I can pull historical MBS prices from TradeWeb and use a cholesky decomposition matrix to simulate correlated random prices.
However, I am interested in doing this using a forward looking metric: duration off Bloomberg.
Let's say I have two assets, [x] with a 2 duration and [y] with a 1 duration.
This implied the formula for line between these two securities' price movements is [x] = 2/1 [y] ... which implies the beta is 2. For the inverse, the beta would be 1.
Where I am getting hung up is that the durations seem to imply a perfect correlation between the two assets. beta_xy = 1 / beta_yx. This situation only holds if the correlation is exactly 1.
So what's the preferred approach? Even if I use a whole loan model with a fancy yield curve simulator, I'm still modeling using the same underlier... The resulting price strips will appear "over correlated" and I miss out on the supply/demand mechanics that could account for variances "within" the durations.
I sort of feel like I'm missing something...