# Fixed income: Reading55 page 265

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…

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.

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

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%.

thanks for posting that 2004028; wasn’t even your question and you went through the trouble, very helpful guy 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%.