MSc Investment Management

Faculty of Commerce, Law and Management · CDU-BUS-INV-900 · MSc · v1.0.0

How a portfolio’s performance is measured and presented: the time-weighted return from sub-period valuations (GIPS), the Modified Dietz approximation when only flow dates are known, the expected return and risk of a two-asset portfolio with its minimum-variance mix, and the tracking error and information ratio of an active manager.

Lineage

Conquest Designer University, 2026 — authored from the brief, GIPS 2020 and the CFA Institute body of knowledge; no prior institution is claimed

Final research project

Measuring a manager honestly: time-weighting, the Dietz approximation and the information ratio

Syllabus

Performance measurement: sub-period returns, geometric linking, annualisation rules (GIPS 2020)
Approximations: the Modified Dietz return and its day-weighted flows
Portfolio construction: two-asset mean and variance, correlation, the minimum-variance portfolio
Active management: active return, tracking error, information ratio, annualisation

Reference

Time-weighted return: Π (1 + r_i) − 1, r_i = V_i ÷ (V_(i−1) + CF_(i−1)) − 1 with a valuation at each external flow
Modified Dietz: (EMV − BMV − ΣCF) ÷ (BMV + Σ w_i·CF_i), w_i = fraction of the period remaining after the flow
Two-asset variance: w²σA² + (1−w)²σB² + 2w(1−w)ρσAσB
Information ratio: mean active return ÷ tracking error (sample standard deviation of active returns)
Annualisation: GIPS: returns for periods of less than a year must not be annualised

Units

Time-weighted return (GIPS) · Modified Dietz return · Two-asset portfolio risk and return · Tracking error and information ratio

Role when narrated: You are an investment performance analyst presenting results to a trustee board. Say which method was used and why, show the numbers, and say what the number does and does not tell them about skill.

Time-weighted return (GIPS) · time_weighted_return

Try with the example

What is the time-weighted return across these sub-periods, removing the effect of the client’s own flows?

Reference: GIPS for Firms (2020): time-weighted returns with the portfolio valued at each large external cash flow; sub-period returns geometrically linked; no annualisation under one year

Returns

subPeriodReturns: Each sub-period return (6 dp)
twr: Linked time-weighted return
annualisedReturn: Annualised when the period is at least a year; otherwise null

The example

{
  "values": [
    1000000,
    1050000,
    1200000,
    1180000
  ],
  "flows": [
    0,
    100000,
    -50000
  ],
  "years": 1
}

Agents: POST /faculty/msc-investment-management/time_weighted_return with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Modified Dietz return · modified_dietz

Try with the example

When the portfolio was not valued at each flow, what return does the Modified Dietz method approximate?

Reference: Dietz, P. O. (1966) Pension Funds: Measuring Investment Performance; GIPS 2020 — an approximation of the time-weighted return for sub-periods between valuations

Returns

netFlows: Σ flows
weightedFlows: Σ (1 − timing)·flow
modifiedDietz: The return

The example

{
  "beginningValue": 1000000,
  "endingValue": 1180000,
  "flows": [
    100000,
    -50000
  ],
  "flowTiming": [
    0.25,
    0.75
  ]
}

Agents: POST /faculty/msc-investment-management/modified_dietz with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Two-asset portfolio risk and return · two_asset_portfolio

Try with the example

What are this mix’s expected return and risk, and which mix of the two assets has the least risk?

Reference: Markowitz (1952) mean–variance portfolio theory; CFA Institute CBOK, Portfolio Management

Returns

expectedReturn: w·RA + (1 − w)·RB
volatility: Portfolio standard deviation
minimumVarianceWeightA: Weight in A that minimises variance (unconstrained)

The example

{
  "weightA": 0.6,
  "returnA": 0.1,
  "returnB": 0.06,
  "volatilityA": 0.2,
  "volatilityB": 0.1,
  "correlation": 0.3
}

Agents: POST /faculty/msc-investment-management/two_asset_portfolio with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Tracking error and information ratio · tracking_error_ir

Example filled in — consult below

How far did the portfolio stray from its benchmark, and how much active return did it earn per unit of that risk?

Reference: Grinold & Kahn (2000) Active Portfolio Management: information ratio = active return ÷ active risk; sample standard deviation; annualised by periods per year

Returns

meanActiveReturn: Mean of portfolio − benchmark, per period
trackingError: Annualised sample standard deviation of active returns
informationRatio: Annualised active return ÷ annualised tracking error

The example

{
  "portfolioReturns": [
    0.012,
    -0.004,
    0.021,
    0.008,
    -0.011,
    0.015
  ],
  "benchmarkReturns": [
    0.01,
    -0.002,
    0.018,
    0.009,
    -0.013,
    0.011
  ],
  "periodsPerYear": 12
}

Agents: POST /faculty/msc-investment-management/tracking_error_ir with JSON {pan, …inputs} and the x-402-payment header. Manifest.