Wondering about the ralationship between:
 Price to Earnings (P/E)
 Price to Book value (P/B)
 Return on Equity (ROE).
Equity (Shareholder’s Equity) is synonymous with Book value.
Given a certain P/E, won’t a better P/B mean a worse ROE?
If company A has a P/E of 10, and a P/B of 2, the ROE is 20% (since the earnings is 20% of the book value).
If company B has a P/E of 10, and a P/B of 1, the ROE is 10% (since the earnings is 10% of the book value).
So when comparing two companies with same P/E, the worse the P/B, the better the ROE?
(There is a small difference between the book value used in these two ratios: In P/B we use current book value, while we in ROE look at the average book value through the period, but for a small period, like 12 months, there shouldn’t be much difference in book value through the period, in most cases).
The triangle P/E, P/B and ROE

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Re: The triangle P/E, P/B and ROE
Well, yes, but think of it this way.
Start with a P/E=10 company that has a P/B=1 and zero debt. Now borrow half a B's worth of money and buy back half the shares(*). You now have the same company with the same earnings except P/B=2 because the capital structure is different.
Before: Assets = P and Liabilities = 0 so Equity = P => P/B=1
After: Assets = P and Liabilities = 1/2P so Equity = 1/2P => P/B=2
(*) WLOG, presume that the share price stays the same. Before anyone starts nitpicking, compare two companies of the same size and kind rather than transforming one into the other.
You'll usually see companies with steady and reliable earnings use lots of debtfinancing to maximize their ROE. Companies with random earnings have to carry less debt to avoid bankruptcy. The former type are typically old and established businesses (utilities, tobacco, ...) and the later tend to be risky or growth. Indeed, part of what the market pays the P for when establishing the P/E is the future growth potential. If belief in that potential goes away, then *poof* resets the P/E.
Re: The triangle P/E, P/B and ROE
Yes. This is usually due to intangibles. Consider a simple example. Two bakeries, each has the same book value of 2k for ovens, but one has a much more talented and innovative baker, so earnings are 100k for specialyummycookies bakery vs. 20k for sameoldcookies bakery, so market prices the innovative bakery at 1000k and the boring bakery at 200k. Price/Earnings is 10 for both bakeries, B is the same for both bakeries, but Earnings/Book is better for the more innovative bakery with more intangible assets.
In terms of the underlying math, ratios can provide meaning, but they can also hide information. In the example above, the P/E ratio alone "hides" the actual earnings of Bakery A (yummy) vs Bakery B (bleh) which would be 5:1 , but this information is revealed with the inclusion of the P/B ratio in the story problem.
In terms of the underlying math, ratios can provide meaning, but they can also hide information. In the example above, the P/E ratio alone "hides" the actual earnings of Bakery A (yummy) vs Bakery B (bleh) which would be 5:1 , but this information is revealed with the inclusion of the P/B ratio in the story problem.

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Re: The triangle P/E, P/B and ROE
It would likely not be too far off the mark to model the market pricing like this:
P/E = a+b*x, where a is the market's desired earnings yield (relative to e.g. bonds), x is the "expected growth rate", and b is a some constant that relates to how much people are willing to pay extra for growth, somewhere around one earnings multiple per one percent of growth rate. In particular, a's and b's relation to inflation is interesting.
Re: The triangle P/E, P/B and ROE
Another example would be if fertility = earnings, would you be better off choosing 18 year old Twiggy, who has not yet given birth, or 28 year old Jane Mansfield, who has already had 3 children, given that both women possess the same Waist to Hip ratio?
Re: The triangle P/E, P/B and ROE
If you buy the company and repay all its debt, the firm would not owe any interest expense to financiers. This will positively impact the bottom line and P/E ratio would decrease.
If a company is selling for below its book value (P/B < 1) you could buy it to liquidate its assets in scrap for a profit. Such companies are worth more dead than alive.
But why stop there...
If you want a measure that is nonchalant to capital structure then there is EV/EBITDA.
It remains unchanges as interest expense is below EBITDA and do not have an impact.
EV/Revenue is suitable for companies which have not reached profitability or experience volatile bottom line.
EV/Revenue is unsuitable for mature companies with stable cash flows as it does not reflect profitability so it makes more sense to use EV/EBITDA instead.
Then again Charlie Munger says whenever you see EBITDA replace it with bullshit earnings.
If a company is selling for below its book value (P/B < 1) you could buy it to liquidate its assets in scrap for a profit. Such companies are worth more dead than alive.
But why stop there...
If you want a measure that is nonchalant to capital structure then there is EV/EBITDA.
It remains unchanges as interest expense is below EBITDA and do not have an impact.
EV/Revenue is suitable for companies which have not reached profitability or experience volatile bottom line.
EV/Revenue is unsuitable for mature companies with stable cash flows as it does not reflect profitability so it makes more sense to use EV/EBITDA instead.
Then again Charlie Munger says whenever you see EBITDA replace it with bullshit earnings.
Re: The triangle P/E, P/B and ROE
@jacob That makes sense. When there are buybacks, the P/E and ROE stay the same, while P/B increases. So there should be an adjustment for that. And opposite when new shares are issued.
But given equal number of shares, will there then be a triangle as I described, or are there other caveats?
But given equal number of shares, will there then be a triangle as I described, or are there other caveats?