This refers to the Q11, fixed income (book4), page 193: bond yield is 7.19%, stdev of the bond is 11.3%, asking for 99.7% CI of yield (z=3): A. [6.32%, 8.04%] B. [5.56%, 8.81%] C. [4.57%, 9.63%] Answer: C one thing schwesser explains for stdev(Y) from stdev(Bond) is: 7.19%*11.3%; why is this true? Thanks.
CI of 99.7% = 3 std. dev away from mean 3*11.3% = .339 7.19% = mean Upper CI = 7.19 * 1.339 = 9.6274% Lower CI = 7.19 * (1 - .339) = 4.7526% (I assume this # is transposed incorrectly; 4.57% vs. 4.75%) Closest would be C
Hi, FinNinja: For CI: it is calculated as mean_x +/- z * stdev_x, here x represents yield and z is 3. We need to use stdev of yield but we are given stdev of bond and mean of bond. Schwesser calculates: stdev(yield) = mean(yield) * stdev(bond), eq(1) My question is why this eq(1) is true!!! Otherwise, if one plugs in the numbers here, one will get the same result as schwesser.
Eq(1) is the standard eq for a CI inclusive of 1 st dav from the mean; level I The question asks for 3 st dev’s from the mean, so multiply the given stdev by 3. Is this what you are asking?
stdev(yield) = mean(yield) * stdev(bond), eq(1) I think it is because stdev(bond) is standard deviation of percentage yield change. It is not standard deviation of the yield itslef. Therefore you need to multiply it by mean yield.
FinNinja: the 3 is captured by z score in the formula mean_x +/- z * stdev_x given above. pfcfaataf: This is the question I am asking; I am hardly convinced by the eq(1): stdev(yield) could be associated with associated with level of bond price. I just want to see some theoretical justification for eq(1). From the question itself, the question doesn’t state stdev(bond) to be stdev(Return(bond)); even though it is return on bond (P(t)/P(t-1) -1), the eq(1) doesn’t necessary hold true.
I may still not be on the right track of what you are asking, but I will try again. when they say st dev of bond, I believe they are refering to the bond’s yield not to the bond’s price. Since they give you the bond yield to begin with you can reasonably asume that the st dev of the bond refers then to the yield as well.
FinFinja: If this is the case, there is no need to adjust stdev(yield) with eq(1), which the schwesser answer is based on. Do you see the problem here? Thanks anyway.
no i do not. finninja is right in the method of calculation. the 11.3% they are giving you is the std. dev of the change in yield, actually.