quant prop problem / please solve

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jbnjc

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If the probability of a stock index generating a return greater than 15% in any given year is 6.68%, what is the standard deviation of the returns assuming the mean return is 5%? Assume returns are normally distributed.


a. 6.08
b. 6.66
c. 10.00
d.44.36


Please work and advise. I am having trouble finding the right Z stat to solve for standard deviation in Z formula.
 
I'm a bit rusty, but here goes.

The probability is 6.68%, or .0668. If you consider the area under the distribution curve to be equal to one, then you are looking at the right hand side of the cuve. All the area up to that point is the probability of the return NOT being greater than 15%. This value is 0.9332.

The area of the curve on the left hand side of the mean is equal to 0.5. The area under the curve up to the value representing 15% is then 0.9332-.5000, or 0.4332

If you look in a z-distribution table for the value of .4332, you will find it to be where z=1.5.
 
Everything Stealth said above is right, but he didn't quite finish.

The z=1.5 means that the point you are looking at is 1.5 standard deviations away from the mean.

So that implies that the 15% point referenced in the question is 1.5 standard deviations away from the mean which is given as 5%.

Divide the gap between those to points of 10% by the 1.5 std deviations that it represents to get one standard deviation is equal to 6.66 for answer B.
 
Super I Wrote:
-------------------------------------------------------
> Everything Stealth said above is right, but he
> didn't quite finish.
>
> The z=1.5 means that the point you are looking at
> is 1.5 standard deviations away from the mean.
>
> So that implies that the 15% point referenced in
> the question is 1.5 standard deviations away from
> the mean which is given as 5%.
>
> Divide the gap between those to points of 10% by
> the 1.5 std deviations that it represents to get
> one standard deviation is equal to 6.66 for
> answer B.


Thanks,

Super that is definitely the right answer and the quickest solution.
 
Super I Wrote:
-------------------------------------------------------
> Everything Stealth said above is right, but he
> didn't quite finish.

well, I figured jbnjc was a pretty intelligent person and once he got the z value it would be smooth sailing. FWIW, I agee that (b) is the correct answer.
 
StealthPlanner Wrote:
-------------------------------------------------------
> Super I Wrote:
> --------------------------------------------------
> -----
> > Everything Stealth said above is right, but he
> > didn't quite finish.
>
> well, I figured jbnjc was a pretty intelligent
> person and once he got the z value it would be
> smooth sailing. FWIW, I agee that (b) is the
> correct answer.

Thank you to you too Stealthplanner!
 
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