Economic Capital

Economic capital is capital a financial institution or other trading organization determines—based on its own risk analyses—is an appropriate buffer against possible losses from a transaction, a business line or its operations overall. Economic capital is calculated and utilized in ways similar to those of regulatory capital under the Basel Accords. Differences in how it is calculated are intended to better reflect the “true” or “economic” risks a particular firm faces, hence the name “economic capital”. Firms calculate economic capital at their own initiative and for exclusively proprietary purposes related to capital allocation and performance measurement.

Regulators have always been interested in the capital ratios of the financial institutions they oversee, but it was during the 1970s and 1980s that they started to implement explicit capital adequacy regulations. To do so, they had to specify formulas for a firm’s capital and a system of capital charges. Regulatory capital equals the sum of capital charges, perhaps with offsets to reflect hedging or other mitigating factors. Banks are required to hold capital in excess of regulatory capital.

Economic capital works similarly. Firms may define capital differently, but it generally includes owners equity, retained earnings, and subordinated debt. Capital charges are modified to better reflect a firm’s perceptions of its own risks. Offsets to reflect hedging and diversification tend to be more aggressive than with regulatory capital. Summed capital charges, less offsets, is economic capital. Firms seek to hold capital in excess of economic capital. They also incorporate economic capital into return-on-capital and risk-adjusted-return-on-capital calculations for the purpose of assessing transactions and/or lines of business on an ex-ante or ex-post basis. Ex-ante, such analyses facilitate capital allocation. Ex-post, they facilitate performance measurement. These techniques originated with return-on-asset calculations, as described below.

Traditionally, return on assets (ROA) was used as a bank-wide performance measure. This is defined as:

Widespread use of derivatives and other leveraged instruments rendered the accounting notion of assets a meaningless indicator of a bank’s risk or the financial resources it deploys. For assessing bank-wide performance, return on equity (ROE) largely replaced ROA:

While widely used by equity analysts and investors, ROE has two shortcomings that limit its use for internal purposes:

• Like assets, book-value equity is a poor indicator of a firm’s risk.
• While ROE is defined firm-wide, it is not defined for individual transactions or business lines.

By replacing equity with capital in formula [2], we obtain return on capital (ROC):

Formula [3] applies firm-wide. For a business line or transaction, it is modified by replacing capital in the denominator with the economic capital allocated to the particular business line or transaction. Also, income earned on that economic capital may be added to revenue:

where

In formula [4], the “income from capital” term is included because allocating capital to a business line or transaction is different from investing the capital in the business line or transaction. Capital is held in addition to any assets invested in the business line or transaction. The capital is presumably invested somewhere, and ROC should reflect any extra income from that investment. Since the capital is supporting a risky business line or transaction, it (hypothetically) should be invested in something risk free. Accordingly, it is ascribed income at the risk-free rate. In formula [3], such income would already be included in revenue.

Because capital charges are based (at least in theory) on the riskiness of a business line or transaction. ROC, as implemented at the business line or transaction level by [4], is a risk-adjusted performance measure (RAPM).

ROC can be used prospectively or retrospectively. Firms can decide which business lines or transactions to fund based on the anticipated ROC of each. This is capital allocation. Retrospectively, firms can assess the actual ROC achieved by individual transactions or business lines. This is performance measurement.

When ROA, ROE or ROC are used to assess a firm’s (actual or projected) performance, they are generally applied to one year’s (actual or projected) results. This may not be appropriate when ROC is applied to assess a business line’s or transaction’s performance. If the purpose is to select desirable business lines or transactions to invest in, one-year’s projected ROC may be misleading. A business line or transaction might be expected to lose money in its first year only to become profitable in subsequent years. Accordingly, when ROC is used for internal decision making, the ROC of a business line or transaction is typically calculated as an average ROC over several years or the life of the transaction.

The first firm-wide implementation of ROC at all levels of a firm was a system Bankers Trust implemented during the 1980s. They employed a variant of the ROC formula [4], which they called risk-adjusted return on capital (RAROC).

Bankers Trust was a commercial bank that had adopted a business model much like that of an investment bank. It had divested its retail deposit and lending businesses. It actively dealt in exempt securities and had an emerging derivatives business. Such wholesale activities are easier to model than the retail businesses Bankers Trust had divested, and this facilitated the development of the system. RAROC was well publicized, and during the 1990s, a number of other banks developed their own firm-wide systems. Those firms and their consultants came up with various names for the versions of ROC they implemented, including return on risk-adjusted capital (RORAC) and risk-adjuster return on risk-adjusted capital (RARORAC). The names were more buzzwords than anything else. Today, most any RAPM based on ROC is simply called RAROC. Perhaps the most common definition of RAROC is ROC with an explicit adjustment for expected loss:

Ex-ante, expected loss is the mean of the loss distribution associated with the business line or transaction—most typically it represents expected loss from defaulting loans or from operational risk. Ex-post, it is actual loss.

Today, economic capital systems implemented by financial institutions and other trading organizations all trace their origins to Bankers Trust’s RAROC system. RAROC was more than a RAPM. It was an entire framework for supporting economic capital allocation and performance assessments at all levels of the firm. The original Bankers Trust RAROC system provided results on an after-tax basis. Today, systems typically perform calculations before tax. The 1988 Basel Accord was apparently motivated by Bankers Trust’s RAROC system. Economic capital and regulatory capital systems have continued to influence each other since.

Economic capital is far from perfect. While the overall formulas [4] and [6] for ROC or RAROC are simple, the calculations for their respective inputs can be complicated, entailing many assumptions.

Capital charges are especially problematic. If a bank has a lending business and a trading business, it will face credit risk with one and market risk with the other. Credit risk and market risk are fundamentally different—like comparing apples and oranges. How can the firm equitably assign capital charges to the two business lines? Are 1.5 apples equivalent to one orange, or should that be 1.8 apples to one orange? The question—whether applied to apples and orange or credit risk and market risk—is essentially meaningless, but it cannot be avoided. If the bank’s RAROC system later concludes that the lending business outperforms the trading business on a risk-adjusted basis, will the conclusion be economically meaningful, or will it merely indicate that the bank’s RAROC system gives the lending business an unfair advantage in how it assigns capital charges?

Inevitably, whenever a firm implements an economic capital system, the process is political. Department heads take a keen interest in how capital charges are to be assessed. The methodology that gets implemented typically reflects more a political compromise on capital charges than it does the actual nature of the risks the various departments are taking.

Because of problems like this, not all financial institutions or trading organizations implement an economic capital system. Among those who do, practice varies considerably.