### Capital Adequacy is a Balance Sheet Ratio

Financial analysts analyze company performance with different sets of ratios; e.g., earnings per share, return on equity. As a ratio, capital adequacy is just a special solvency ratio, not greatly unlike the classic debt-to-equity ratio. But *capital adequacy* connotes a financial institution’s capital, so it’s really a bank-specific version of the solvency ratio. A firm is insolvent when its debt exceeds its assets, in which case book equity is negative. That’s a balance sheet perspective rather than a cash flow (or income statement) perspective. Solvency is different than liquidity. A bank is solvent when its assets exceeds its liabilities. Liquidity is effectively a cash-flow perspective: does the bank have high-quality assets (e.g., can it sell them quickly?) in order to fund short-term obligations? Solvency does not ensure liquidity: a bank can have valuable assets but an inability to sell them quickly enough to fund immediate obligations.

What is the “capital” in capital adequacy? It is either *economic* or *regulatory* capital. *Economic capital* concerns each bank’s specific and internal perspective on their risk capital. Economic capital is a deep, evolving and important perspective, but I won’t go into here. The other key perspective is *regulatory capital*, and to many people, this refers firstly to the Basel rules. In this way, I think of *capital adequacy* as a reference to solvency–and to a lesser degree liquidity–ratios that are promulgated by Basel (but just note that “capital adequacy” can also refer to the bank’s internal perspective on the adequacy of its economic capital, or both economic and regulatory capital, as modern banks need to be aware of both). The Basel III regulations look carefully at both solvency and liquidity, with ratio requirements for both. The Basel regulations can be found here.

Isn’t capital just the same as equity which is assets minus liabilities? Nope. The book equity of a modern bank is more or less meaningless.

### Bank Capital is Very Difficult to Measure

Before I review the capital adequacy ratios, I want to elaborate on this idea that bank book equity is meaningless. Banks are *necessarily* fragile and complicated creatures in the economic system. Banking is an industry but banks broker (intermediate) funds between savers (households) and businesses, so they are part of the operating system of the economy. This brokerage role includes, very importantly, risk transfer. Their unique role implies it will never be easy to measure “capital adequacy.” Why? First, unlike a non-financial corporation, a bank is always highly leveraged in relative terms. And leverage is fragility. Historically, banks have debt-to-equity ratios of 5.0 or 6.0 or even greater; so even the equity of a conservative bank is wiped out if assets decline by 15%.

We’ll see below that Basel’s leverage ratio requirement is 3.0%. If that sounds like a small number, it surely is. If a bank has a unrealistically simple capital structure of 97.0% debt and 3.0% equity, it meets the 3.0% leverage ratio requirement, but this means that an asset decline of only 3.0% wipes out all the equity!

Second, unlike many non-financial corporations, the capital structure of a bank itself is incredibly hard to measure, line by line, and therefore in total. Steve Waldman explains this, albeit philosophically, in a classic post here (including many insightful comments) . Many of the instruments on the bank’s balance sheet are complex: they have ultimately subjective present values. And then there are the off balance sheet positions which includes derivatives.

It is the nature of derivatives that we cannot easily measure their risk. We explore this deeply in the Financial Risk Manager (FRM). If a bank invests $10.0 million in a plain old bond, the expected loss and exposure are relatively easy to figure. If the bank writes a credit default swap instead, to similarly get paid for credit risk, the measurement is more difficult. An interest rate swap has zero value at inception, but what is its future exposure? Sure it can be answered but it’s more like there are several different valid answers. An an honest answer comes with a confidence interval attached. When we roll all of this up, we get to Steve Waldman’s conclusion. The equity value—at any given point in time–of a large financial institution is up for debate and depends on all of the assumptions.

### Basel history: I, II, III

The first Basel Accord (aka, Basel I) was published in 1988. It established the original regulatory ratio of 8.0%, which remained the foundation for years.

