Hold that bank while rates are high, hopefully you sold off bonds before they got too high, cuz now is the time to buy buy buy. Plus your bank should be seeing some nice stock value to cushion any negative impact from bad loans, maybe. But if the recession is THAT bad, any benefits from high rates may be completely negated by bad loans and/or under value bonds if you didn't drop them at first sign of rising rates.
I personally hate banks because they buy and sell bonds automagically. Annoys the shit out of me.
But, if you are sitting on two billion... Here is a nice strategy in line with your idea of buying struggling companies... Buy a struggling company with issued bonds and a high tax loss carryover. Make sure the bonds are available for purchase.
Liquidate just a little of the assets and use the cash to buy back some of its bond at discounted rates.
Make a cash capital contribution to new company (not an advance, so it shows as new equity) in small amounts as needed to continue buying bonds back; and if you can, buy back discounted bond with loan money before doing any capital contribution. If you do it right, you should be able to buy back the bonds at a huge discounted rate, I'm talking like 50-70% of value. As you buy back the bonds your paper balance sheet will improve immediately. You should be able to turn a company you bought for ~1billion into a 2 or even close to 3 billion dollar company easily. The income it makes off buying its bones back should be sheltered by its tax loss carryover, too. Pure profit.
If it was me, I'd then sell off its corporate assets and use it to repeat the process on a new company.
And if you want to be really tricky, you can buy some of the company bonds with your personal account before buying them back with the company, you'll see a small profit from that too.