hard · FRM Part 2 Risk & Investment Management
An institutional allocator uses a risk-budgeting (equal risk contribution) approach for a portfolio of three asset classes. Two assets, X and Y, have identical standalone volatilities and identical marginal contributions to risk at the current weights, but X has a HIGHER correlation with the rest of the portfolio than Y. The allocator rebalances toward true equal risk contribution (ERC).
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?
- 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
- X's weight must fall and Y's must rise because the higher-correlation asset has a larger marginal risk contribution that volatility-weighting cannot see
- Both weights must converge to equal values because ERC and equal-volatility-weighting coincide whenever standalone volatilities are identical
- Y's weight must fall because its lower correlation gives it a diversification benefit that ERC penalizes to keep total contributions equal across assets
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