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Value-at-Risk and Capital Allocation

Eric Falkenstein 10/20/03

Value-at-Risk (VaR) is very useful, but its relevance for capital allocation is limited, and it’s useful to know this in order to avoid wasting time. It may appear that the idea that some VaR statistic dictates capital allocations is a straw man argument. 

Yet I have seen it tried too often, and it reflects a profound ignorance about the precision and the practical relevance of risk measures and capital within diversified financial institutions.   Below I outline how one should use VaR in the capital allocation process. 

Economic capital allocation is driven by the thought that equity is “a cushion for a bad times.”  As such, you can judge its adequacy by its relation to adverse scenarios.  Merton and Perold (Fall 1993, “Theory of Risk Capital in Financial Firms”, Journal of Applied Corporate Finance) laid what appears solid foundation by outlining the idea that as equity is the value of a put option on the firm that would guard against burning through all the equity.

The popularity of economic or risk capital arose out of the combination of VaR and Stern Stewart’s EVA™ concept, which argued for charging business lines within a company for the capital it used.  Further, risk capital suggested a new way to amend the patently flawed existing risk based capital standard adopted by Basel in 1988.  It was a promising synergy of new concepts for financial firms, an area that for too long neglected risk and capital usage in performance evaluations. 

For example, many are still compensated for net revenues regardless of risk and the cost of equity capital.  To give a desk the same recognition as another with equal net revenues, but which generated half the VaR, is a common problem.  The new idea of VaR developed greater urgency when considered as a method for driving economic capital allocation. 

Now Value-at-Risk, the idea that one should have an estimate of the histogram of an activity’s cash flows, especially the ‘bad tail’, is useful by itself.  One should know this information so that one can properly anticipate adverse scenarios.  Certainly many of the disasters of the past decade were only disasters because they were naively unexpected (eg, Orange County ‘94, American Express ’01).   But given the buzz around economic capital allocation there was little incentive to downplay the sexiest part of VaR, its application to capital allocation.  As John Maynard Keynes said, “everything is always decided for reasons other than the real merits of the case.”  So if people embraced VaR primarily to apply economic capital, or to better Basel ’s Risk Based Capital standards, it seemed picayune to highlight criticisms.

But the main problem is straightforward.  The market doesn’t seem to allocate capital this way, and the market never gave ‘best practice’ firms any premium for their efforts.

Let us take a look at the capitalization rates of banks, and plot that against their net income/assets volatility.  If the market requires more capital for more volatility, there should be some clustering of points that show higher risk implies higher capital ratios.  I used data from 1980-2002, and calculated the standard deviation of a bank’s net income/book assets, and plotted this against the bank’s average equity/asset ratio (346 observations with at least 5 years of data).  As you can see below, there is no correlation. [the chart looks the same under every conceivable permutation:  if you use beginning of period capital ratio, end-of-period capital ratios, alternative capital ratios, or thrifts instead of banks].

Thus from an empirical standpoint, there is no justification for the belief that volatility is a major driver for marginal—ie, almost all—capital allocation decisions.  Just as risk as measured by volatility or beta is not found in practice to generate different expected returns among equities, so is volatility empirically irrelevant to most capital allocation decisions. 

So how do you allocate capital?  First you look at creating a synthetic position out of marketable securities.  For example, replace a portfolio of loans with a portfolio of corporate debt with similar default rates, fund according to your current capital allocation and present value the cash flows.  The resulting ‘capital’ is the market’s current capital allocation, and properly holds the business line accountable for what an average manager should generate in his position.  In golf it would be considered par, and a business manager should realize that their alpha is their betterment from this base.  

Secondly, you look for comparables, from stand-alone enterprises, or industry whisper numbers from consultant surveys, or other sources.  The goal is to create a level of capital that managers are accountable to, and it is driven primarily from market analogies, not statistics.  It is important to note that most business lines that generate positive net revenues contain very little ‘individual alpha’.  This isn’t to denigrate managers, but just as academics rarely say things that are uniquely insightful, managers rarely do things that are uniquely productive.  By holding a business line manager accountable for the appropriate level of capital you avoid the misdirection created by allowing managers to spin the ‘individual alpha myth’ that is so common, self-serving and confusing (see last week’s ‘Alpha Deception’ column). Analogies and market knowledge are the supreme skills, not graduate-level mathematics.

Capital allocation benefits from a juxtaposition with VaR.  You can bring forth the VaR of other activities, together with their capital allocations and revenues, and revisit whether this represents an opportunity or not.  Usually the vast divergence in the profit/VaR ratio is due to customer flows, which do not allow one to increase capital to the activity in any meaningful way.  But occasionally it can make you think the market is generating a risk premium that is incommensurate with risk, and act accordingly. 

To be a complete risk manager, as opposed to a mere investor relations tool, it is important to prioritize tasks large enough to matter but small enough to be feasible.  Risk capital sets an unrealistic expectation of making business decisions by itself, which it simply can not do.  Learn how to  how to calculate the VaR for a portfolio, a skill that many quants are uniquely capable of, and something that is very useful to know.  But also know how to use this information properly.  This involves finding relevant comparable data, and creating synthetic versions of  activities based on market datapoints.  This puts VaR in its proper perspective, as an essential but ultimately modestly informative tool.