeze out spending too much time on the other skill. I have always tried to stay balanced, which helps me as a businessman, actuary and investor. Good problem solving requires looking at a problem from many angles, and then choosing the right analogy/tool to do the job.

One of my readers, Steve Milos, forwarded to me a piece from Merrill Lynch’s life insurance analyst suggesting that Price-to-Book — Return on Equity [PB-ROE] analyses were simply low P/E investing in disguise. I tossed back a comment “The Merrill analyst doesn’t understand what he is talking about. PB-ROE analyses are richer than low PE, though in a few environments, like the present, they are similar.”, prompting Steve to say, “LOL, I love that – now tell me what you really think!”

I decided to let the matter drop until Zach Maxfield, one of the analysts from Bankstocks.com, posted a laudatory article on Ed Spehar’s piece. I didn’t learn what I am about to write in a day, so let me take you on a journey explaining how I came to learn that PB-ROE analyses are valuable.

Back in 1982, I was a graduate teaching assistant at UC-Davis. The professor that I worked for used regression analysis in financial analysis to try to separate out effects that might be more complex than current modeling would admit. I did not get a chance to use the idea though, until 1992, when I began value investing, after my Mom gave me a copy of Ben Graham’s “The Intelligent Investor.” As I began investing, I noted that some stocks seemed better valued using book, others by earnings, and some by other metrics. Initially I began doing rule-of-thumb tradeoffs like Price to (book plus 5 times earnings). Eventually I wondered whether I had the right tradeoff or not, and how I might work in other metrics like dividends, sales, cash from operations [CFO], and free cash flow [FCF].

I’m not sure when it hit me, but I decided to run a regression of price versus earnings, book, sales, FCF, and CFO. Reasoning that sectors have different economic models, I did separate runs by sector. Truly, I should have done it by industry, or subindustry, as I do it today, but my initial attempts still found promising inexpensive stocks.

It was not until 1998 that I ran into PB-ROE analysis for the first time. Morgan Stanley was marketing a derivative instrument that would reduce book, turn it into earnings, and reduce taxes at the same time. I became the external expert on that derivative instrument, while hating its sliminess. (The whole story is a hoot, but it would take too long, and isn’t relevant here. Suffice it to say that the EITF and the IRS killed it six months after the first transaction got done.)

For those who believed PB-ROE analysis, the derivative was a godsend — less book, more earnings. With my more general model, I said, “So what, give up book, get “earnings,” which come back to book value anyway. These are just accounting shenanigans.” I didn’t see the value of PB-ROE then.

By 2001, I was a corporate bond manager. The Society of Actuaries Investment Section recommended the book, “Investing by the Numbers” by Jarrod Wilcox. An excellent book, I learned a lot from it, and he explained the PB-ROE model to me for the first time. To the best of my knowledge, it is the only place where I have seen it explained.

Where does the PB-ROE model come from? It is a simplification of the dividend discount model. In 2004, I gave a talk to the Southeastern Actuaries Conference. The relevant pages are 5-11, where I go through an example of a PB-ROE analysis, and give the limitations of the analysis. There are several limitations, here they are:

  1. Encourages maximization of ROE in the short run, rather than the long run
  2. Revenue growth is often equated with earnings growth in practice
  3. “Run rate earnings” is adjusted (operating) GAAP earnings, versus distributable earnings (free cash flow)
  4. Implicit assumption of constant earnings growth, required return, and dividend policy in the Price to Book versus ROE metric
  5. The model assumes that capital is the scarce resource needed to produce more earnings.
  6. ROA is more critical than ROE; it’s harder to achieve. In bull markets, anyone can add leverage.

Items 4 & 5 are the only problems intrinsic to the PB-ROE model; the rest are problems with how the model gets abused by practitioners. I don’t think that any industry fits those conditions perfectly, but I usually think that the are good enough for a first pass, and after that I make adjustments for different expected growth rates, excess capital, earnings quality and more.

PB-ROE is equivalent to low P/E investing when the regression line comes close to going through the origin (0,0). From my experience, that rarely happens. For my nine insurance subgroups (bigger than Mr. Spehar’s analysis — I cover them all), almost all of the intercept terms are different than zero with statistical significance. Or, as a colleague of mine said to me recently, “Thanks for teaching me how to do PB-ROE analysis,it really helped with my analyses on Japanese banks and US investment banks.”

Now, there is a seventh problem with PB-ROE, but it is more complex. So you run he regression and get the tradeoff of P/B versus ROE that the market is currently pricing. Is that the right tradeoff in the intermediate term, or are investors overvaluing or undervaluing ROE? Hard to tell, but when the regression line is flat or downward sloping (it happens every now and then), one has to question whether the market’s judgment is right or not.

In some environments, PB-ROE and low P/E investing will be similar, but that will not always be true. Do not accept a false simplification, even though it may be true at present. The PB-ROE model is richer, and works in more environments, after adjusting for the limitations listed above. PB-ROE is a very useful tool, and not “gobbledygook.”

7 Comments

  • PaulinKansasCity says:

    I hope Zack reads this; but thanks for the background story. With regard to point 5 I think it could be argued that capital is not scarce currently; it’s really the opportunity/ability to deploy it efficiently! That is where the ability to evaluate management competence is so critical.

  • BriG says:

    Trying to get a handle on this, Zach Maxfield it would seem considers the E part of the ROE equation to be equal to current Bookvalue. I assume you’re using Average shareholders’ equity over time to compute the E part?

  • Paul, if capital is not scarce there are alternative calculations that can be run. One would be to net out excess capital, and run PB-ROE on the adjusted book, with a reduction to earnings from reduced investment income/ increased interest paid, then add the capital back in at the end.

    The other way is to figure out what is scarce in the industry. It might be end user demand — at that point substitute sales for book value, and at that point the regression becomes price-to-sales as a function of profit margins.

    BriG, you can use any shareholders equity measure you like, so long as it is the same one in both variables. I use trailing book for both. Sometimes I will use it on a tangible basis, and/or ex-FAS 115, but changes both the P/B figure as well as the ROE figure. They have to be kept consistent.

  • PaulinKansasCity says:

    Thanks David for those insights; to say you didn’t you learn to do this in a day is an understatement! Have a great weekend!

  • BriG says:

    Ok I took a second look and figured out the discrepancy. Mr. Maxfield rigged his example by using the same book value for all 3 companies. When it comes to linear regression 2by3 isn’t the same as 4by6, or 6by9.

    He was trying to claim from a purely mathematical standpoint that they were the exactly the same(PB-ROE vs P/E), but clearly that’s false.

  • OK says:

    (P/B)/(E/B)=P/E? No?

  • OK, your math is right as far as it goes. So long as the intercept of the regression equation is near zero, PB-ROE and low P/E investing are similar. There are times in the market when book value is prized, and times when earnings growth is prized. In both cases, the intercept will not be zero.

    Paul, thanks.

    BriG, thanks also. He may have been trying to give a stylized example. Ed Spehar’s note had more data behind it.