Concept of Skewness (Chap 3. Basic Statistics)

[Amirali Tejani]

Hello,

I was going through Miller Chapter 3 - Basic Statistics. In Skewness Topic, Miller mentioned that Skewness is important because investors might have different take on investment with same mean, same Standard Deviations but different skewness. He further states that investment with Negative skewness is generally considered more risky.

Had a hard time conceptualizing why investment with negative skew would be considered more risky than its counterpart investment with positive skew??

Any idea?? Appreciate any help

Thanks,

 

[brian.field]

An investment with negative skew would suggest that losses are more likely than gains..... Make sense? If an investor is considering two investments, 1) with skewness = 0 and 2) with skewness < 0.

All else equal, the second investment would be less attractive since, compared to the first, it exhibits higher likelihood for losses, and consequently, lower likelihood for positive returns, than the first investment.

Brian

 

[brian.field]

An investment with positive skew suggests that positive returns are more likely than negative returns, so clearly, and investment with positive skew would be preferable to an investment with negative skew, ceteris paribus.

 

[ShaktiRathore]

Yes Brian yes a negative skew means more chance of losses for an investment everything else equal.
Skew = summation(x-mean)^3/vol^3 a negative value would suggest more deviation (x-mean)of x valuess on the left side of the mean as compared to the right side. If we assume x values are equidistant from one another this implies more of the x values shall lie on the left side of the mean as compared to the right side so Brians conclusion that losses are more likelier than gains hence investment is inferior with negative skew than more positive one. If you also consider two possibilities of return x1 and x2 for two investments A and B Skew(A)<skew(B)then x1 is more negative for A as compared to B or the magnitude of loss for A is more than B hence Var(A)>Var(B) hence A with more negative skew is more risky than B.
Thank

 

[Amirali Tejani]

Thanks Shakti and Brian. Makes sense