# Portfolio Risk and Capital Allocation Measure combined exposure and stress dependency assumptions. Use this workbook alongside the course. Write your answers before opening the solutions. Practical work is self-reviewed; scored knowledge checks are in the Academy. ## 1. Aggregation ### Shared factors Aggregate exposure in consistent units before applying risk summaries. Several positions with different labels can reference the same underlying factor. Gross, net and factor-adjusted views answer different questions and should not be conflated. ### Net versus gross Correlation measures association over a specified sample and horizon. It can change during stress. A low historical average does not prove that positions cannot lose together when liquidity or common drivers change. ### Liquidity concentration Nonlinear positions require scenario repricing or suitable sensitivity analysis. Summing notional values alone can miss option convexity or basis exposure. State the approximation and where it may break down. ### Hidden leverage Concentration can arise by instrument, strategy, counterparty, session or data dependency. Diversifying entry rules does not necessarily diversify the failure source if all rely on the same feed or funding channel. ### Worked example Three strategies each hold a long gold position. Separate strategy names do not make the aggregate exposure diversified against a gold decline. The account holds the combined position under the relevant units. ### Independent exercise Build a risk inventory that groups positions by both market factor and operational dependency. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 2. Stress ### Correlation shifts Stress tests define hypothetical changes in prices, volatility, liquidity or funding. They reveal consequences under assumptions, not the maximum conceivable loss. Include why each scenario is relevant to the portfolio. ### Gap scenarios Joint shocks should consider relationships that may change. Assuming the same diversification offsets in every stress can understate combined loss. Examine correlation convergence or simultaneous adverse moves where plausible. ### Margin pressure Liquidity stress includes wider spreads, reduced executable size and delayed exits. A mark-to-model loss can differ from the cost of actually reducing the portfolio. Include the need to transact across all relevant legs. ### Drawdown sequences Funding stress concerns cash requirements and access over time. A position may have a tolerable eventual valuation but an unaffordable interim obligation. Keep cash-flow timing separate from terminal P&L. ### Worked example Two positions usually offset, but a stress scenario makes both lose 50 while exit costs rise to 10 each. Combined scenario loss is 120, not the near-zero value suggested by their normal offset. ### Independent exercise Calculate the combined loss if one position loses 70, the other 30 and each costs 8 to exit. State one limitation of the result. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 3. Allocation ### Risk budgets Allocation should follow the portfolio objective and constraints rather than the highest recent return alone. Expected returns and risk estimates are uncertain. A highly optimized weight can be fragile to small input changes. ### Capacity Risk budgets may be expressed through exposure, volatility, scenario loss or another measure. The measure should match the decision and be consistently calculated. A percentage label without a defined denominator is incomplete. ### Rebalancing costs Marginal contribution asks how changing one position changes a chosen portfolio risk measure. It depends on the model and the rest of the portfolio. It is not an immutable property of the instrument in isolation. ### Capital constraints Rebalancing incurs turnover, costs and possibly tax or contractual consequences. A rule should specify triggers and review rather than rebalance every small estimated change automatically. Compare net benefits with a simpler policy. ### Worked example An optimizer assigns almost all capital to one strategy because its estimated mean is slightly higher. Small changes in the sample reverse the ranking, revealing dependence on noisy estimates. ### Independent exercise Propose constraints or a simpler comparison that would expose this fragility without claiming a universal optimal allocation. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 4. Capital decision committee ### Compare marginal risk contributions Compare marginal contributions under the documented model and under alternative plausible conditions. A decision committee should understand which exposures dominate the result and which estimates are uncertain. ### Stress correlation convergence Stress correlation convergence and shared liquidity problems. Diversification based only on normal-period estimates may fail when positions need to be reduced together. Identify common exit bottlenecks. ### Reserve liquidity for adverse scenarios Reserve liquidity according to a defined planning process that considers obligations and adverse scenarios. The curriculum does not prescribe a universal cash percentage. Document the reason and the circumstances that would trigger review. ### Document allocation decisions and their uncertainty Record allocation decisions, assumptions, dissenting evidence and review dates. A later outcome should be evaluated against what was known at the time, while still allowing the policy to change when its assumptions fail. ### Worked example A portfolio appears diversified by asset but all positions depend on one provider and one funding account. A provider outage can affect every exit simultaneously despite different market exposures. ### Independent exercise Write a committee note separating market diversification from operational concentration and propose a testable mitigation review. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## Course project Produce a scenario-based portfolio risk dossier. ### Self-review rubric - Concepts and reasoning: 25% - Calculations, data and evidence: 30% - Process and risk controls: 25% - Limitations and communication: 20% Record one correction and one next practice task. This rubric is not automatically graded. ## Worked solutions ### Exercise 1 List quantities, multipliers, currencies and direction, then identify shared underlying drivers, counterparties and data or execution services. Keep gross and net measures explicit and note nonlinear or uncertain relationships. ### Exercise 2 The scenario loss is 70+30+8+8 = 116. It is conditional on the assumed shocks and exit costs, not a guaranteed bound; worse liquidity or different joint movement could produce another result. ### Exercise 3 Compare capped or equal-weight baselines, perturb inputs, include turnover costs and report the range of outcomes. The appropriate constraint depends on objectives; stability analysis informs rather than guarantees a weight choice. ### Exercise 4 Identify shared dependencies, describe the outage scenario and assess feasible contingency arrangements. Record what has actually been tested; a second login or an untested provider relationship is not proof of recoverability. ## Further reading - https://www.investor.gov/introduction-investing/getting-started/asset-allocation - https://www.itl.nist.gov/div898/handbook/