Isolation rules

CFA Level I Quant
#1

Hi Analyst Forum

When solving for one unknown is there then a general rule for how to isolate it?

For example:

Two stocks A and B:
- Correlation of 0.50
- Covariance of 0.0043
- Standard deviation of stock B of 26%

Find the standard deviation of returns for Stock A.

In that case I write
Corr(A,B) = Cov(A,B) / sigma_A * sigma_B => 0.50 = 0.0043 / sigma_A * 0.26

<=> Isolate for sigma A by multiplying 0.26 on both sides and dividing by 0.0043

sigma_A = (0.50*0.26) / 0.0043 = 30.23 (and now I have to divide 1/30.23 to get the right result).

If I go the correct way and
<=> Isolate for sigma A by multiplying sigma_A on both sides and dividing by 0.50 I get the correct result

sigma_A = 0.0043 / 0.50 * 0.26 = 0.0331.

Is there something I’m missing or a general rule of how to solve/isolate equations?

Kind regards,
Christoffer

#2

1 / sigma_A = (0.50*0.26) / 0.0043 = 30.2325581395

Rounding to 30.23 has introduce round off error! :-1:

#3

Yes - you’re absolutely right.

What I was most worried about is whether there is a correct procedure to isolate sigma_A? You know if I should always move the unknown to the opposite side - it just does not make sense in my headf, that I have to divide 1 by sigma_A… :slight_smile:

#4

If I take the reciprocal of 1/A, then I also have to take the reciprocal of 30. That becomes A = 1/30. :nerd_face:

Algebra!!! :+1: :raised_hands:

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