Quiz: Capital and Profitability

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6 questions to check your understanding of the chapter “Capital and Profitability”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.

1. Question 1

   As a hypothetical example, consider the Financial Services Agency (FSA) of Japan's capital ratio notice (the full text updated in August 2026). Suppose an international-standard bank includes the market risk equivalent in its calculation, with total credit risk-weighted assets of 30 billion yen, a market risk equivalent of 800 million yen, and an operational risk equivalent of 400 million yen. Rounding to the nearest 0.1 billion yen, what is its RWA?

   1. A.31.2 billion yen
   2. B.40.0 billion yen
   3. C.45.0 billion yen
   4. D.30.1 billion yen
   Answer and explanation

   Answer: C

   In the notice's formula, RWA is the total credit risk-weighted assets plus each of the two equivalents divided by 8%. The market risk equivalent of 800 million yen divided by 8% is 10 billion yen, and the operational risk equivalent of 400 million yen divided by 8% is 5 billion yen. Adding 30 + 10 + 5 gives RWA of 45 billion yen.

   Adding the three amounts as they are gives 31.2 billion yen. Dividing by 8% converts each equivalent into an asset amount, the same unit as credit risk-weighted assets. Multiplying each of the two equivalents by 8% and adding them gives 30.1 billion yen, which goes in the wrong direction. Leaving out the operational risk equivalent gives 30 + 10 = 40 billion yen, which misses 5 billion yen.

   Learn more: Risk-Weighted Assets (RWA)

2. Question 2

   A bank that calculates credit risk-weighted assets under the standardized approach trades a derivative with a counterparty that is not a qualifying central counterparty. The trade is subject to CVA. Which RWA does this trade produce?

   1. A.The CVA portion is included within the default portion and becomes one amount
   2. B.Both the default portion and the CVA portion, with the CVA portion found from the CVA risk equivalent
   3. C.Both the default portion and the CVA portion, each found by multiplying the credit equivalent amount by the risk weight
   4. D.The CVA portion, entering separately from the default portion as market risk
   Answer and explanation

   Answer: B

   The same trade produces two kinds of credit risk-weighted assets. The default portion is the derivative's credit equivalent amount multiplied by the counterparty's risk weight. The CVA portion is the amount found from the CVA risk equivalent. Both are added to credit risk-weighted assets.

   The CVA portion is added on top of the default portion (the counterparty credit risk portion), so folding it into the default portion is wrong, and so is treating CVA as part of market risk. It is also wrong to find the CVA portion the way the default portion is found, by multiplying the credit equivalent amount by the risk weight. The CVA portion is found from the CVA risk equivalent. A trade with a qualifying central counterparty is outside the scope of CVA.

   Learn more: Risk-Weighted Assets (RWA)

3. Question 3

   As a hypothetical example, a desk holds options, and its daily P&L is split by multiplying the previous day's sensitivities by the move in each risk factor (the gamma contribution is the move squared times gamma divided by 2). Delta is 100,000 yen per 1 yen, gamma is −20,000 yen per squared 1-yen move, vega is 200,000 yen per 1 percentage point of volatility, and theta is −80,000 yen per day. The underlying rose by 4 yen, volatility rose by 2 percentage points, and actual P&L was +450,000 yen. What is the unexplained P&L?

   1. A.+110,000 yen
   2. B.−190,000 yen
   3. C.+50,000 yen
   4. D.−110,000 yen
   Answer and explanation

   Answer: D

   The delta contribution is 100,000 × 4 = 400,000 yen. The gamma contribution is 0.5 × (−20,000) × 4 × 4 = −160,000 yen. The vega contribution is 200,000 × 2 = 400,000 yen, and the theta contribution is −80,000 yen. The four add up to 560,000 yen, which is the explained P&L.

   Unexplained P&L is actual P&L minus explained P&L, so 450,000 − 560,000 = −110,000 yen. Subtracting actual from explained instead gives +110,000 yen, with the sign reversed. Forgetting to divide the gamma contribution by 2 makes explained P&L 400,000 yen and the result +50,000 yen. Forgetting theta makes explained P&L 640,000 yen and the result −190,000 yen.

   Learn more: P&L Attribution

4. Question 4

   A bank hedges the CVA of an uncollateralized trade with a hedging instrument that qualifies under the regulation. What happens to the KVA of this trade?

   1. A.It does not change, because CVA capital is not part of the required capital
   2. B.It falls, because the CVA capital charge falls
   3. C.It rises, because the capital for the hedge trade is added
   4. D.The CVA part falls, but the counterparty default capital falls by the same amount
   Answer and explanation

   Answer: B

   The capital required for KVA includes CVA capital. If a qualifying hedge reduces the CVA capital charge, the KVA on CVA capital falls too. KVA falls by as much as the CVA capital falls.

   The view that CVA capital is not part of the required capital is wrong, because CVA capital is part of the capital required for KVA. A hedge trade can need capital of its own, but total capital does not always rise. Counterparty default capital does not fall by the same amount as CVA capital either. The capital for counterparty default and the market risk capital remain, and KVA does not become zero.

   Learn more: Capital Valuation Adjustment (KVA)

5. Question 5

   How does the denominator of a bank's leverage ratio (the "total exposure amount" in the notice) differ from RWA, the denominator of the capital ratio?

   1. A.It applies no risk weights, and adds together balance sheet assets and derivatives, among others
   2. B.It applies risk weights to the balance sheet assets and derivatives amounts
   3. C.It is the balance sheet total assets figure itself, without derivatives
   4. D.It is the same amount as RWA, and only the numerator differs, using Common Equity Tier 1 capital
   Answer and explanation

   Answer: A

   The leverage ratio was introduced as a simple measure that uses no risk weights, to supplement the capital ratio. The total exposure in the denominator is the sum of four amounts: on-balance-sheet assets, derivatives and similar transactions, repo and similar transactions, and off-balance-sheet transactions. The numerator is Tier 1 capital, the sum of Common Equity Tier 1 capital and Additional Tier 1 capital.

   Risk weights are applied on the RWA side. The view that derivatives are left out of the denominator is wrong, and so are the view that the denominator is the total assets figure itself and the view that the numerator is Common Equity Tier 1 capital alone. The amount for derivatives and similar transactions is also measured by a separate method and included in the denominator.

   Learn more: The Leverage Ratio

6. Question 6

   Under the March 2016 guidance of the US Federal Reserve, the Federal Deposit Insurance Corporation (FDIC), and the Office of the Comptroller of the Currency (OCC), what does a bank's funds transfer pricing (FTP) refer to?

   1. A.It is the price set for tax purposes on intragroup transactions across borders, and means the same thing as tax transfer pricing
   2. B.It is an internal procedure that allocates only the cost of liquidity for stress periods to business units
   3. C.It is an internal procedure in which a central management unit allocates funding costs and benefits to business units and products
   4. D.It is an adjustment to the value of a trade for the cost of the regulatory capital held until the trade matures
   Answer and explanation

   Answer: C

   FTP is a procedure in which a central management unit allocates the funding costs and benefits measured at the time a trade is made to business units, products, and activities. It is an internal funding price, used for example to measure the profitability of business units.

   The price set for tax purposes on intragroup transactions across borders is tax transfer pricing, which is a different thing from FTP. It allocates two costs, funding costs and contingent liquidity costs, not only the cost of liquidity for stress periods. The adjustment for the cost of the regulatory capital held until maturity is KVA. KVA is an adjustment to a trade's value, whereas FTP is an internal calculation allocated to business units.

   Learn more: Funds Transfer Pricing (FTP)