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CFA Examination Level II
Table 3 shows prices as a function of yields for four tranches of a collateralized mortgage obligation (CMO).
| PRICES FOR FOUR CMO TRANCHES AT SELECTED YIELDS | |||||
| YIELD (%) | |||||
| CMO Tranche | 6 | 6.5 | 7 | 7.5 | 8 |
| T-1 | 111.5 | 105.5 | 100 | 95 | 90.5 |
| T-2 | 107.5 | 104 | 100 | 95.5 | 90.5 |
| T-3 | 112 | 105.5 | 100 | 95.5 | 92 |
| T-4 | 104.5 | 102 | 100 | 98.5 | 97.5 |
a. Calculate the effective duration of Tranche T-3. Assume that the relevant current yield is 7.0 percent. Show your work.
b. Identify the tranche with the negative convexity. Calculate the effective convexity of this tranche. Show your work.
Table 4 shows the option-adjusted spread for four different mortgage pass-through securities.
| MORTGAGE PASS-THROUGH OPTION-ADJUSTED SPREADS (ASSUMING INTEREST RATE VOLATILITY OF 8 PERCENT) | |
| Security | Option-Adjusted Spread (in Basis Points) |
| A | 43 |
| B | 70 |
| C | 89 |
| D | 99 |
c. Identify which of the patterns of option-adjusted spreads shown in Table 5 is plausible if the assumed interest rate volatility is 12 percent rather than the 8 percent assumed in Table 4. Justify your choice.
| MORTGAGE PASS-THROUGH OPTION-ADJUSTED SPREADS (ASSUMING INTEREST RATE VOLATILITY OF 12 PERCENT) | ||
| OPTION-ADJUSTED SPREAD (IN BASIS POINTS) | ||
| Security | Pattern A | Pattern B |
| A | –13 | 103 |
| B | 20 | 120 |
| C | 49 | 129 |
| D | 69 | 129 |
