June 2007 Capital Adequacy Extension © Copyright 2007, CCRO. All rights reserved. Page 52 of 92 Insert 5.1 Bond Approach Example Take for example a counter party that has the following two bonds outstanding Principal Maturity Coupon Price $100 0.5 $6.5 $99.5 $100 1.0 $5.935 $100.5 We ultimately want to determine the one-year default probability, however in order to do so, we must determine the zero-coupon rate (R) for the bond maturing in ½ year first. Since there is only one coupon payment remaining with the principal repayment, and we know the current bond price, the zero-rate can be determined from the present value equation (100 + 6.5) e-R * 0.5 = 99.5 R (t=0.5) = .1360 = 13.6% We now know that the discount rate for the 6 month period is 13.6%. We apply the same present value equation to the one year maturity bond to determine its zero-coupon yield, by applying the ½ year discount rate to the coupon payment due in ½ year, as determined above, and solving for the rate implied at maturity by the current price. 5.935 e-.1360 * 0.5 + (100 + 5.935) e-R * 1.0 = 100.5 R (t=1.0) = .1095 = 10.95% This procedure can be carried out for as far as there are tradable bonds for a counter- party, to achieve a full zero-coupon yield curve. This curve will be useful in assessing credit migration over longer time periods. Let us assume that the zero-coupon rate for a 1 year Treasury is 5.00%. Assuming the spread over treasuries is entirely compensation for expected defaults, the present value of expected default on the one year bond would be the difference between the discounted values of the Treasury and corporate bonds 100e-0.05 * 1.0 – 100e-.1095 * 1.0 = 5.49 1 yr Treasury 1 yr Corporate Now that we have the PV of expected defaults, the expected default loss can be computed as follows 5.49 / 100e-0.05 * 1.0 = .0577 = 5.77% This means that 5.77% of the no default value of the position with this counterparty can be expected to be lost to default within one year. This process will have to be completed for all counterparties in the portfolio to achieve a total expected loss from credit events.