# PCA on a portfolio of spot and forward contracts

I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l.

Would it be just a matter of me regression historical p/l over the spot, forward points, 1-year govi yield, convexity (assuming historical convexity data exists) and perhaps a 10-1 gov spread via a PCA process? or given that forwards are based on the interest rate differentials, do I need to bring in foreign currencies curves and their basis to the equation too?

You have a portfolio, $$P$$, filled with many positions, which are specifically dependent upon various asset price movements, say $$X,Y and Z$$. These price movements are random variables, but they may contain some inherent correlations. Suppose $$X$$ and $$Y$$ are highly correlated but $$Z$$ has small correlation to both $$X$$ and $$Y$$.

Now by asking "what is the exposure of my portfolio to just the AUD curve" you are effectively asking the analogous question what is the exposure of $$P$$ to just $$Z$$.

This is a difficult question.

What you might do as a starting point is assume some fixed correlations and volatilities and then vary $$Z$$. If $$Z$$ increases by 1, $$X$$ and $$Y$$ are assumed to increase by 0.2, and 0.4 respectively due to their assumed volatilities. Now revalue your portfolio. This is your risk to $$Z$$, correlation adjusted for $$X$$ and $$Y$$.

Say you get a value, i.e. 1000 USD exposure, there might be a high confidence in that value (eg. if you portfolio were exposed solely to the price of $$Z$$ then it would be exact), but it may have inherent uncertainty (if you portfolio is exposed solely to the price of $$X$$ then it depends entirely on the assumption of the correlation between $$X$$ and $$Z$$, and $$X$$'s volatility). If the correlation is not realised your exposure might be larger, zero or the negative of what you predicted.

Therefore as well as measuring your exposure to $$Z$$ you have a measure of the uncertainty in your measurement, which depends upon the fragility of your assumptions.

Note that PCA is a statistical technique that bases itself on covariance/correlation also so contains the same problem.