**This regulatory ratio capital is conceptually simple:**

- Basel I: regulatory capital / Credit risk-weighted assets (RWA) >= 8.0%, or equivalently
- Basel I: regulatory capital >= 8.0% * Credit risk-weighted assets (RWA)

This is analogous to an equity/asset ratio of at least 8.0%. But instead of book (accounting-based) assets, the assets are adjusted for risk, which turns out to be a difficult and often subjective exercise. Similarly, regulatory capital is not exactly book equity. Further, in a traditional view, the first accord only included credit risk. Risk-weighted assets included loans and credit exposures; the key perceived risk was default.

The BIS committee constantly updates the regulations, sometimes slowly. By the time Basel II was introduced, the regulatory ratio had expanded to include **market risk** and **operational risk**.

- Basel II: regulatory capital / [Credit risk + Market risk + Operational risk] >= 8.0%; or equivalently,
- Basel II: regulatory capital >= (credit RWA * 8.0%) + market risk charge (MRC) + operational risk charge (ORC)
- Please note: Market Risk = MRC * 12.5 because 1/12.5 equals 0.08. By multiplying MRC and ORC by 12.5, Market Risk and Operational Risk can be conveniently added to Credit Risk, then the sum constitutes the denominator of a ratio that must exceed 8.0%. This is the same as saying that regulatory capital must cover the full MRC and ORC in addition to 8.0% of the Credit risk-weighted assets.

Basel II was lengthy and detailed, but it looked at least comprehensive when it was published in 2004. It expanded the types of risks covered by regulatory capital and greatly increased the sensitivity of risk measurement (the chief innovation was adding three approaches to each of the major risk buckets, so smaller banks could use a standard off-the-shelf approach while more sophisticated banks could employ their own internal metrics subject to supervision). But the global financial crisis (GFC) proved Basel II to be incomplete.

Basel III is the current rule set. It adds to the complexity of regulatory capital adequacy by supplementing the adequacy ratio I’ve just introduced with two liquidity ratios and a leverage ratio. Wait a second, isn’t the regulatory capital ratio already a leverage (aka, solvency) ratio? Yes, it really is. But the chief regulatory capital ratio is very sensitive to the approach used. Basel basically put in a simple, blunt backstop: in addition meeting the primary capital adequacy requirement, a bank also needs to have simple leverage (Tier 1 equity / assets) of at least 3.0%.

But that’s not all. Basel III also further parsed the primary adequacy ratio into several slices. Why? Mostly because not all capital (equity) is equally safe buffer. Basel III phases in requirements for Core Tier 1 (common equity), Tier 1 and Total (Tier 1 plus Tier 2). But Basel III retains the Basel II ratio. Basically, the ratio of 8.0% in Basel II maps to the Total Capital (Tier 1 + Tier 2) ratio in Basel III, which I will illustrate below.

### Core, Tier 1 and Tier 2

Basel proposed to phase-in the capital adequacy requirement over time. You can see their phase-in calendar here.

As of 2019, when the rules are fully phased in, the following regulatory capital adequacy ratios will apply:

- Common equity (core Tier) 1 must be 4.5%
- Tier 1 must be 6.0%
- Total capital must be 8.0%
- Leverage ratio must be at least 3.0%

These are the essential capital adequacy ratios. The global financial crisis taught many lessons. One brutal lesson was that liquidity matters in addition to solvency. So Basel III added liquidity ratios. Specifically, the liquidity coverage ratio (LCR) and the net stable funding ratio (NSFR).

### Illustration of Capital Adequacy Ratios

Let’s look at an illustration to see how the regulatory capital ratios are calculated. Here is a copy of the spreadsheet I built for this example. Keep in mind this is a simplified illustration that also *does not include market and operational risk*. Actual risk weights can be more granular than shown. For example, “Loans to foreign banks” have different risk weights depending on the host country’s risk classification (CRC, country risk classification). Nevertheless, we can appreciate Basel’s intent with even a simple example. Below is the asset side of the balance sheet for a hypothetical bank. This bank has Total Assets of $2,810.0 million. I also listed off-balance sheet items without specific notional amounts (”$abc”) just to emphasize their existence; but I won’t dive into the lengthy topic of computing their risk-adjusted credit-equivalent value. However, they do need to be included in the total risk-weighted assets. Notice that each asset is multiplied by its risk-weighting to produce a risk-adjusted value. For example, cash has a weight of zero, so cash does not contribute to a bank’s risk-adjusted assets. In this example, commercial and consumer loans receive 100% weight. Residential mortgage assets with book value of $520.0 million are weighted 50% such that only $260.0 million accrue to risk-weighted assets (this applies to first liens with loan-to-value of 60% to 80% but the weight can vary from 35% to 100%).

