Sigma Bank has the following balance sheet in millions of dollars. Unless mentioned otherwise, all assets are associated with corporate customers (not governments or sovereigns). Values are in millions of dollars. Refer to table 20-8 for appropriate risk weights $$\begin{array} { | l | r | l | r | }
\hline \text { Cash } & \$ 40 & \text { Deposits } & \$ 370 \
\hline \begin{array} { l }
\text { Municipal General } \
\text { Obligation Bonds }
\end{array} & \$ 60 & & \
\hline \begin{array} { l }
\text { Residential Mortgages } \
\text { l-4 family } \
( 80 \% - 90 \% \text { LTV) }
\end{array} & \$ 100 & \begin{array} { l }
\text { Perpetual Preferred } \
\text { Stock }
\end{array} & \$ 20 \
\hline \begin{array} { l }
\text { Commercial loans } \
\text { BB + rated }
\end{array} & \$ 200 & \text { Equity } & \$ 10 \
\hline \text { Total Assets } & \$ 400 & & \$ 400 \
\hline
\end{array}$$ Off balance sheet contingent liabilities (Refer to Table 20-10)
$40 million direct-credit substitute standby letters of credit issued to a U.S. corporation.
$40 million commercial letters of credit issued to a corporation
Off-balance sheet derivatives (Refer to Table 20-11)
$200 million 10-year interest rate swaps
$100 million 2-year forward DM contracts
-What is the minimum required Tier I and Total risk-based capital for the on-balance-sheet assets in order for the DI to be adequately capitalized?

Question

Sigma Bank has the following balance sheet in millions of dollars. Unless mentioned otherwise, all assets are associated with corporate customers (not governments or sovereigns). Values are in millions of dollars. Refer to table 20-8 for appropriate risk weights $$\begin{array} { | l | r | l | r | } 
\hline \text { Cash } & \$ 40 & \text { Deposits } & \$ 370 \
\hline \begin{array} { l } 
\text { Municipal General } \
\text { Obligation Bonds }
\end{array} & \$ 60 & & \
\hline \begin{array} { l } 
\text { Residential Mortgages } \
\text { l-4 family } \
( 80 \% - 90 \% \text { LTV) }
\end{array} & \$ 100 & \begin{array} { l } 
\text { Perpetual Preferred } \
\text { Stock }
\end{array} & \$ 20 \
\hline \begin{array} { l } 
\text { Commercial loans } \
\text { BB + rated }
\end{array} & \$ 200 & \text { Equity } & \$ 10 \
\hline \text { Total Assets } & \$ 400 & & \$ 400 \
\hline
\end{array}$$ Off balance sheet contingent liabilities (Refer to Table 20-10)
$40 million direct-credit substitute standby letters of credit issued to a U.S. corporation.
$40 million commercial letters of credit issued to a corporation
Off-balance sheet derivatives (Refer to Table 20-11)
$200 million 10-year interest rate swaps
$100 million 2-year forward DM contracts
-What is the minimum required Tier I and Total risk-based capital for the on-balance-sheet assets in order for the DI to be adequately capitalized?

Quizplus · Accepted Answer

First, we need to calculate the risk-weighted assets (RWAs) for on-balance-sheet assets:

- Cash: 0% risk weight, so RWAs = $0
- Municipal bonds: 20% risk weight, so RWAs = $60 x 20% = $12
- Mortgages: 50% risk weight, so RWAs = $100 x 50% = $50
- Commercial loans: 100% risk weight, so RWAs = $200 x 100% = $200
- Total RWAs for on-balance-sheet assets = $262

Next, we calculate the minimum Tier 1 and Total risk-based capital required:

- Tier 1 capital = 6% x RWAs = 6% x $262 = $15.72 million
- Total risk-based capital = 8% x RWAs = 8% x $262 = $20.96 million

Finally, we add the off-balance sheet items to determine if the bank is still adequately capitalized:

- Direct-credit substitute standby letters of credit: 100% credit conversion factor (CCF), so RWAs = $40 x 100% = $40
- Commercial letters of credit: 50% CCF, so RWAs = $40 x 50% = $20
- Interest rate swaps: 1.6% CCF (assuming net notional amount after netting with counterparty), so RWAs = $200 x 1.6% = $3.2
- Forward currency contracts: 6% CCF, so RWAs = $100 x 6% = $6
- Total RWAs for off-balance-sheet items = $69.2
- Total risk-weighted assets = $262 + $69.2 = $331.2

The bank's Tier 1 capital ratio is now $15.72 million ÷ $331.2 million = 4.74% and its Total risk-based capital ratio is $20.96 million ÷ $331.2 million = 6.33%.

To be adequately capitalized, the bank needs to maintain a Tier 1 capital ratio of at least 4% and a Total risk-based capital ratio of at least 8%. Currently, the bank is below the required levels. To meet the requirements, the bank needs to raise an additional $1.5 million in Tier 1 capital and $1.9 million in Total risk-based capital.

Therefore, the answer is C.

Sigma Bank Has the Following Balance Sheet in Millions of Dollars