Leptokurtic vs Platykurtic

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Onestar

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Could someone please explain the difference between a Leptokurtic and Platykurtic distribution in relation to returns?
Why does a Leptokurtic distribution have “more frequent extremely large deviations from the mean than a nomal distribution?”
I would have thought a Platykurtic distribution would have extremely large deviations from the mean as the observations are more spread out over a larger area than a Leptokurtic distribution?
Huge appreciation for anyone that can shed light on this!
 
Kurtosis is a measure of “peakedness”, that is, a the curve is placed higher relative to the normal distribution if it has more kurtosis. This means that the curve’s tails at both sides are fatter as a result of it being higher. A leptokurtic distribution has a higher level kurtosis than a platykurtic distribution so its tails are fatter, hence implying that it has more extreme deviations from the mean.
 
ayousaf wrote:Kurtosis is a measure of “peakedness”, that is, a the curve is placed higher relative to the normal distribution if it has more kurtosis. This means that the curve’s tails at both sides are fatter as a result of it being higher.
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This is somewhat inaccurate: it isn’t possible for the entire curve to be higher than a normal distribution because the area under each curve (and above the x-axis) has to be 1.
A leptokurtic distribution is higher than a normal distribution near the center (say from -1σ to +1σ), and at the ends (say, below -3σ and above +3σ), but in the midranges (between -3σ and -1σ, and between +1σ and +3σ) the leptokurtic distribution is lower than a normal distribution.
Thus, in a leptokurtic distribution, you are more likely to see values near the mean or at the extremes, but less likely to see values moderately above or below the mean (compared to a normal distribution).
I wrote an article on kurtosis that may help (it has pictures): http://financialexamhelp123.com/kurtosis/.
 
Thanks S2000! The article and your explanation above really helps!
So from an investor’s perspective, generally which distribution would be preferred if there was excess kurtosis?
Would it be a Platykurtic distribution as the values are more moderately spread out than a Leptokurtic distribution?
 
Onestar wrote:Thanks S2000! The article and your explanation above really helps!
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My pleasure. I’m happy it helped.
Onestar wrote:So from an investor’s perspective, generally which distribution would be preferred if there was excess kurtosis?
Would it be a Platykurtic distribution as the values are more moderately spread out than a Leptokurtic distribution?
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A lot would depend on the skewness of the distribution. If the returns are positively skewed (generally rare), leptokurtosis is probably preferable; if the returns are negatively skewed (more common), platykurtosis is probably preferable. When the distribution is not skewed (or only mildly skewed), it depends more on the risk tolerance of the investor. I would require a higher risk premium for higher kurtosis.
 
lepto = fatter tails = more extreme values = more risks
platy = the other way around.
btw, where did you find this question?
 
S2000magician wrote:
A leptokurtic distribution is higher than a normal distribution near the center (say from -1σ to +1σ), and at the ends (say, below -3σ and above +3σ), but in the midranges (between -3σ and -1σ, and between +1σ and +3σ) the leptokurtic distribution is lower than a normal distribution.
Click to expand...
So when it refers to “fatter tails”, this is referring to the very extreme deviations that are not visible in most graphs of a leptokurtic distribution? I’ve been having difficulty with this concept, because in most visualizations of a leptokurtic, normal, and platykurtic distributions, it looks like the platykurtic has the fattest tails, and then normal, and then leptokurtic. Maybe I am misunderstanding what “fat tails” means. Thanks for any help you can provide!
 
schneid wrote:
S2000magician wrote:A leptokurtic distribution is higher than a normal distribution near the center (say from -1σ to +1σ), and at the ends (say, below -3σ and above +3σ), but in the midranges (between -3σ and -1σ, and between +1σ and +3σ) the leptokurtic distribution is lower than a normal distribution.
Click to expand...
So when it refers to “fatter tails”, this is referring to the very extreme deviations that are not visible in most graphs of a leptokurtic distribution? I’ve been having difficulty with this concept, because in most visualizations of a leptokurtic, normal, and platykurtic distributions, it looks like the platykurtic has the fattest tails, and then normal, and then leptokurtic. Maybe I am misunderstanding what “fat tails” means. Thanks for any help you can provide!
Click to expand...
You’re correct.
When you get to the tails, the probabilities are so low that it’s hard to see which distribution has the higher (or lower) probabilities.
Leptokurtic distributions generally have higher probabilities in the tails; platykurtic distributions generally have lower probabilities in the tails.
 
S2000magician wrote:
schneid wrote:
S2000magician wrote:A leptokurtic distribution is higher than a normal distribution near the center (say from -1σ to +1σ), and at the ends (say, below -3σ and above +3σ), but in the midranges (between -3σ and -1σ, and between +1σ and +3σ) the leptokurtic distribution is lower than a normal distribution.
Click to expand...
So when it refers to “fatter tails”, this is referring to the very extreme deviations that are not visible in most graphs of a leptokurtic distribution? I’ve been having difficulty with this concept, because in most visualizations of a leptokurtic, normal, and platykurtic distributions, it looks like the platykurtic has the fattest tails, and then normal, and then leptokurtic. Maybe I am misunderstanding what “fat tails” means. Thanks for any help you can provide!
Click to expand...
You’re correct.
When you get to the tails, the probabilities are so low that it’s hard to see which distribution has the higher (or lower) probabilities.
Leptokurtic distributions generally have higher probabilities in the tails; platykurtic distributions generally have lower probabilities in the tails.
Click to expand...
Thank you.
 
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