13_Fixed_Income_Portfolios

002 very small the probability that the senior tranche

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Unformatted text preview:   1.89M−1.236M = 0.654M lel over for the junior tranche, for a loss of 18.25%. •  If senior tranche’s interest is less senior than junior tranche’s capital, then –  Senior tranche gets its capital back, 1.2M –  1.89M−1.2M = 0.7M lel over for the junior tranche, for a loss of 12.5% Example, con:nued •  In any case, the senior tranche’s capital is untouched if there are four or fewer defaults. •  The number of defaults also greatly influences how well or badly the junior tranche performs. Independent defaults •  If defaults are independent, the probability of k=4 or fewer defaults is ⎛ 10 ⎞ n 10 − n 0.1 0.9 = 0.910 + 10 ⋅ 0.1 ⋅ 0.9 9 + 45 ⋅ 0.12 ⋅ 0.9 8 ∑⎜ n ⎟ ⎠ n=0 ⎝ k 10! 10! ⋅ 0.13 ⋅ 0.9 7 + ⋅ 0.14 ⋅ 0.9 6 3!⋅ 7! 4 !⋅ 6! ≈ 0.348678 + 0.387420 + 0.193710 + 0.057396 + 0.011160 + ≈ 0.998 •  The probability that the senior tranche loses...
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