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Inspect the complete assumed matrix
This original counterexample gives all three assets variance 1 and all three pair correlations −0.8. Each pair label lies between −1 and 1, but those labels cannot all describe one joint covariance record.
Display the assumptions
| A | B | C | |
|---|---|---|---|
| A | 1 | −0.8 | −0.8 |
| B | −0.8 | 1 | −0.8 |
| C | −0.8 | −0.8 | 1 |
Apply an equal-weight test
With weights 1/3 each, the three diagonal terms sum to 1/3. Six off-diagonal terms contribute 6×(1/9)×(−0.8)=−8/15. Total variance is −1/5, or −0.2. Variance cannot be negative, so the supplied joint model is incoherent.
Use the relevant matrix requirement
A valid covariance matrix must be symmetric and positive semidefinite: every weight vector must have nonnegative quadratic variance. The vector of equal weights already supplies a counterexample here. Testing one vector that passes would not establish the whole requirement.
Respect the calculator’s size
The two-asset tool validates a pair’s domain; it does not validate a larger matrix. Investigate estimation dates, missing-data methods and the source of any inconsistent entries before using a multi-asset model.