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Compute the opposed exposures
Assume exact negative correlation, standard deviations 20% and 10%, and capital weights 40% and 60%. Weighted exposures are 0.08 and 0.06. Their difference is 0.02, so variance is 0.0004 and standard deviation is 2%.
Check covariance with the portfolio
Cross-asset covariance is −0.02. Cov(A,P)=0.4×0.04+0.6×(−0.02)=0.004. Cov(B,P)=0.4×(−0.02)+0.6×0.01=−0.002. Positive holdings therefore do not guarantee positive covariance with the portfolio.
Divide and apply weights
| Asset | Marginal contribution | Weighted contribution | Risk share |
|---|---|---|---|
| A | 0.2 | 0.08 = 8 percentage points | 400% |
| B | −0.1 | −0.06 = −6 percentage points | −300% |
| Sum | Not an additive total | 0.02 = 2% | 100% |
Keep a signed display
The shares sum to 100%, but they do not resemble positive capital percentages. A signed table or bar representation preserves the offset. Taking absolute values would report 14 percentage points, a different quantity. Exact negative correlation is a stipulated teaching assumption.