John Thanassoulis
The case for intervening in bankers' pay
Journal of Finance | Volume 67, Issue 3 (Jun 2012), 849–895

Many policy makers in the E.U., U.S., and G20 have criticised bankers' pay. The European Union even introduced regulations to outlaw bonuses which are greater than base salary. My study asks whether it would be optimal to regulate bankers' pay, and if so how.

I present a model of banker remuneration in a competitive market for banker talent. I show that there is a market failure in the competition between banks for bankers in that one bank's hiring activities has the effect of raising rival banks' cost of labour and raises their risk of default. I demonstrate that this negative externality adds significantly to default risk. Optimal financial regulation will involve some intervention in the competitive market for bankers' labour. In particular it will involve weak caps on bonus payments in proportion to bank assets.

1: Comparison of remuneration to dividends plus share repurchases for some systemically important banks
The graph shows the median and 90th-percentile of remuneration payments as a proportion of shareholder equity (SHE) for 21 systemically important banks. The remuneration payments are compared against the total dividends paid out plus any sums spent on repurchasing shares by the banks as a proportion of their shareholder equity. The graph demonstrates that remuneration payments are on average approximately double dividend payments plus repurchases and so make a significant contribution to a bank's default risk.

Competition for top talent increases pay but reduces the bank's equity

High aggregate pay bills add to the financial fragility of banks as they remove funds which would otherwise cushion the bank from poor investment realizations. The level of aggregate pay can be a very significant proportion of shareholder equity. Payouts to staff also considerably exceed payouts to shareholders in the form of buy-backs and dividend payments. This is demonstrated in Figure 1.

The intuition is that because the level of pay is a significant portion of shareholder equity, by bidding for bankers that they will ultimately not succeed in hiring, banks raise their rival's costs, and so add to their rival's fragility. The costs associated with fragility and default, are not a gain to the banker. They are a negative externality. Optimal risk regulation, by acting to lower the market levels of pay whilst preserving the optimal assignment of banks to bankers would reduce this externality.

The model

I model multiple banks of different sizes competing to hire a team of bankers from a population of bankers who are differentiated in terms of their skill. As any default event will be a low probability event, I model the extremes of investment realizations using Extreme Value Theory. This allows me to formulate a tractable and yet very general functional form. Using this approach the expected value of a bank of asset size S, and liabilities (excluding capital) D, which hires a team of bankers with expected return α, pays them a bonus rate of q, and a fixed wage of w is 
   alpha cdot  left( 1-q right) S-w- lambda cdot S cdot underbrace{G cdot  left[  frac{w+D}{ alpha cdot S cdot left( 1-q right) } right] ^{ gamma }}_{ substack{ text{Probability of}  RAWBACKBACK;  text{default event.}}}

The parameters γ and G capture the shape of the bank's returns distribution in the tail of very poor realization of returns. The tail is modelled as having a polynomial shape with index γ, and is scaled up by the constant G. The parameter λ is a cost of a default event.

Banks care about risk because if investment realizations are poor they will suffer extra costs. These could be enhanced costs of capital, or the costs of the premature selling of assets, for example. The banks therefore avoid risk even when they are modelled as being risk neutral. It therefore follows that banks benefit by sharing risk with their staff. This implies that:

The competitive outcome will be for the bankers to be paid entirely in bonus.

Bonuses have a role beyond an incentivization tool. They are a means by which risk can be better shared. When returns are poor, bonuses shrink, just when a bank needs to reduce calls on its capital.

This insight allows us to solve the full general equilibrium model of bankers pay and determine the equilibrium bonus rates and assignment of teams of bankers to banks. Using this machinery one can then explore the different possible regulatory tools which can be deployed to deal with the negative externality a bank has when it bids for bankers.

Bonus Limits
A modest cap on the proportion of bank assets which can be used for bonuses lowers default risk and raises the value of the largest banks. Compensation levels for all banks fall and in addition the risk problems of fixed wages are avoided. However very stringent bonus caps, or a requirement to use wages rather than bonuses are not optimal.

The market rate of pay is determined by how much a rival bank is willing to bid. In bidding for bankers they don't ultimately hire, the losing bank is pushing up pay for the hiring bank. This pushes up risk for the hiring bank and so creates larger expected costs from a default scenario. A modest cap on bonuses affects the marginal bidder more than the employing bank. This is because the marginal bidder will be the bank which is recruiting for a smaller set of assets, and so is applying a larger bonus rate to a smaller pot to try and attract the bankers. The bonus cap forces the bidding bank to use wages, but these have poor insurance properties. The bidding bank is therefore willing to bid less hard. This lowers the banker's pay and raises the employing bank's value and robustness to risk. As the employing bank secures more value from its bankers, it is less aggressive in its bidding for even better bankers. This effect is reinforced up the chain so that all the large banks save money and become more robust to risk.

If the cap is too severe however, then fixed wages will rise. This raises bank risk.

A financial regulator might consider taxing the bonus pools of banks. The taxation policy does lower the amount delivered to bankers, but it leaves bank default risks unaffected. In a competitive equilibrium, the amount a bank is willing to pay to hire a better banking team depends upon the quality of the alternative bankers it can hire. The tax does not alter this calculation. Though default risk is not altered, money is diverted from bankers' pay to the government.
Increase capital adequacy ratios
The problem of bank fragility can be dealt with by increasing capital ratios, or altering the risk weights. If extra capital is not raised, an increase in the required capital ratio is met by altering the portfolio of assets to include more assets which have a lower risk weight. This limits the freedom of the bank and lowers bank value.

The paper explores the optimal financial regulation which maximizes the profits of banks subject to a maximum default probability. To characterize the optimal regulatory intervention the paper defines maximal weak bonus caps. The maximally weak bonus cap for a bank is the most stringent cap on the proportion of the bank assets which can be used for bonuses without causing the bank to recourse to increased fixed wages for its staff.

This cap is strictly lower than the bonus paid without a cap.

The optimal financial regulation requires bonus caps for all banks at least as strict as the maximally weak bonus caps.

If a regulator only controls a subset of the banks, use of a bonus cap more binding than the maximally weak bonus caps cannot be optimal for all regulators.

The paper calibrates how large a reduction in the bonus pool would be required to achieve the maximally weak bonus cap in 2007. The result is given in Figure 2.

2: Calibrated reduction in bonus pool to achieve maximally weak bonus cap
The central estimate is plotted as a dot in the graph and depicts the set of dollar reductions to the annual bonus pools of these 20 banks which together would lower the bonuses paid to the level of the maximally weak bonus caps. The line depicts the range captured by the two extreme estimates for the level of tail risk. The graph shows that optimal regulatory intervention would not be of a trivial magnitude. The banks are ordered by 2006 total assets in U.S. dollars with conversion to U.S. dollars provided by Datastream. 922060=Merrill Lynch; 951048=Wachovia Corporation.

The paper concludes that some regulation of remuneration is optimal. However regulations, likely such as the E.U. one-to-one bonus cap, which have the effect of increasing wages are not optimal. Though any reduction in pay levels makes banks safer, risk could be further reduced by allowing banks to use bonuses instead of fixed wages to pay bankers the market rates.



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