{
  "id": "competency:msc-risk--actuarial",
  "code": "CDU-BUS-RSK-900",
  "level": "MSc",
  "name": "MSc Risk & Actuarial",
  "faculty": "Faculty of Commerce, Law and Management",
  "lineage": [
    {
      "institution": "Conquest Designer University",
      "year": 2026,
      "note": "authored from the brief, the IFoA/IAA syllabuses and the Basel framework; no prior institution is claimed"
    }
  ],
  "researchProject": "From a loss distribution to a capital number: value at risk, IRB capital, credibility and the pure premium",
  "description": "The quantities a risk function and an actuarial function sign off: parametric value at risk and expected shortfall, the Basel IRB capital requirement and risk-weighted assets of a corporate exposure, the Bühlmann credibility premium, and the mean, variance and loaded premium of an aggregate loss under the collective risk model.",
  "syllabus": [
    "Market risk: parametric VaR and expected shortfall, horizon scaling, the normal assumption and its limits",
    "Credit risk: PD, LGD, EAD, maturity, asset correlation and the IRB capital formula",
    "Credibility theory: expected process variance, variance of hypothetical means, the Bühlmann factor",
    "Risk models: compound distributions, the collective risk model, premium principles"
  ],
  "reference": {
    "Parametric VaR": "V·(z_c·σ·√h − μ·h)",
    "Normal ES": "V·(σ·√h·φ(z_c) ÷ (1 − c) − μ·h)",
    "IRB K (corporate)": "[LGD·N((1−R)^−½·G(PD) + (R/(1−R))^½·G(0.999)) − PD·LGD]·(1 + (M − 2.5)·b) ÷ (1 − 1.5·b) (Basel II ¶272)",
    "Asset correlation": "R = 0.12·(1 − e^(−50·PD))/(1 − e^(−50)) + 0.24·[1 − (1 − e^(−50·PD))/(1 − e^(−50))]; b = (0.11852 − 0.05478·ln PD)²",
    "Bühlmann credibility": "Z = n ÷ (n + k), k = EPV ÷ VHM; premium = Z·X̄ + (1 − Z)·μ",
    "Collective risk model": "E[S] = E[N]·E[X]; Var[S] = E[N]·Var[X] + Var[N]·E[X]²"
  },
  "role": "You are a chief risk officer and actuary explaining a capital or premium number to a board risk committee. State the model and its key assumption, show the numbers, and say what would make the answer wrong.",
  "feeUsd": 1,
  "version": "1.0.0",
  "qualification": {
    "award": "MSc",
    "nqfLevel": 9,
    "qualificationType": "Master's Degree (HEQSF qualification type 9a)",
    "totalCredits": 180,
    "minCreditsAtExitLevel": 120,
    "iscedFields": [
      "041",
      "054"
    ],
    "standards": [
      "Institute and Faculty of Actuaries curriculum — CS2 Risk Modelling and Survival Analysis (credibility, loss distributions)",
      "International Actuarial Association Education Syllabus",
      "Basel Committee on Banking Supervision (2006) International Convergence of Capital Measurement and Capital Standards (Basel II) ¶272, ¶285",
      "BCBS (2019) Minimum capital requirements for market risk — expected shortfall at 97.5%"
    ],
    "registration": "not registered"
  },
  "modules": [
    {
      "code": "CDU-BUS-RSK-900-901",
      "title": "Coursework — the executable units",
      "nqfLevel": 9,
      "credits": 60,
      "prerequisites": [],
      "coRequisites": [],
      "outcomes": [
        "answer every unit of the qualification against its published reference, with the working shown"
      ],
      "assessment": {
        "formative": [
          "worked examples re-run against the published reference",
          "seeded practice scenarios, deterministic per (pan, unit, attempt)"
        ],
        "summative": "every unit passed once through the seeded assessment (the seeded assessment room)",
        "passMark": 50,
        "subminimum": 40,
        "moderation": "internally assessed by the unit itself — its reference implementation is the marker; the working is published so anyone can re-run the mark (D-13.1 — no model marks anything)"
      },
      "unitIds": [
        "parametric_var_es",
        "basel_irb_capital",
        "buhlmann_credibility",
        "collective_risk_premium"
      ],
      "notionalHours": 600
    },
    {
      "code": "CDU-BUS-RSK-900-902",
      "title": "Research report",
      "nqfLevel": 9,
      "credits": 120,
      "prerequisites": [
        "CDU-BUS-RSK-900-901"
