BAFI6010 · Advanced Investment Management
Risk Budgeting and Risk Allocation
This topic makes the jump from allocating dollars to allocating risk. You learn to decompose total portfolio risk into each asset's marginal contribution to risk (MC_i = w_i × β_i × σ_p, where β_i is the asset's beta against the portfolio), which lets you see that a high dollar weight is not the same as a high risk share. From there it builds risk parity (every asset contributes equal marginal risk, so calm assets get bigger weights) and the risk budget — spreading one total risk allowance across the strategic allocation, tactical tilts and manager selection, in both volatility and tracking-error space. It is examinable in the closed-book mid-semester test and the final, usually as a short calculation plus a discussion.
What this chapter covers
- 011. Why go beyond mean-variance — MV needs fragile return and correlation forecasts and ignores skew and fat tails; risk-based allocation works from the covariance structure alone
- 022. Marginal contribution to risk (MCR) — MC_i = w_i × β_i × σ_p, with β_i = Cov(i,P)/Var(P) measured against the whole portfolio, not stand-alone volatility
- 033. Percentage risk contributions — divide each MC by total risk to get shares that must sum to 100%; the built-in checksum
- 044. The 6-step recipe — build a hypothetical portfolio, form the covariance matrix, screen for positive Cov(i,P), compute betas, then marginal contributions and target weights
- 055. Risk parity — equalise marginal risk so higher-volatility assets get smaller dollar weights and calmer assets get larger ones (the opposite of cap-weighting)
- 066. Risk-parity weights from betas — inverse-beta weighting (w_i proportional to 1/β_i) for a simple long-only sleeve
- 077. Risk budgeting — parcel one total risk budget across SAA, TAA and manager selection, benchmarked to a passive portfolio as a tracking-error range
- 088. Tracking-error space — the same machinery on active weights (fund minus benchmark) for relative-risk budgeting, plus quantitative (max information ratio) vs practical budget-setting
Percentage risk contributions of a three-sleeve portfolio
- +1Assemble portfolio variance as the weighted sum of the covariances-with-the-portfolio: sigma_p^2 = sum w_i * Cov(i,P) = 0.40(0.009) + 0.35(0.004) + 0.25(0.0015) = 0.0036 + 0.0014 + 0.000375 = 0.005375.
- +1Risk share of A = w_A * Cov(A,P) / sigma_p^2 = 0.0036 / 0.005375 = 67.0%.
- +1Risk share of B = 0.0014 / 0.005375 = 26.0% and C = 0.000375 / 0.005375 = 7.0%; the three shares sum to 100%, which is your checksum.
- +1Portfolio volatility = sqrt(0.005375) = 7.33%.
- +1Verdict: this is not risk parity. Sleeve A holds only 40% of the dollars but 67% of the risk, while C holds 25% of the dollars and just 7% of the risk. To move toward parity you would trim A and lift C until each contributes about one third.
Key terms
- Marginal contribution to risk (MCR)
- Each asset's share of total portfolio risk, MC_i = w_i × β_i × σ_p, where β_i is the asset's beta against the portfolio; the marginal contributions add back exactly to total portfolio risk σ_p.
- Portfolio beta (β against P)
- An asset's sensitivity to the whole portfolio, β_i = Cov(i,P)/Var(P). It is the key input to MCR — using the asset's stand-alone volatility instead of this beta is the most common mistake.
- Percentage risk contribution
- MC_i divided by total risk, equal to w_i × Cov(i,P) / σ_p^2. These shares sum to 100%, giving a built-in checksum on any risk-decomposition answer.
- Risk parity
- A weighting scheme in which every asset contributes equal marginal risk. Because volatile assets supply more risk per dollar, they receive smaller dollar weights and calmer assets receive larger ones — the opposite of cap-weighting.
- Risk budget
- The total amount of risk a portfolio is allowed to take, parcelled out across the strategic asset allocation, tactical tilts and manager selection; usually benchmarked to a passive portfolio and expressed as a total tracking-error range.
- Active weight
- Fund weight minus benchmark weight for an asset. Feeding active weights (instead of total weights) into the MCR machinery gives the tracking-error, or relative-risk, version of risk allocation.
- Closet indexing
- An 'active' fund whose tracking error is so low that it effectively delivers the benchmark while charging active fees; a quantitative risk budget imposes a lower tracking-error limit to prevent it.
- Risk decomposition
- Splitting total portfolio risk into per-asset contributions (for volatility or for tracking error) so you can see the sources of risk; it gives an average contribution, which is why portfolios are also stress-tested.
Risk Budgeting and Risk Allocation FAQ
What is the difference between a dollar allocation and a risk allocation?
A dollar (or cap) allocation decides how much money each asset gets; a risk allocation decides how much of the portfolio's total risk each asset is allowed to consume. They can look very different — an asset with a moderate dollar weight can supply most of the risk if it is volatile and co-moves with the book, which is exactly the gap risk budgeting exists to manage.
Why do we use beta against the portfolio instead of the asset's own volatility?
Because an asset's risk contribution depends on how it moves with the whole portfolio, not on its solo volatility. Marginal contribution is w_i × β_i × σ_p with β_i = Cov(i,P)/Var(P); an asset that diversifies the book contributes far less risk than a same-volatility asset that amplifies it. Computing w_i × σ_i instead is a classic error.
Does risk parity give the most volatile asset the biggest weight?
No — it is the reverse. Risk parity equalises marginal risk, so a volatile asset (which supplies a lot of risk per dollar) gets a smaller dollar weight, and calmer, lower-volatility assets get larger weights. If your volatile sleeve ends up with the biggest weight, you have inverted the rule.
What happens if an asset has negative covariance with the base portfolio?
Under a long-only, no-leverage build it then has a negative marginal risk contribution, so you cannot equalise positive risk shares with it and the simple 1/β weights can go negative. The fix is to raise that asset's weight and rebuild the base portfolio, repeating until every covariance-with-the-portfolio is positive, before applying parity.
How is this topic assessed in BAFI 6010?
It appears in both the closed-book mid-semester test (Topics 1-5) and the final exam (all topics except Topic 6). Expect a short calculation — percentage risk contributions or risk-parity weights — plus a discussion point such as why a high dollar weight is not a high risk share, or how the risk budget is set and benchmarked.
Is this page official or affiliated with the University of Adelaide?
No. This is an independent AskSia study resource made to help students revise. It is not produced, endorsed by, or affiliated with the University of Adelaide, and it is not a substitute for the official course materials and Canvas announcements.
Exam move
Anchor everything on one identity: MC_i = w_i × β_i × σ_p with β_i = Cov(i,P)/Var(P), and the fact that the pieces sum to total risk so percentage contributions sum to 100%. Because both the mid-semester test and the final are closed-book with no formula sheet, drill that formula, the 6-step recipe and the inverse-beta parity rule until you can reproduce them from a blank page. Practise the two calculation shapes — turning weights and covariances-with-the-portfolio into risk shares, and turning betas into risk-parity weights — and always finish with the checksum (shares total 100%) and one sentence of interpretation (concentrated vs parity, or which sleeve to trim). Keep the two versions straight: volatility budgeting uses total weights (absolute risk); tracking-error budgeting uses active weights (relative risk). Finally, rehearse the discussion half — why risk-based allocation sidesteps fragile return forecasts, why risk parity overweights calm assets, and how a total risk budget is split across SAA, TAA and manager selection and benchmarked to a passive book — since the final rewards applied reasoning as much as arithmetic.
