问题如下：
Bond B3 will have a modified duration of 2.75 at the end of the year. Based on the representative one-year corporate transition matrix in Exhibit 7 of the reading and assuming no default, how should the analyst adjust the bond’s yield to maturity (YTM) to assess the expected return on the bond over the next year?
选项：
A.Add 7.7 bps to YTM.
B.Subtract 7.7 bps from YTM.
C.Subtract 9.0 bps from YTM.
解释：
B is correct. For each possible transition, the expected percentage price change, computed as the product of the modified duration and the change in the spread as per Exhibit 7 of the reading, is calculated as follows:
From AA to AAA: –2.75 × (0.60% – 0.90%) = +0.83%
From AA to A: –2.75 × (1.10% – 0.90%) = –0.55%
From AA to BBB: –2.75 × (1.50% – 0.90%) = –1.65%
From AA to BB: –2.75 × (3.40% – 0.90%) = –6.88%
From AA to B: –2.75 × (6.50% – 0.90%) = –15.40%
From AA to C: –2.75 × (9.50% – 0.90%) = –23.65%
The expected percentage change in the value of the AA rated bond is computed by multiplying each expected percentage price change for a possible credit transition by its respective transition probability given in Exhibit 7 of the reading, and summing the products:
(0.0150 × 0.83%) + (0.8800 × 0%) + (0.0950 × –0.55%) + (0.0075 × –1.65%) + (0.0015 × –6.88%) + (0.0005 × –15.40%) + (0.0003 × –23.65%)= –0.0774%.
Therefore, the expected return on the bond over the next year is its YTM minus 0.0774%, assuming no default.
请问老师其他回答里的这个公式是怎么得出来的呀，实在想不起来在哪里学过了？谢谢
