Interpreting Portfolio Exposure to a Yield Curve with Correlated Risk Factors
Summary
The document considers how to estimate a portfolio’s sensitivity to movements in one yield curve when positions also depend on correlated prices and rates. It suggests starting with assumed volatilities and correlations: shock the target factor, infer corresponding moves in related factors, and revalue the portfolio. The resulting change is a correlation-adjusted exposure estimate.
The response emphasizes that this estimate carries uncertainty because the assumed relationships may not occur as expected. Exposure to a factor that is not directly driving the positions can depend heavily on correlation assumptions, and the realized portfolio impact could differ substantially. PCA does not remove this issue; as a covariance-based statistical method, it also relies on relationships among variables. The discussion is conceptual and does not provide a specific model, data requirements, or empirical test for the currency portfolio in the question.
Key ideas
- Portfolio sensitivity to a single curve can include assumed correlated moves in other risk factors.
- A starting method is to shock the target factor, estimate related factor moves from volatilities and correlations, and revalue the portfolio.
- The resulting exposure is conditional on the assumed relationships among factors.
- PCA also depends on covariance or correlation structure and therefore does not eliminate this uncertainty.
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Full text
# PCA on a portfolio of spot and forward contracts # 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? ## Answer by Attack68 (score 2) https://quant.stackexchange.com/a/45611 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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