On the asset side (*above*), we have determined that this hypothetical bank carries $2.810 billion in total assets which translate into risk-weighted assets (RWA) of $2.0 billion. Now consider the bank’s Liabilities and Equity (*below*). These accounts inform the denominator of the capital adequacy ratios. We will not assign them weights. Rather, it is a question of buffer quality. Common stock and retainer earning are buffer of the highest quality, the constitute Common Equity Tier 1 (CET1); minority interest is an example of additional Tier 1 (T1) and convertible bonds are an example of Tier 2 capital:

Now we can compute four of the key capital adequacy ratios (under Basel III in any case!):

The four calculated ratios are:

- The leverage ratio = CET1/assets = 90/2,810 = 3.20% which exceeds the required 3.0% leverage
- The common Equity (CET) ratio = CET1/RWA = 90/2,000 = 4.50% which exactly meets the required 4.5% but fails to allocate an additional 2.5% to the capital conservation buffer (CCB)
- The Tier 1 ratio = Tier 1/RWA = 130/2,000 = 6.50% which exceeds the required 6.0% for Tier 1 capital
- The Total (Tier 1 + Tier 2) ratio = (Tier 1 + Tier 2)/RWA = 240/2,000 = 12.0% which easily exceeds the 8.0% required for total capital

This hypothetical bank meets or exceeds each of the ratios (i.e., Common equity, Tier 1 and Total Capital) so it has adequate regulatory capital, with the exception of the capital conservation buffer (CCB). Because it has no buffer, it would be required to retain all of its earnings and could not pay out dividends.

### Basel also includes two other pillars

The ratios above are the essential capital adequacy rules in Basel III. They are the math in Basel, so to speak. They represent *minimum* capital requirements in *quantitative* terms. But capital adequacy is not just a number. The Basel regulations also include two other pillars, Supervisory Review (the Second Pillar) and Market Discipline (the Third Pillar). They don’t get as much attention but they probably should. The Second Pillar has been called the “load-bearing” pillar. It recognizes the quantitative rules in the first pillar are not a total solution, and it puts the burden on national supervisors to ensure each bank has a process and adequate capital for its unique situation. It justifies a supervisor insisting that a bank hold more capital than required under the first pillar (i.e., the first pillar is just a *minimum*). The Third Pillar attaches various disclosure requirements; it trust the market to evaluate and impose discipline. If banks want to rely on their internal models (e.g., if they want to measure market risk with their own value-at-risk, VaR, models rather than standard models), the price is greater disclosure to investors under the third pillar.

### Summary

I first meant to engender sympathy for the complicated Basel ratios by reminding you that banks are fragile, complicated creatures (why else would we need so many perspectives!). Then I quickly summarized the evolution from Basel I to the current Basel III (although I spared you the calculation of market risk and operational risk, did you notice?). Then we looked at the four essential capital adequacy ratios: leverage, common equity Tier 1, Tier 1 and Total Capital. In summary, Basel III will require banks to hold 6.0% in Tier 1 (high-quality equity and equity-like) and 8.0% in Total Capital plus a Capital Conservation Buffer of 2.5%. This represents an increase from Basel II’s 8.0% ratio to 10.5% (along with a tightening in the definition of quality equity).

Fantastic, as always, David! Thank you!

Very helpful and easy to follow article. Thanks a lot!

Thanks for this article.

Thanks for this article.. Just saw this article .. Great last minute revision.

Very helpful.

Very good capsule summation, David. What makes it outstanding is the example that one does not get to see in other blogs. Thank you.

Thank you Vishwa, I appreciate that!

Excellent article!

I just have one observation. The leverage ratio include additional tier 1 as well I think: Total tier1 / Exposure.

It is well explained and simple. Thanks David

Thank you Raj, much appreciated!