Capital is one of the most fundamental concepts in finance. It is also one of the most elusive. Capital is the value of a firm or other investment—the value of assets less the value of liabilities. If a firm's liabilities exceed its assets, the firm is insolvent. Accordingly, capital is the firm's buffer against insolvency. It is available to absorb unforeseen losses so the firm can remain solvent. The more capital a firm has, the more confident stakeholders are that it will meet its obligations to them. Of course, capital alone is no guarantee of solvency. A well capitalized firm can fail due to a lack of liquidity. We may sometimes think of capital as the liquidation value of a firm. If all the assets and liabilities of a firm were liquidated, how much money would be left over for equity investors? Of course, liquidating a firm can be a costly undertaking, so most firms are worth more to equity investors as a going concern than they are liquidated. It is complications like this that make capital an elusive notion. The challenge is to measure capital in a way that is both precise and relevant. According to accountants, capital is book-value assets less book-value liabilities, perhaps with adjustments for off-balance-sheet items. This accounting definition is precise, but it is not always relevant. A firm's assets may comprise undepreciated investments in obsolete technology or "goodwill." A firm may have suffered a large mark-to-market loss but only be gradually accruing it over a ten year period. Even ignoring liquidation costs, such firms might have a liquidation value that is substantially less than the accounting value of their capital. A different metric of capital is the market value of the firm's equity. For a firm with a single class of stock, this equals the number of shares outstanding multiplied by the current stock price. Unencumbered by accounting formalism, market value of equity reflects the market's assessment of the firm's value. Of course, stock prices are subject to human emotions and crowd mentality. A firm's stock price may fluctuate widely without any fundamental change in its business' prospects. If the stock market soars with a speculative bubble or crashes amidst a panic, this says little about the fundamental value of the firm. Regulators and risk managers think of capital as financial resources available to, in some sense, absorb unanticipated losses. From this perspective, capital is those sources of funding that protect parties with claims on the firm's assets from such losses. It can be controversial deciding which items to include in this definition. These might include owners' equity, retained earnings and long-term subordinated debt. How do we tell if a financial institution has sufficient capital? This is the question of capital adequacy. Traditionally, it was addressed with the capital ratio, which is defined in terms of the book value of capital and assets as
Financial institutions tend to have capital ratios in the range of 4% to 10%, depending on the size of the firm, its industry and the definition of capital being used. Deregulation during the 1970s and 1980s exposed financial institutions to increased risk. In this environment, capital became more important as a buffer against losses. The more risk a firm took, the more capital it needs. Because assets is a poor indicator of risk, regulators and practitioners started modifying the traditional capital ratio or abandoning it completely. Modifications took the form of the risk-adjusted capital ratio:
where risk-adjusted assets are calculated by multiplying the value of each asset by a risk weighting and summing the results. This was the approach employed by the 1988 Basel Accord. Somewhat crudely, it applied weights based on assets' credit risk:
Another approach to assessing capital adequacy might generally be referred to as capital requirements or required capital calculations. These evolved out of the Bankers Trust RAROC methodology of the 1980s, US insurance regulators' risk-based capital requirements developed during the 1990s, and refinements of the Basel Accords during the 1990s. Generally, a firm's risks are identified, perhaps including market risks, credit risks and operational risks. An amount of capital is specified to support each. The amounts are called capital charges. They are summed across all the identified risks, perhaps with adjustments to reflect hedging or diversification effects. If the sum capital charge exceeds the firm's capital, the firm needs either to raise more capital or reduce some of its risk. Holton (2004) describes the process: ... capital requirements are based upon a model for how banks operate. According to this model, every bank has a large mattress stuffed full of cash. This hypothetical cash is called capital. Any time a bank suffers an unanticipated loss, money is taken from the mattress to cover the loss. In this way, capital “absorbs” losses in the same way that a car’s suspension absorbs bumps in the road. Every day, the bank takes all the money and dumps it out on the bedroom floor. It lines up its market, credit and operational risks, and places a little pile of its capital next to each. If risks hedge or diversify each other, there are rules for reducing the piles. The entire process is called capital allocation. Hopefully, there will be enough capital to build all the necessary piles, in which case the bank’s capital is deemed adequate. Otherwise, it is inadequate ... Capital charges are assigned in a manner appropriate for each risk. These can be crude formulas or sophisticated analytic techniques, such as value-at-risk (VaR). For example, in certain circumstances, the Basel Accords require a bank to calculate the 10-day 99% VaR for its trading book. A capital charge equal to three times this value is then applied for the trading book's market risk.
More problematic is how to adjust capital charges for hedging or diversification across risk types. How, for example, does one calculate the correlation between a bank's market risk and its credit risk? Solutions are inevitably crude. One is to simply sum capital charges across risk types, recognizing no diversification benefits. Another is to square the various risk's capital charges, sum them, and then take the square root. This approach assumes the risks are uncorrelated, reducing the sum capital charge to recognize the diversification effect. Over the years, regulators have formalized risk-based capital requirements in various regulations. These have defined rules for calculating a firm's capital and suitable capital charges. The goal is to ensure that a firm has sufficient capital to remain solvent in the face of losses that might arise from risks taken by the firm. These analyses are called regulatory capital calculations. They have been employed in the 1996 amendment to the Basel Accord, Basel II, the National Association of Insurance Commissioners risk-based capital requirements, and Europe's Solvency II directive for insurers. Financial institutions and other trading organizations have used internally-developed risk-based capital requirements to support performance assessment and decision making within those firms. The idea is to assign capital charges to individual business lines or transactions based on their risk. Performance is assessed by comparing the profitability of a business line or transaction to its capital charge. Some metric of a business line's or transaction's return on capital can then be calculated. With this methodology, a financial institution will pursue those businesses or transactions that offer the highest return on the associated capital charges. In a sense, senior management becomes like venture capitalists, deciding in what ventures to invest their limited capital. The process is called capital allocation. Conceivably, firms might perform such capital allocation based on the formulas for capital and capital charges specified by applicable regulations. While some firms have done this, most have not. The problem is that regulatory capital and regulatory capital charges are designed for more modest goals than analyzing specific business lines or transactions. They generally don't make fine distinctions between the riskiness of similar but modestly different transactions. For example, the 1988 Basel Accord assigned a uniform 8% capital charge for all corporate debt—so banks would have to hold as much capital for debt issues to a AA-rated borrower as a BB-rated borrower. For this reason, financial institutions have developed their own proprietary formulas for capital and capital charges. To distinguish these from regulatory capital calculations—and to emphasize the goal of more accurately capturing the economic impact of specific business lines or transactions—these are referred to as economic capital calculations. While economic and regulatory capital calculations are defined differently and serve largely different purposes, the two are philosophically similar. They have evolved together over the years. Regulators have borrowed concepts from the economic capital calculations performed by banks. Economic capital calculations have similarly benefited from the innovations of regulators.
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G-10 government debt
