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?
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.
If A were $500 million and B $100 million, the asset-weighted standard deviation would be:
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.
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!