Explain how risk budgeting is used when building a portfolio
The idea
Risk budgeting sets how much risk the portfolio may take in total, usually as a target active risk, and allocates it across sources so that each source's share of risk matches the reward expected from it. A position's contribution to portfolio variance is its weight × its covariance with the portfolio. These contributions sum to total variance, and contributions to active risk are found the same way using active weights. The portfolio is efficiently budgeted when the ratio of marginal expected alpha to marginal contribution to risk is equal across positions. The trap is budgeting by weight rather than by risk contribution: a small holding in a volatile, highly correlated stock can use more risk than a larger defensive one.
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