Portfolio risk and return - Question

CFA Level I Portfolio Management
#1

Hello

I have a qus as the explanation provided in CFA book is not very clear.

Pg 339, Q 32-34

An analyst has made the foll return projections for each of the three possibe outcomes with an equal likelihood of occurence

Asset outcome 1 outcome 2 outcome 3 exp return (all in %)

1 12 0 6 6

2 12 6 0 6

3 0 6 12 6

q. which pair of assets is perfectly negatively correlated

Ans. the book says asset 2 and 3, but I am confused why not 1 and 2 as they also move in the opposite directions at the same magnitude? I think i m missing the concept here. There are 2 more qus but if I can get the concept right then I can answer all.

Can someone help?

Thanks

Vishal

#2

It’s because Asset 2 maximizes its return when Asset 3 minimizes it, and vice versa. On the other hand, asset 1 and asset 2 both maximize their returns with outcome 1.

#3

Asset 1 and 2 are positively correlated, because all of the outcomes yield an uneven return, they can’t be perfectly negatively correlated.

The correlation between (12,12) and (0,6) is not even negative.

#4

Rather than asking us what the correct answer is and why, you should calculate the correlation coefficients for each pair of securities; there are only three such pairs, so it’s not a difficult job, and you’ll see for yourself what the answer is and why.

Please post your calculations when you do them.

#5

Thanks a lot. Its clear now. as with 12 percent return on asset 1 only asset 3 has corresponding 0 return and vice versa. so they are perfectly negatively correlated . I was confusing between 6 and 0 but 6 is not the maximum, 12 is.

Thanks :slight_smile:

#6

hello S2000magician

Maybe I am missing something but with the info given can we calculate the correlation coefficents? I couldnt see any calculation in the CFA explanation, and to be honest that was my first thought as to how can I calculate the coefficents? Could you advise?

Thanks a lot

#7

Here’s an article I wrote on covariance and correlation; it includes the calculations: http://financialexamhelp123.com/covariance-and-correlation/.

#8

Calculate the covariances (3) and the standard deviations (3). correlation coefficient for 1,2 = cov(1,2)/(sd1*sd2)… follow this procedure for the others.

OR

Use a process of elimination on your question. Assets 1 and 2 both start with a downward movement, from 12% (can’t be perfectly negatively correlated), where as asset three start lower and moves higher. So, looking more critically, asset 3 and asset 2 move exactly in opposite directions and magnitude (up six and down six, respectively) for each outcome. Assets 1 and 3 move in opposite directions when looking at outcomes 1 and 2, but move in the same direction from outcome 2 to 3 (cant be perfectly negatively correlated). So, we can conclude asset 2 and asset 3 are perfectly negatively correlated.

#9

Thanks a lot to both of you!!

#10

My pleasure.

#11

By the way, I hate the way this question is worded. It isn’t the assets themselves that have negative correlation (or any correlation, for that matter): the assets aren’t quantities. It’s _ the assets’ returns _ that have negative correlation.

This may sound like a mere semantic difference, but this kind of sloppy language (with which the financial industry is rife) leads to sloppy thinking: people – even smart, well-educated people – start to confuse correlation of returns and correlation of prices: they think that if the returns have a strong, negative correlation then the prices will also have a strong, negative correlation. It just ain’t so, but the sloppiness of the language helps ideas like this one fluorish.

#12

Glad to help!

#13

fully agree and I also read that in the link you had sent. I am not as experienced as you but maybe I will learn in the right way :slight_smile:

#14

Even though anamolies exist, more often than not, price converges on return.

#15

I have no idea what this means. As written, it makes no sense.

#16

If the returns of two assets are strongly negatively correlated, then their respective price movements should also behave simillarly.

#17

Why?

I just went to Yahoo! Finance and grabbed the two highest-volume stocks listed: BAC and RAD. Over the past 60 months, the correlation of their prices is +0.5623 and the correlation of their returns is +0.3109. Over the past 48 months the numbers are +0.7681 and +0.2632, respectively: they’re diverging. Over the past 340 months (nearly the entire history of BAC), they’re -0.0304 and +0.3111, respectively.

Correlation of prices and correlation of returns don’t have anything to do with each other.

#18

Because value is a function of return, and price tracks value.

#19

But correlation of returns doesn’t track value.

I think you misunderstand how correlation works. Look at the example I posted above, for two stocks that were chosen essentially at random.

#20

How is return calculated in this example, capital gain+income on the stock or net income on the IS? R^2?