While the term
economic capital is a more recent development, the concept it represents
dates to the 1980s. Regulators have always been
interested in the capital ratios of the financial institutions they
oversee, but is 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
required capital. Intended for
regulatory purposes, these were not always suitable for corporate internal
purposes—so regulatory capital and economic capital diverged.
The purpose of regulatory capital is to enforce minimum
capital requirements. Tools such as capital ratios or
risk-based capital are
used for this purpose. Economic capital is primarily used by financial
institutions to support decisions about what business lines or
transactions to pursue. A firm defines its economic capital as comprising,
among other things, owners equity, retained earnings, and subordinated debt. Formulas
are specified for assigning economic
capital charges to
specific business lines or transactions. The focus is on identifying those
business lines or transactions that offer, in some sense, the best use of
the firm's limited economic capital. To make such assessments, firms employ
metrics (RAPMs). A RAPM is a performance metric that is based on a
standard accounting performance metric but with some adjustment to reflect
"true" or "economic" risk.
RAPMs have their origins in the accounting notion of
return on assets (ROA), which was long used as a
bank-wide performance metric:
Widespread use of
derivatives and other off-balance-sheet items have largely rendered the accounting notion of
assets a meaningless indicator of a bank's risk or the financial resources
it has deployed. For assessing bank-wide performance,
return on equity (ROE) has largely
While widely used by
equity analysts and investors, ROE
has two shortcomings that limit its use for internal purposes:
accounting notion of equity can be a poor indicator of a bank's risk.
ROE is defined bank-wide, it is not defined for individual business lines
By replacing equity with capital in formula ,
we obtain return on capital (ROC):
Because economic capital reflects "true" or "economic"
risk, this is our first example of a RAPM. When applied to individual
business lines or transactions, the formula may be modified
Here, capital is the capital charge for the business line
or transaction, and
income from capital = capital (risk-free
In formula , the "income from
capital" term is included because allocating capital to a business
line is different from investing the capital in the business line or
transaction. Typically, 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 the 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. Occasionally, a bank will actually invest in a business line or
transaction the capital allocated to that business line or transaction. In
this case, formula  will still be correct so long as
the expenses term in the numerator includes a transfer pricing charge for
the financing cost of the capital.
When ROA, ROE or ROC are used to assess a bank'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 turn
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 same consideration applies to other RAPMs described
During the 1980s, Bankers Trust developed a firm wide RAPM
that they called risk-adjusted return on capital (RAROC).
Bankers Trust was a
bank that had adopted a business model much like that of an
bank. It had divested its retail deposit and lending businesses. It
actively dealt in
securities and had an emerging derivatives business. Such wholesale
activities are easier to model than the retail businesses Bankers Trust
had divested, and this certainly 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 these, 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 derived from ROC is simply called
RAROC. Perhaps the most common definition of RAROC is simply ROC with an
adjustment for expected loss:
where expected loss is the
of the loss distribution associated with some activity—most typically it
represents expected loss from defaulting loans or from
The original Bankers Trust RAROC system provided results on an after-tax
basis. Today, systems typically perform calculations before tax.
management Techniques for protecting a firm's solvency in the context of accrual accounting.
A committee of representatives from central banks and regulatory
authorities that has played a leading role in standardizing bank
regulations across jurisdictions.
A firm's value—assets minus liabilities.
credit risk Risk due to
uncertainty in a counterparty's ability to meet its obligations.
profit Profit in excess of the opportunity cost of capital.
risk management Practices by which a firm optimizes the
manner in which it takes financial risk.
market risk Exposure to the uncertain market value of a portfolio.
operational risk Risk of
loss resulting from inadequate or failed internal processes, people and systems,
or from external events.
capital Capital held in accordance with statutory or
Ads by Contingency Analysis
discusses bank capital generally from a practitioner's
perspective. Belmont (2004)
takes a more focused look at economic capital, RAROC and related
topics. For researchers or theoretically inclined practitioners,
20 Mar 2001
RAROC: time horizon and trades with negative marginal risk.
scaling of VaRs to annual horizons ... 08 Jun 2000
Challenges of scaling value-at-risk to long horizons.
18 Jan 2000
References on risk-adjusted return on capital (RAROC).
21 Dec 1999
What banks were using RAROC in 1999?