There is a thing that I have never quite understood, in which investment banks have a "cost of equity" and it is a number, and that number is constant over the long term, and people get really upset if banks can't meet their cost of equity and really ecstatic if they can beat it, though of course that is not usually how "costs" work. (Usually if you can't meet the cost of a thing you don't get that thing.) Anyway here is a Bloomberg News story that sort of supports that notion. In this story -- and I'm taking certain liberties here -- Goldman Sachs equity investors are lining up outside 200 West Street every morning hoping to get a glimpse of Lloyd Blankfein so they can grab him, look maniacally into his eyes, and say: "Lloyd! What is your target for return on equity?"

Because then they can go back to their homes throughout the land and be like, "okay, we can breathe again, Goldman's ROE target is 14 percent" or whatever the number is, I don't know. I don't get it? The concern here is not even *Goldman's return on equity*; it is whether or not Goldman will *announce a public target for a return on equity:*

“Most investors prefer clarity over uncertainty,” said Christopher Lee, a money manager focused on financial firms at Boston-based Fidelity Investments, the second-biggest mutual-fund company. “In the absence of having explicit targets, whether you believe them or not, it can in general be an overhang.”

What? If I were Lloyd I'd be like, "we're trying to make as much money as we can, leave us alone." I guess that's actually what Lloyd's doing. Really, I don't get the appeal of the explicit target. The target is "more," right?

That said, the real worry is that Goldman may be secretly setting a target of 10 percent return on common equity, which would lead those frantic investors to gnash their teeth and rend their clothes because I guess some of them expect 15 percent, and back in the good old days Goldman made 20 percent. This worry seems to be fueled in part by the fact that Goldman's compensation targets for its executive officers are based on a 10 percent return on common equity, though that is only sort of true.^{1}

In the interests of being servicey here is a rather busy chart I threw together:^{2}

So here we graph Goldman's return on assets (dark blue line, left-hand scale) and return on common equity (light green line, right-hand scale). Obviously these two lines move fairly closely together: They have the same numerator, net income, so if income is up, ROCE and ROA are both up. But just as obviously there's a sharp break: pre-2009, ROCE is more than 20 times ROA; after 2009, it is less. (Return on assets bounces around but averages a bit less than 1 percent.)

The reason for the break is pretty straightforward: It's the denominator. Before the financial crisis, banks had less capital for a given amount of assets than they do now. From 2005 through 2008, Goldman averaged assets of around 26x its common equity. Now that number is just over half that, around 13x. (The orange line graphs the inverse of this, equity as a percentage of assets.) And so, unsurprisingly, return on equity is around half what it was through 2008, for any given level of return on assets.

So the dashed purple line shows what return on equity "would have been" if Goldman had been 13x levered, instead of 26x, throughout 2005-2014.^{3}
You can think of that number as sort of the historical return on equity "normalized" to current capital requirements. That number is rather lower than the actual return on equity in 2005-2008. It averages around 11x.

What I'm saying here is that Goldman's return on equity, though low compared to the glory days, doesn't seem to be low because of underperformance or uncertainty or whatever. It seems to be low because of arithmetic: because capital requirements are higher. That doesn't seem to be going away.

You can have a pretty simple model of big investment banks that goes like this:

- Return on assets is about 1 percent.
- Various nonsense -- the Volcker Rule, bad trading strategies, whatever -- might threaten your 1 percent return on assets, but people are smart and can adjust to the nonsense in the long term, returning banks to that 1 percent equilibrium.
- Return on equity is, arithmetically, your leverage ratio (assets divided by equity) times your return on assets.
- If you have assets of 25 times your equity, you can have an ROE target of over 20 percent.
^{4} - If you have assets of 13 times your equity, you probably can't.

That model is maybe insufficiently sensitive to things like risk differences and interest rates, and maybe assumes too much about banks' abilities to adjust to non-capital regulation (Volcker, etc.) and too little about their ability to adjust to capital regulation (Basel, etc.).^{5}

But I suspect it is a better model of reality than the model that tells you to grab Lloyd Blankfein's feet and not let go until he tells you that his target return on equity is 20 percent. Even if you can make him say it, that doesn't mean that it will come true.

^{1}
Check out page 37 of Goldman's proxy, which has the targets for return on equity. Executives get 100 percent of their target long-term incentive plan payout if average ROE over a multi-year period is 10 percent. They get 150 percent of the target if ROE is 15 percent, 50 percent if ROE is 5 percent, and linear scaling in between. Below 5 percent ROE and you get nothing. Above 15 percent ROE and you get nothing **more** than the 150 percent of target that you get for 15 percent ROE. (This applies only to half of your LTIP notional; the other half is based on book value per share increase. It's all a bit more complicated than this.)

So, suuuuure, the target is a 10 percent return on equity, because that gets you 100 percent of your target bonus (really LTIP payout, whatever, but I'm going to say "bonus" because it sounds better). But 11 percent ROE gets you 110 percent of your target, and 15 percent ROE gets you 150 percent of your target. Why would you target 100 percent of your target bonus when you could target 150 percent of your target bonus? The target is not the thing on a piece of paper next to the word "Target." The target is "more."

That said, the comp stuff is a little weird, in that a 15 percent ROE is the "maximum": You get no more reward for a 20 percent ROE than you do for a 15 percent one. So I hereby announce that Goldman's target return on equity is 15 percent, for comp purposes anyway.

By the way, that doesn't seem to motivate particularly hedge-fundy behavior: The goal really should be "more," not "get to 15 percent, then stop." Still, it's misleading: There's a multi-year period, for one thing, so you should bank high ROEs in good years to protect yourself against bad years. And of course your **real **comp is that you own piles of stock, and the more you can make the stock go up the better.

^{2}
What do you want to know about this chart? The data is from Bloomberg. The design is a joint effort between me and Microsoft Excel. The likely arithmetic errors are my own.

^{3}
This is done super dumbly, by just dividing actual ROE by the actual leverage ratio (26 or whatever) and then multiplying by 13. So it doesn't take into account the fact that a less-levered Goldman would have had lower interest expense, which matters.

Incidentally, Bloomberg News quotes Lloyd Blankfein saying "People throw out that number, 10 percent, I happen to think that’s a pretty high number given that the risk-free rate of return is zero," and that's a fair point: Why should bank return on equity expectations always be X percent, where X is a constant, when other rates of return vary? Here's a version of my chart that shows, not the return on equity, but the return on equity **minus** 3-month Treasury bill rates. If you normalize that by the current 13-ish assets-to-equity ratio you get a long-term average of about 9.6 percent.

^{4}
You might miss it, obvs! More leverage = more risk = sometimes you lose money. But it's your "target," sure.

^{5}
Personally I have some bias toward thinking that, in the long run, banks will be able to adjust to capital regulation and get a bit closer to pre-2008 return on equity numbers. Which would imply higher-than-historical return on asset numbers.