Please help me to understand the underlying concept in this problem.

CFA Level I
#1

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurence.

Asset Outcome1(%) Outcome2(%) Outcome3(%) Expected return(%)

1 12 0 6 6

2 12 6 0 6

3 0 6 12 6

which pair of assets is perfectly negatively correlated?

A. Asset 1 & Asset 2

B. Asset 1 & Asset 3

C. Asset 2 & Asset 3

#2

Correlations are used to calculate the standard deviation of a portfolio. The correct answer is C, so if you have a portfolio of 50% with asset 2 and 50% with asset 3 you will have all the ways 6% return assured because the perfect negative correlation.

Regards

#3

To see the correlation clearly, plot the corresponding pairs of points:

  • 1&2: (12, 12), (0, 6), (6, 0)
  • 1&3: (12, 0), (0, 6), (6, 12)
  • 2&3: (12, 0), (6, 6), (0,12)

If they have perfect positive correlation, the points will lie on a line with a positive slope.

If they have perfect negative correlation, the points will lie on a line with a negative slope.

#4

Basically, negatively correlated means that if one goes up, the other goes down and the other way around.

So if you want to look quickly at this, look at this like that:

First outcome of 1 is 12. Second outcome of 1 is 0. So outcomes (#) decrease between #1 and #2.

So to be negatively correlated, the corresponding asset must have outcomes that increase between #1 and #2.

Compared with A, B has decreasing outcome between #1 and #2 which is the same as A so not negatively correlated to A. You can clear answer A.

Compared with A, C has increasing outcome between #1 and #2, which is the other way around of A so could be negatively correlated to A.

However between 1’s second outcome (0) and third outcome (6) it increases and between 2’s second outcome (6) and 2’s third outcome (12) it increases as well. So both moves in the same way so not negatively correlated. You can clear answer B.

You are left with answer C that can be confirmed with the below summary

Asset Change from #1 to #2 Change from #1 to 3 Change from #2 to #3

1 down down up

2 down down down

3 up up up

You can see that 2 and 3 have opposite changes for all three outcomes.

Hope that clarifies.

Cheers.

Alexx

1 Like
#5

Thanks for clarifying the concept in different ways.

1 Like
#6

My pleasure.

#7

After plotting these points, I found the answer. Thank you,

Do you know if not perfectly positive/negative, which one has lower/higher correlation?