Hypotheses help us understand the world. But they can prove to be wrong, or to be right for reasons we don't understand.

In trying to assess performance, bank stock investors and management teams may choose to benchmark return on equity against the theoretical cost of equity capital. If ROE exceeds this cost, bank management is doing a good job. Otherwise, it isn't.

But what if the tool we use to measure the cost of equity capital is flawed or misapplied?

The tool that people use to measure cost of capital is the Capital Asset Pricing Model. Explaining the CAPM is beyond the scope of this article, but here are some observations about the theory and its application:

Suppose I estimate that, based on a risk-free rate of 2.5%, a beta of 1.3 and an equity risk premium of 5.9%, shareholders of Wells Fargo (WFC) expect a return of 10.2% (as banking industry consultant J.V. Rizzi did in his article on this topic recently). Then, imagine Wells Fargo's stock rises 10.2% tomorrow. The expected return, according to CAPM, changes by … nothing! Expected return is assumed to be drawn from the same normal distribution on both days. So that price move doesn't alter the risk/reward trade-off offered to potential buyers of Wells stock.

Some practitioners use the 10-year Treasury note yield while others use the 30-year Treasury bond yield for the risk-free rate – that is, the theoretical return on a riskless investment. In recent years both rates have been "nudged" downward by the Federal Reserve's quantitative easing and by a rush of scared capital into Treasuries. Rates are now at or near lows not seen in 60 years. When QE is unwound and a safe haven is no longer necessary, those rates should rise, perhaps materially.

Financial economists caution that the average historical equity risk premium – the stock market's return over and above the risk-free rate – is not an estimate of the prospective risk premium. What you expect to get and what you end up with aren't necessarily the same thing. But practitioners use the average historical premium anyway. And they can't even agree on what the "right" historical premium is.

The applicability of beta, a gauge of an individual stock's historical volatility, is also questionable. Did Eastman Kodak's long-run historical beta appropriately reflect the prospective risks it faced at the advent of digital cameras?

What do practitioners do with the cost of capital, once it's calculated? Research analysts rarely show how their valuation estimates vary as the cost of equity capital varies. But investment bankers do, in merger proxies. And the conclusions they reach can sometimes defy logic.

My favorite was written in 2011 by a top-ranked bank M&A advisory firm. It argued that an increase in cost of capital from 9% to 14% would reduce the value of the firm's client (the target) by only 12%. Here's a reality check: a one percentage point increase in the 30-year Treasury rate today would reduce the value of a 30-year bond by 16%. Stocks are perpetual, implying that their change in value should be even more sensitive to interest rate changes. It's charitable to call this firm's conclusion "wrong"; "professionally negligent" might be better.

The CAPM is of questionable value even if applied properly, it rarely is applied properly, and if it's applied improperly as a benchmark in today's ultralow interest rate environment, it gives a "gentleman's C" to banks with disappointingly low ROEs.

There's a more intuitive way to think about bank risk and return.

Assume a bank has $10 of book value. If it has an ROE of 10% and a 50% dividend payout ratio, it could pay a 50-cent dividend next year, which would grow at the same rate as book value, or 5% a year. The higher the bank's ROE, the higher the dividend and its growth rate. But it's hard to maintain a high ROE and grow rapidly, so risk is also higher.

If I buy this bank for book value, I earn a 5% dividend yield, and I'll realize 5% capital appreciation if the multiple holds firm. The higher the multiple of book value I pay for the bank, the lower my dividend yield. Capital appreciation holds at 5%, as long as the valuation multiple remains constant. But the higher the multiple, the greater the risk it contracts and costs me some capital appreciation.

How great is that risk, and how much might the multiple contract? There's no simple answer, but looking at earnings yield (the reciprocal of the P/E) proves useful qualitatively. If a bank's earnings yield is low, its price/book multiple is high relative to its ROE. The earnings yield of many healthy banks is in the 9% to 11% range. But some institutions have earnings yields as low as 6%. Are they less risky? The CAPM would lead you to answer "yes"; lower expected return implies lower expected risk. And yet many of these banks have large short interest positions, so some investors are betting that they are overvalued.

Albert Einstein once said, "Make everything as simple as possible, but not simpler." In a more normal environment, where the risk-free rate was in the 6% to 7% range, a misapplication of the CAPM wouldn't be all that dangerous. Being one percentage point too low on cost of equity capital wouldn't cause an analyst's "fair value" estimate to balloon, nor would it lead a bank management team to approve a value-destructive, low-ROE investment.

But with risk-free rates being a lot lower now, costly mistakes are much more likely. I think Rizzi would like to see low-ROE banks shrink or sell rather than chase growth. I certainly would. Will a flawed 9% cost of equity estimate encourage these banks to do the right thing?

Harvard Winters, a former investment banker, writes research on banks.