hard · FRM Part 2 Risk & Investment Management

Relative to the current allocation, what must happen to the weights of X and Y, and why is a naive 'equal-volatility-weighting' heuristic insufficient here?

1. Because marginal risk contributions are currently equal, equalizing TOTAL risk contributions requires lowering whichever asset has the larger weight; volatility-weighting ignores covariance and so generally fails to equalize the covariance-inclusive contributions
2. X's weight must fall while Y's must rise, because the higher-correlation asset X carries a structurally larger marginal risk contribution to total portfolio variance that a simple volatility-weighting heuristic is mathematically unable to detect at all.
3. Both weights must converge to an identical value because ERC and naive equal-volatility-weighting always coincide whenever the two assets' standalone volatilities are equal, regardless of how each is correlated with the rest of the fund's total portfolio holdings.
4. Y's weight must fall because its comparatively lower correlation with the rest of the book gives it a diversification benefit that true ERC actively penalizes in order to keep total risk contributions equal across all three asset classes held in the fund's book overall.

Sign up free to see the explanation and track your rank →