another quote from msg board
The Credit Swap Default problem in Numbers and Problem Root
Assumptions at outset:
-Borrower wants to borrow 10 Million at 10% interest only for 10 years then baloon payment of principal
-Bank has 11 Million
-Reserve Requirement at Federal Reserve account (9%)
-CDS dealer has 10 Million
-default risk is 5% and credit exposure is 10 Million + 10 years x $900,000 = $19 Million at the outset. Exposure (Value-at-Risk) goes down by $900,000 each year until year 10 when it's $10 Mill. CDS is for full replacement. Recovery is 50% (CDS dealer assumes Borrower's asset and recovers $5 Mill).
1) Loan goes through: Bank has a 10 Million loan portfolio making $900,000 interest per year for 10 years. Keeps 1 Million in reserve as required.
2) Bank enters into credit default swap with CDS dealer for the following premium schedule (yield) to insure for full replacement of principal plus remaining interest in case of a default credit event:
Year 1 5% x $19.0 Mill= $950,000 -$50,000
Year 2 5% x $18.1 Mill= $905,000 -$5,000
Year 3 5% x $17.2 Mill= $860,000 $40,000
Year 4 5% x $16.3 Mill= $815,000 $85,000
Year 5 5% x $15.4 Mill= $770,000 $130,000
Year 6 5% x $14.5 Mill= $725,000 $175,000
Year 7 5% x $13.6 Mill= $680,000 $220,000
Year 8 5% x $12.7 Mill= $635,000 $265,000
Year 9 5% x $11.8 Mill= $590,000 $310,000
Year10 5% x $10.9 Mill= $545,000 $355,000
Total profit: = $7,475 Mill (CDS dealer)
= $1,525 Mill (Bank)
3) Since bank has a risk free, CDS-insured loan, loan is "off books" (reserve-free, 0% fractional reserve required) and bank can make new loan for $10 Mill using $1 Mill in vault as reserve for next loan, then insure again, then make loan again and again.....
4) CDS bank needs reserve to cover credit exposure x risk which is 1/20 loans at $19 Mill in the first year. So CDS bank insures 20 similar $10 Mill loans earning $950,000 x 20 in the first year = $19 Mill and needs 5% in reserve for that CDS portfolio, i.e. $950,000
Since CDS bank has 10 Mill it can insure 20 x $10 Mill/$950,000 = 211 loans
That's 211 x $950,000 (first year premium) = $200,450,000 profit
Notional amount on 211 CDS = 211 x $19 Mill =$4,009,000,000 (year 1)
5) Bank who made all these 211 loans has $1 Mill in reserve, 211 x -$55,000 ($11,605,000) in short-fall over first two years, then 211 x $40,000 = $8,440,000 profit in year 3. In order to cover this short-fall over first two years Bank borrows $12,000,000 from European Bank at 3%, 2-year-term.
We now have the following conditions:
1) 211 borrowers each $10,000,000 in the hole owing $900,000 annual interest for 10 years
2) A CDS dealer with Cash flow of $200,000,000 in year one and with a 5% probability of a credit event to pay-out $19,000,000 with a recover of $5 Mill----> $14,000,000 x 0.05 x 211 = $147.7 Mill---> profit after pay-out and recovery: $52.3 Mill (year one)
3) A bank with $13,000,000 in reserve (1 mill own + 12 Mill borrowed), a $12,000,000 obligation plus interest to a European bank and negative cash flow in year one and two (interest payments - CDS premiums), then profit of $8,440,000 in year 3.
4) A European Bank with a loan asset at $12 Mill
Total cash committed by all parties: $23 Mill
Total debt outstanding: $4,021,000,000
Leverage: 175/1
So, Ladies and Gentlemen, that is the set-up. Now assume that after year 1 10% of borrowers default (2x estimated credit default rate) and the recovery of the borrower asset is stalled due to a credit crunch (asset cannot be liquidated).
We now have a CDS dealer who ows 211 x 0.1 x $19,000,000 - $0 = $401,000,000, but only has $10,000,000 (reserve) + 0.9 x 211 x $950,000 = $180,000,000 cash flow.
We also have 2 banks in the hole (21 x 10 Mill= 210 Mill and 12 Mill) and 21 borrowers bankrupt.
Does this help explain the problem?
If so, multiply all figures by 200 and you get approximately the maximum magnitude of the subprime problem.
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