The current yield on a bond is 7.19% and the bond’s standard deviation is 11.3%. The 99.7% confidence interval for the yield is closest to: A. [6.32%,8.04%] B.[5.56%, 8.81%] C.[6.38%, 8.00%] D.[4.75%, 9.63%] Please show your detail work. Thanks
I could be way off, as I haven’t worked a single FI problem yet, but here goes: 99.7% Conf Interval = 3 std devs from expected value so 11.3% of 7.19 = .812 * 3 std devs = 2.43%. Add and subtract 2.43% from 7.19% to get D) 4.75 - 9.63
why do you multiply 11.3% to 7.19??/
back to flipping coins. C and D are the only ones where 7.19% is the midpoint. god, back to my L1 approximate days. wasn’t 1 std dev like 64%, 2 std dev 95%, 3 std dev away around 99%? so .113 x 7.19 = 0.81247. multiply by 3 = 2.437410. 7.19 +/- 2.437410 = I’ll take my shot at answer D.
D (i think) assuming normal distribution and rounding 99.7% conf interval to 3 stdev 7.19% +/- 3 stdev’s (2.4375%) 4.75% - 9.63% 1 stdev = 11.3% * 7.19% = 0.8125% 3 stdev = 2.4375%
why do you multiply 11.3% to 7.19??
To build a confidence interval, you need to know the value of a standard deviation about the mean. since 7.19% is the mean or expected value, we need to figure out what one standard deviation is equal to, so we multiply 11.3%, which is stated as the stardard deviation, times the expected value, 7.19. So .8125 is equal to one standard deviation around 7.19%.
okay, everyone, I am really embarrassed by my stupidity. But I need to clarify this. why cannt I just use 11.3 the std give, but have to mutily the mean to it??? isn’t the CI formula just m+3*std???
It is but you’re confused about standard deviation here. It’s 11,3 PERCENT. So the actual standard deviation is this percentage * value which is what bannisja and ilvino did.
If you’re confused about this question, I wouldn’t worry about it. The question confuses me too. Let’s see: “The current yield on a bond is 7.19%” So the yield on the bond is a calculated ytm which is the discount rate needed to equate cash flows with the market price. What do I know about the distribution of that thing? Maybe I know something but it depends on stochastic interest rate models or something. It certainly isn’t a smaple mean or anything close. “the bond’s standard deviation is 11.3%” Yield vol is 11.3% I guess. Hmm. “The 99.7% confidence interval for the yield is closest to:” Didn’t they just tell us that the yield was 7.19%? I don’t know why I would try to estimate something which is completely known. A C.I. is about estimating some unknown parameter. What would the unknown parameter we are trying to estimate here be, anyway? The people who write these stats questions are such idiots.
D this seems like an L1 kinda question…ya’ll really think we’ll see stuff like this on june 7th?
Perhaps as question 1 to give you some confidence which they will then crush in the 119 questions after that.
This question is 7 ways from stupid. You won’t see it on the exam.
i work in fixed income quant strategy and we look at volatility and yields all day long, and that is a very novice way to look at the relationship between vol and ytm. it screams “guy sitting in a room writing a textbook that has never had a real job on wallstreet”