Bank equity risk under bailout programs of loan guarantee and/or equity capital injection

- A lending function with loan guarantee is a call option with capital injection.
- Loan guarantee and/or capital injection improve bank equity return and risk.
- A bank may prefer the combined package to either the solo bailout.
- The government may prefer either the solo bailout to the combined package.

We analyze the implication of a bailout package including a loan guarantee and a direct equity capital injection on the equity risk of a distressed bank at the taxpayer costs. The lending function with a loan guarantee of the bank creates the need to model equity as a down-and-out call (DOC) option with a capital injection due to the bank in distress. We provide validation of the DOC model by showing that the values of down-and-out call at various levels of bailout are economically significant for the distressed bank. We show that a loan guarantee, a capital injection, or a combination of the two tends to be successful in improving bank equity return. From an equity-return perspective, the bank prefers the combined package to either the solo bailout. Alternatively, from an equity-risk perspective, the government (and thus the taxpayers) prefers either the solo bailout to the combined package. The results may cast doubt on the effectiveness of the combined rescue program to simultaneously exert equity return-increasing and equity risk-reducing effects on the distressed bank.