can someone tell me in what situation the equal-weighted standard deviation will be greater or smaller than asset-weighted standard deviation? I know we don’t need to calculate it, buy how are we calculating these two?
Greater when the smaller positions have higher volatility and the larger positions have lower volatility; lower otherwise.
asset-weighted standard deviation means those with greater asset value will have higher weight when calculating the standard deviation?
It does.
I still don’t get it
Like I did a mock where we were asked to determine if the asset-weighted standard deviation was greater than the equal weighted standard deviation and I got it wrong. I don’t think I even understood your above statement
Suppose that you have two portfolios in the composite: A & B.
A is valued at $100 million and has a standard deviation of returns of 10%.
B is valued at $500 million and had a standard deviation of returns of 6%.
For simplicity, assume that the correlation of returns is zero. Note that that gives us a good diversification benefit.
Asset-weighted:
\sigma_{composite} = \sqrt{\left(\frac{100}{600}\right)^2\left(10\%\right)^2 + \left(\frac{500}{600}\right)^2\left(6\%\right)^2} = 5.27\%
Equal-weighted:
\sigma_{composite} = \sqrt{\left(\frac{1}{2}\right)^2\left(10\%\right)^2 + \left(\frac{1}{2}\right)^2\left(6\%\right)^2} = 5.83\%
If A were $500 million and B $100 million, the asset-weighted standard deviation would be:
\sigma_{composite} = \sqrt{\left(\frac{500}{600}\right)^2\left(10\%\right)^2 + \left(\frac{100}{600}\right)^2\left(6\%\right)^2} = 8.39\%
When the larger portfolio has the smaller standard deviation, asset-weighted gives a smaller composite standard deviation than equal-weighted.
In short, asset-weighted biases the composite standard deviation toward the standard deviation of the larger portfolio.
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Trick is to see the distribution of asset values across the data and corresponding deviation.
ok i think I needed to visually see this. Thank you! 