- Strange object on 737-800 exterior?
- Requirements for complex and high-performance endorsement?
- How come nobody survived Air Moorea 1121, yet other people have survived crashes from altitudes more than 90x higher?
- Why is the Eurofighters nose gear door shorter than the bay?
- What does “v'ha” mean?
- “New TOR Circuit for this Site” changes all tabs IP addreses
- How to completly remove influence of bone to mesh
- Motion Blur at different frames
- Trackpad with Surface Book cannot navigate 3D View
- Tracking scene moves markers from points in 3D view
- Smooth transition between distorted and undistorted result of Movie Distortion node
- How do you access the ruler?
- Object not showing up in full render
- How to say “pay exact amount of money”
- How to use the word 'suitable' properly?
- why the answer in this question is “(A)”?
- What's the difference between drug and medication?
- Which auxiliary verb or copular to refer to uncountable nouns?
- Is there difference between bedding, bedclothes and linen or are consider synonym?
- What would you call someone who sneaks into and stays in places where they have to be signed up, e.g. classes/country clubs

# Normalize Returns in PCA Hedging?

Lets say I want to form a portfolio of $N$ correlated instruments that minimizes the variance of my daily PnL, given by

$$

PnL = \sum_{i=1}^N h_i \Delta S_i

$$

where $h_i$ are the number of units of instrument $i$ and $\Delta S_i$ is the daily difference in price.

To minimize the variance, I find the covariance matrix of $\{\Delta S_i\}_i$ and perform PCA on this covariance matrix. I then take the eigenvector with smallest eigenvalue and use the entries as my hedging ratios.

My question is, if the daily difference in instruments are vastly different, say on average $\Delta S_1 = \$10$ while $\Delta S_2 = \$0.1$, does it make sense to normalize these before performing PCA?

I an inclined not to because they are in the same units, and I think it makes sense for instruments with a larger variance to contribute more; however, I have always thought I needed to normalize the data before performing PCA, so I am hesitant to do otherwise now.