C is correct. Economic capital (EC) is derived using the following Equation:
EC = ULₚ * CM

where ULₚ (unexpected loss of the portfolio) is derived using Equation (4.13) and CM = 7.3 (given).

Given:

• n = 12
• ULᵢ = JPY 85,000,000
• ρ = 0.3

First, derive ULₚ:
ULₚ = ULᵢ * √[n + ρ(n² − n)]
ULₚ = 85,000,000 * √[12 + 0.3(144 − 12)] = 610,581,690

Therefore,
EC = 610,581,690 * 7.3 = JPY 4,457,246,337 = JPY 4.457 billion

A is incorrect. JPY 2.234 billion is the incorrect result obtained by taking the product of UL of each asset, the correlation factor, the number of assets, and the multiplier. (That is, JPY 2.334 billion = UL * ρ * 12 * 7.3).

B is incorrect. JPY 4.078 billion is the incorrect result obtained by multiplying the UL contribution of each asset by the number of assets and by the multiplier (That is, JPY 4.078 billion = UL * √ρ * 12 * 7.3).

D is incorrect. JPY 7.446 billion is the product of capital multiplier, UL of a credit asset, and the number of credit assets in the portfolio.

Learning Objective: Describe how economic capital is derived.
Reference: Gerhard Schroeck, Risk Management and Value Creation in Financial Institutions (New York, NY: John Wiley & Sons, 2002). Chapter 5. Capital Structure in Banks (pages 170-186 only).