MMC Bank has an equity trading portfolio that consists of long positions of 2,750 shares of McDonald's Corp.at a price of $97.50;3,500 shares of Duke Energy at a price of $65.00;and 1,000 share of the Swiss firm USB Bancorp at a price of $47.50.In addition the bank has sold short 1,500 shares of the Japanese technology firm Sony at a price of $32.00 and 750 shares of McDonald's Corp.What is the amount of capital that MMC Bank is required to keep against this portfolio according to the Basel Standardized approach?

Question

Quizplus · Accepted Answer

According to the Basel Standardized approach, the risk weight for equities is 8%.

To calculate the capital requirement, we need to find the market value of each long position and the net position after the short sales.

Market value of long positions:
McDonald's Corp. = 2,750 x $97.50 = $268,125
Duke Energy = 3,500 x $65.00 = $227,500
USB Bancorp = 1,000 x $47.50 = $47,500

Net position after short sales:
Sony = -1,500 x $32.00 = -$48,000
McDonald's Corp. = 2,750 - 750 = 2,000
Therefore, the net market value of the equities portfolio is:
$268,125 + $227,500 + $47,500 - $48,000 = $495,125

The capital requirement is 8% of the net market value:
0.08 x $495,125 = $39,610

However, the minimum capital requirement under Basel III is 8% of the sum of risk-weighted assets, which includes other assets and off-balance sheet items. Without information about these items, we cannot determine the exact capital requirement.

Among the choices given, the closest to the calculated capital requirement is D, $116,044.60. It is possible that this amount includes other assets and off-balance sheet items that are not mentioned in the problem. Refer to Example 15-8 for risk bucket determination, risk weights for each bucket, and correlation parameters. Additionally, the following formulas (also from example 15-8) are used:
 
 Bucket risk exposure:
 where pij is the correlation parameter between equities i and j.
11efbab0_e85d_3eee_8e22_932c1f75121f_TB1314_00 
Equity Risk Capital:
 where  11efbab1_0bbf_03ff_8e22_7f00123bed53_TB1314_00  and yS1U1B1bcS1U1B0 is the correlation parameter between buckets b and c.
 
11efbab1_20ec_0170_8e22_3368f10e3b5c_TB1314_00
Buckets and Risk Weights:
 McDonald's and Duke Energy are risk bucket (b) #5, a risk weight (RW) of 30 percent, are both long positions so a correlation parameter of 20 percent.
 UBS and Sony are risk bucket (b) #8, a risk weight (RW) of 50 percent, one is long one is short so the correlation parameter is 20 percent.
 
 K5 = [(0.30)S1U1P12S1S1P0({2,750 - 750} * $97.50)S1U1P12S1S1P0 + (0.30)S1U1P12S1S1P0(3,500 * $65.00)S1U1P12S1S1P0 +
 2(0.20)(0.30)({2,750 - 750} * $97.50)(0.30)(3,500 * $65.00)]S1U1P11/2S1S1P0 = $98,373.59
 
 K8 = [(0.50)2(1,000 * $47.50)S1U1P12S1S1P0 + (0.50)S1U1P12S1S1P0(1,500 * $32.00)S1U1P12S1S1P0 +
 2(0.20)(0.50)(1,000 * $47.50)(0.50)(1,500 * $32.00)]S1U1P11/2S1S1P0 = $36,987.33
 
 Equity Risk Capital
 Cross correlation between buckets 5 and 8 is 20 percent.
 
 ERC ={[($98,373.59)S1U1P12S1S1P0 + (36,987.33)S1U1P12S1S1P0] + 2(0.20)[(0.30)(2,000 * $97.50) + (0.30)(3,500 * $65.00)] [(0.50)(1,000 * $47.50) + (0.50)(1,500 * $32.00)]}S1U1P11/2S1S1P0 = $116,044.60.

MMC Bank Has an Equity Trading Portfolio That Consists of Long