      ],
      "coRequisites": [],
      "outcomes": [
        "From a loss distribution to a capital number: value at risk, IRB capital, credibility and the pure premium"
      ],
      "assessment": {
        "formative": [
          "worked examples re-run against the published reference",
          "seeded practice scenarios, deterministic per (pan, unit, attempt)"
        ],
        "summative": "the research report, assessed against the qualification’s published reference block",
        "passMark": 50,
        "subminimum": 40,
        "moderation": "internally assessed by the unit itself — its reference implementation is the marker; the working is published so anyone can re-run the mark (D-13.1 — no model marks anything)"
      },
      "unitIds": [],
      "notionalHours": 1200
    }
  ],
  "units": [
    {
      "id": "parametric_var_es",
      "name": "Parametric value at risk and expected shortfall",
      "answers": "Under a normal model, what loss is exceeded only with probability 1 − c over the horizon, and what is the average loss beyond it?",
      "example": {
        "portfolioValue": 10000000,
        "dailyVolatility": 0.012,
        "horizonDays": 10,
        "confidence": 0.99,
        "dailyMeanReturn": 0
      },
      "reference": "J.P. Morgan/Reuters RiskMetrics Technical Document (1996): parametric VaR, square-root-of-time scaling; BCBS (2019) market risk framework: expected shortfall at 97.5%",
      "signature": {
        "input": {
          "portfolioValue": {
            "type": "number",
            "describe": "Current portfolio value",
            "min": 0.01
          },
          "dailyVolatility": {
            "type": "number",
            "describe": "Standard deviation of daily returns",
            "min": 0.000001,
            "max": 1
          },
          "horizonDays": {
            "type": "number",
            "describe": "Holding period in days",
            "min": 1,
            "max": 250
          },
          "confidence": {
            "type": "number",
            "describe": "Confidence level, 0.9–0.999",
            "min": 0.9,
            "max": 0.999
          },
          "dailyMeanReturn": {
            "type": "number",
            "describe": "Expected daily return",
            "min": -0.1,
            "max": 0.1,
            "default": 0
          }
        },
        "output": {
          "z": {
            "type": "number",
            "describe": "Standard normal quantile at the confidence level"
          },
          "valueAtRisk": {
            "type": "number",
            "describe": "VaR over the horizon"
          },
          "expectedShortfall": {
            "type": "number",
            "describe": "ES over the horizon"
          }
        }
      }
    },
    {
      "id": "basel_irb_capital",
      "name": "IRB capital for a corporate exposure",
      "answers": "What capital, risk-weighted assets and expected loss does the Basel IRB formula assign to this corporate exposure?",
      "example": {
        "pd": 0.01,
        "lgd": 0.45,
        "ead": 1000000,
        "maturity": 2.5
      },
      "reference": "Basel II (BCBS 2006) ¶272 (corporate risk-weight function), ¶285 (PD floor 0.03%); RWA = K × 12.5 × EAD",
      "signature": {
        "input": {
          "pd": {
            "type": "number",
            "describe": "One-year probability of default, 0–1",
            "min": 0,
            "max": 0.9999
          },
          "lgd": {
            "type": "number",
            "describe": "Loss given default, 0–1",
            "min": 0,
            "max": 1
          },
          "ead": {
            "type": "number",
            "describe": "Exposure at default",
            "min": 0
          },
          "maturity": {
            "type": "number",
            "describe": "Effective maturity in years, 1–5",
            "min": 1,
            "max": 5
          }
        },
        "output": {
          "pdUsed": {
            "type": "number",
            "describe": "PD after the 0.03% floor"
          },
          "correlation": {
            "type": "number",
