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.


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