Fixed income: Reading55 page 265

CFA Level II
#1

reading 55, page 265, question 21: why annualized standard deviation for daily yield is 7%, currently yield is 5%, then 5% * 7% is the new annualized standard deviation? (from the answer). I’ve stuck on this questions for along time and don’t get it…

#2

It’s not annualized standard deviation for daily yield… It is annualized standard deviation for the change in the daily yield that is 7%. So, the change times prevailing value (5%*7%) equals the expected change which is 35 basis point. Don’t know if this helps. Don’t be fooled that they both are stated as % sign, but they are not the same level.

#3

I don’t understand your question. what are you asking, and what is the original textbook question?

#4

Original Question: Suppose that the annualized standard deviation for the change in the 2-year Treasure yield based on daily yields is 7% and the current level of the 2-year Treasury yield is 5%. Assuming that the probability distribution for the percentage change in 2-year Treasury yields is approximately normally distributed, how would you interpret the 7% annualized standard deviation? Note: The mean of change in yield is 0. So, 68.3% of change is -7% to 7%. Now we know what the change is, apply that to the yield which is 5%.

#5

thanks for posting that 2004028; wasn’t even your question and you went through the trouble, very helpful guy :slight_smile: I agree with your answer too; if the current yield is 5%, and the annual standard deviation of changes in yield is 7% of the current level (with normal distribution), then you expect the following: 68% chance that after a year, the current yield will be in the range of 5% +/- 1sd 95% chance that after a year, the current yield will be in the range of 5% +/- 2sd 99% chance that after a year, the current yield will be in the range of 5% +/- 3sd 1 sd = 7% of 5% = 0.35% so actually, the 68.3% chance range is from 4.65% to 5.35% (+/- 7% of 5%), but I get what you were saying with the "So, 68.3% of change is -7% to 7%. " thing, you didn’t mean those as the current yield, you meant them as the relative change from 5%.