CFA textbook says positively skewed preferred. Why?

[jiminssy]

I am studying for a lvl1 of the CFA exam.
One of the chapters deals with normal distributions of returns and goes on to discuss the skewness and I have a few questions about it.
The textbook says in a positively skewed returns:
- mode - investors are more attracted because the mean return falls above the median.
Here is an image of positively skewed distribution from wikipedia.
http://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_media...
I don’t understand how the mean is bigger than mode and media.
I don’t understand why the investors are more attracted to positively skewed distribution in general.
Could somebody help me understand these things?

 

[pdub]

that graph is ugly, but it does show you the difference
the mean is the average…and a graph is just showing you the distribution of results..if it is positively skewed, then that means there are larger positive results than negative results…if u have larger positive results it pulls the graph to the right…hence, positive skew
..if you were investing in something would you want to invest in something that has a higher probability of giving you high returns, a high probability if giving you low returns, or an equal probability of giving you either?
just remember the mean part..if its positive skew its pulling the average to the right..if its negative skew its dragging the average to the left
then just remember its alphabetical.. so either mode, median, mean or mean, median, mode

 

[ohai]

Imagine this distribution: {1, 1, 2, 100, 10000000}. Mode = 1. Median = 2. Mean = something very large. Ta da!

 

[simply_put7]

The following is a better picture:
http://billkosloskymd.typepad.com/lexicillin_qd/2007/09/mean-vs-median-.html
Remember: Positively skewed tails point toward the positive end of the graph heading toward positive infinity.
Negatively skewed tails point toward the negative end of the graph, heading toward negative
infinity, (in most cases 0).
Because neither positively skewed or negatively skewed have a normal distribution (bell curve), their mean, median and modes will not have a central tendancy (all fall in the middle of the bell).
For positively skewed the mode (the number that appears most often) will be less than the median (middle number of the data) because there is more data near 0 than there are heading towards positive infinity; and the mean (average) will be greater than the both because the very few data points that are large, will skew the mean to a larger value positive value.
For negatively skewed the mode (the number that appears most often) will be greater than the median (middle number of the data) because there is more data near the higher positive values than low positive values; and the mean (average) will be lower than the both because the very few data points that are large, will skew the mean to a lower (negative) value.

 

[radicaldreamer]

To exaggerate on ohai’s example:
Find the mode, median, and mean of the following distribution:
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1000000000000}
One huge outlier is all you need.

 

[radicaldreamer]

And to answer your second question (why investors would prefer a positively skewed distr.):
Imagine you’re at a casino. There are two games going on, and you can choose to play either game.
The first game has the following possible payouts:
{$1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1}
The second game has the following possible payouts:
{$1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1, $1000000000000} (positively skewed distr.)
Which game would you play, and why?

 

[spaiydz]

Easiest way to remember difference between positvely and negatively skewed distribution:

• Imagine you are a teacher and looking at the test results of your class.
• ‘Skewed’ sounds like ‘Screwed’.
• If class results are postively skewed (heavy on left end), you are positively screwed
• If class results are negatively skewed (heavy on right end), you are negatively screwed

 

[chibwack]

mode is always the peak, and mean is always in the direction of the skew, while median falls somewhere in between the two. Mode is easy to remember as it’s the most frequently occuring data point, so after that just remember the order.