Equal Weighted SD vs Asset Weighted SD

CFA Level III Portfolio Management
#1

Could anyone explain difference bt Equal Weighted SD vs Asset Weighted SD? In which scenario one would be greater than the other?I am confused? Value of equal weighted sd will always be higher than sset weighted sd?I wanted to know the reasoning?

#2

What is SD? Standard Deviation?

#3

South Dakota.

(That’s the secret CFA Institute code name for standard deviation.)

#4
\sigma =\sqrt{\frac{\sum_{i=1}^nw_i\left(X_i - \mu_x\right)^2}{\sum_{i=1}^nw_i}}

If the w_i = k (usually 1), then it’s an equal-weighted standard deviation. If w_i = asset\ value_i, then it’s an asset-weighted standard deviation.

When the weights on the larger deviations are larger, the result is larger.

Not always.

#5

Assuming SD = standard deviation and not spread duration.

SD = standard deviation = volatility.

Calculation of volatility requires weight of portfolios in the composite along with variance-covariance matrix. SD should not be computed by simple arithmetic average or asset weighted average.

@Rishi_Gupta - where did you read this? which volume and what page #?

#6

GIPS allows equal-weighted standard deviation for composites.

#7

Thank you!

This is given on page # 331 and # 332 of volume 6.

Regards,