Well the issue is you don't have the empirical hedge.

You could do the following ad hoc approach:

1. price butterfly
2. bump curve according to your pca factors
3. reprice butterfly

hedge = (newprice - oldprice)/(bump size)

On Sat, Aug 27, 2011 at 8:40 PM, amit jain <buddyhi@indiatimes.com> wrote:

> Hi everyone,
>
> I want to hedge level and slope of a treasury curve. I found the pca
> loadings using prcomp function of R. I used 2yr, 5yr, 7yr, 10yr and 30yr
> points with 3m data and found the pca loadings. Then i reduced these 5 PC
> factors to just 3 and obtained the new loadings and rotation. Now i am
> unclear on how to use these PCA loadings to come up with hedging ratios for
> level and slope specifically in a butterfly for eg 2yr, 5yr and 7yr curve,
> how do i find the pca weighted risk weightings for the butterfly.  I used
> following code:
>
>  mypca = prcomp(YC, scale = T)
>  print(mypca)
>  summary(mypca)
>  plot(mypca)
>  mypcaX = mypca$x %*% t(mypca$rotation)
>
> where YC has last 3 months of generic rates data.
> Thanks in advance for your help. If you need any more clarification to help
> me better, please let me know i would be happy to provide more details of
> what i did and tried.
>
> Thanks
> Amit
>
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