            "describe": "Asset correlation R"
          },
          "capitalRequirement": {
            "type": "number",
            "describe": "K, per unit of EAD"
          },
          "riskWeight": {
            "type": "number",
            "describe": "K × 12.5"
          },
          "riskWeightedAssets": {
            "type": "number",
            "describe": "K × 12.5 × EAD"
          },
          "expectedLoss": {
            "type": "number",
            "describe": "PD × LGD × EAD"
          }
        }
      }
    },
    {
      "id": "buhlmann_credibility",
      "name": "Bühlmann credibility premium",
      "answers": "How much weight should this risk’s own experience get against the collective, and what premium results?",
      "example": {
        "observations": 5,
        "sampleMean": 1200,
        "collectiveMean": 1000,
        "expectedProcessVariance": 40000,
        "varianceOfHypotheticalMeans": 10000
      },
      "reference": "Bühlmann, H. (1967) Experience rating and credibility, ASTIN Bulletin 4(3); IFoA CS2 — the Bühlmann model",
      "signature": {
        "input": {
          "observations": {
            "type": "number",
            "describe": "Number of periods (or exposures) of own experience",
            "min": 1
          },
          "sampleMean": {
            "type": "number",
            "describe": "Mean claims of this risk",
            "min": 0
          },
          "collectiveMean": {
            "type": "number",
            "describe": "Mean claims of the collective (μ)",
            "min": 0
          },
          "expectedProcessVariance": {
            "type": "number",
            "describe": "EPV: expected variance within a risk",
            "min": 0
          },
          "varianceOfHypotheticalMeans": {
            "type": "number",
            "describe": "VHM: variance of risk means across the collective",
            "min": 0.000001
          }
        },
        "output": {
          "k": {
            "type": "number",
            "describe": "EPV ÷ VHM"
          },
          "credibilityFactor": {
            "type": "number",
            "describe": "Z = n ÷ (n + k)"
          },
          "credibilityPremium": {
            "type": "number",
            "describe": "Z·X̄ + (1 − Z)·μ"
          }
        }
      }
    },
    {
      "id": "collective_risk_premium",
      "name": "Collective risk model and loaded premium",
      "answers": "What are the mean and spread of aggregate claims, and what premium does the expected-value principle charge?",
      "example": {
        "frequencyMean": 2,
        "frequencyVariance": 2,
        "severityMean": 5000,
        "severityVariance": 4000000,
        "loading": 0.2
      },
      "reference": "Klugman, Panjer & Willmot, Loss Models (compound distributions); IFoA CS2 — the collective risk model; the expected-value premium principle",
      "signature": {
        "input": {
          "frequencyMean": {
            "type": "number",
            "describe": "E[N], expected number of claims",
            "min": 0
          },
          "frequencyVariance": {
            "type": "number",
            "describe": "Var[N] (equal to the mean for Poisson)",
            "min": 0
          },
          "severityMean": {
            "type": "number",
            "describe": "E[X], expected claim size",
            "min": 0
          },
          "severityVariance": {
            "type": "number",
            "describe": "Var[X]",
            "min": 0
          },
          "loading": {
            "type": "number",
            "describe": "Safety loading θ, 0–5",
            "min": 0,
            "max": 5
          }
        },
        "output": {
          "aggregateMean": {
            "type": "number",
            "describe": "E[S]"
          },
          "aggregateVariance": {
            "type": "number",
            "describe": "Var[S]"
          },
          "aggregateSd": {
            "type": "number",
            "describe": "√Var[S]"
          },
          "premium": {
            "type": "number",
            "describe": "(1 + θ)·E[S]"
          }
        }
      }
    }
  ]
}