### CFA Practice Question

There are 434 practice questions for this study session.

### CFA Practice Question

A portfolio with 10 stocks has a weighted average return of 5.5% and a variance of 25. What is the 85% confidence interval for the weighted average?
A. [-35.625%, 46.625%]
B. [-30.5%, 41.5%]
C. [3.22%, 7.78%]
Explanation: The variance is 25, which corresponds to a standard deviation of 5%. The 85% confidence interval is given by: X-bar +- 1.44s = 5.5 +- 1.44 x 5/10^0.5 = [3.22, 7.78]

User Comment
cfahopeful This seems to be wrong. Using Chebyshev's inequality, .85 = 1 - (1/k^2) k = 2.58 Therefore, 85% of observations will lie between 5.5 + 2.58 * 5 and 5.5 - 2.58 * 5 -7.4 to 12.4
tony1973 The answer's correct. The confidence interval calculated by Chebyshev's formula will always be wider.
mm04 So which one should we use for the exam? I found this from another question too.
garachen Yes, Chebyshev is only when you have no idea of the underlying distribution. Since you can assume portfolio returns are normal you must use a normal distribution. I can't see remembering that 85% is 1.44 st deviations though.
synner yeah, how do you know that 85% is 1.44 st.dev?
jack48084 we know 90% is 1.645, therefore 85% must be less. So answer C is the only one could be correct.
Pieter One way to approach it would be to remember that +/-1 stdev covers 65%
+/-2 stdev covers 95%
Therefore, 85% is somewhere in between, approx. close to +/-1.5 stdev.
eddeb In the z table :
85% / 2 (two tailed) = 0.425
At 0.425 we have a 1.44 z score.

I just don't know why we use the z table.. N is under 30, so we should use the t table. Using a r numbers rule, I have obtained a t score of 1.605.
danlan Variance of 25 is the variance of the portfolio. It is not the variance of a sample.
Nightsurfer Isn't 1.44 standard deviations 92.51%, not 85%?
EtnicPlaymaker (1 - 0,9251) = 0,075
0,075 * 2 = 15. Everything is ok.
uberstyle stupid question here, but why is it given that if the portfolio variance is 25, standard error is 5?
jackwez std deviaion is the sqrt of the variance
Yohan3109 This question is logique, no need to calcul. Just think logicaly. Mean is 5,5 and standard deviation 5. The mean of the interval is 5.5 add 2 standard deviation for each side -5.5% to 15.5%.
check A and B are totally wrong event 3 standard divation doesnt fit.
Mariecfa This is a two tail test. Alpa/2: (1-.85)=.15/2=.075
Probability of .075 on left tail from Z table gives -1.44 for the SD.
Probability of (1-.075)=0.925 (This is what the probability is that lies to the left of the Right-tail critical value. On the Z table 0.925 shows 1.44. This is what gives you the Standard deviations. Hope this helps.
showmethemoney gotta use t-test. the question doesn't assume normal dist. can't just use z test.
charlie You already know the population variance, so it's a z test, not t test.
homersimpson To sum up, we use Z test cos we know the population variance and we multiple it by 5 instead of standard error (5/10^2) because it is a population, not a sample.
Marinov Even if we do know the population variance, we still need to divide it by the square root of n. This is the formula of the standard error.