BAFI6010 · Advanced Investment Management
Investment Return and Risk Objectives
This is the foundation of BAFI 6010 — the stage of the Investment Management Process that turns an investor's situation into explicit, defensible objectives before any asset allocation happens. You learn to state a return objective (absolute vs relative; the endowment spending stack), a risk objective (absolute vs relative risk measures, ability × willingness, path dependence), the right return and risk measures (gross vs continuously compounded returns, VaR, tracking error, drawdown), and how to justify a benchmark against the five tests. It is examined on both the closed-book mid-semester test and the applied final, so both the calculation and the discussion have to be automatic.
What this chapter covers
- 011. Investment Management Process — the four-stage arc; Topic 1 builds stage 1 (objectives, constraints, spending policy, benchmark)
- 022. Functions of asset management — selection, objective-driven diversification, liquidity, cost reduction, acting for investors
- 033. Return objective is two-dimensional — adding a risk objective turns return-seeking into mean-variance optimisation
- 044. Absolute vs relative objectives — stand-alone target (CPI + x%) vs match/beat a benchmark (passive vs active)
- 055. Endowment return objective — spending rate s = NCF / W0; required real return = spending + real growth + fees − donations
- 066. Risk objectives & tolerance — absolute (std dev, VaR, drawdown) vs relative (beta, tracking error); ability × willingness; path dependence; LLTTU constraints
- 077. Measuring returns — holding-period/gross return vs continuously compounded (log) return for time series
- 088. Benchmarks — the five tests (unambiguous, investable, measurable, appropriate, reflective) and weighting schemes
An endowment's real total-return objective
- +2Spending rate = payout ÷ assets = 18 ÷ 400 = 4.5%. (Equivalently, for a perpetual endowment r = NCF / W0, the sustainable real return equals the payout rate.)
- +2Stack the required real return additively — spending + real growth + fees − donations. Fees are a debit, donations a credit: 4.5% + 1.5% + 0.75% − 1.25% = 5.5% real.
- +1Classify as absolute — the target is tied to the museum's own spending and real capital preservation, not to beating a market benchmark. Add expected inflation i for the nominal figure.
- +1Set a risk objective as a downside/shortfall cap, e.g. 'keep the probability of a real capital decline over any rolling 3-year window below 10%' — growth-biased but not aggressive.
Key terms
- Investment Management Process
- The four-stage arc that governs a mandate: (1) establish objectives, constraints, spending policy and a benchmark; (2) set strategy (SAA, TAA ranges, rebalancing); (3) implement (risk budgeting, manager selection, trading costs); (4) review (performance attribution). Topic 1 builds stage 1.
- Absolute vs relative objective
- An absolute objective is a stand-alone target such as 'CPI + x%'. A relative objective is defined against a benchmark: passive managers aim to match it, active managers to exceed it (earn active return). The same split applies to risk measures.
- Required return
- The minimum return an investor needs to fund their obligations. If those obligations are inflation-prone (endowment spending, pension payouts), it is stated in real terms and inflation is added back for the nominal figure.
- Endowment spending stack
- The additive build of an endowment's required real total return: spending rate + real growth target + fees − donations. Spending rate = payout ÷ assets = NCF / W0 for a perpetuity.
- Continuously compounded (log) return
- The natural log of the gross return, ln(Pt / Pt−1). The course uses it for financial time series because log returns add cleanly across periods; it is always below the simple return for a gain.
- Value at Risk (VaR)
- The loss (in dollars or %) under normal conditions over a set horizon at a given confidence level — it needs BOTH a horizon and a confidence level. Estimated by historical (non-parametric), variance-covariance (parametric) or Monte Carlo methods.
- Tracking error
- The standard deviation of the return difference between a fund and its benchmark (or of the single-index residual). A benchmark-relative risk measure that passive managers minimise.
- Path dependence of risk
- The risk of missing objectives depends on the ORDER of returns, not just their average. An early drawdown hurts an endowment far more than the same dollar loss later, because it keeps spending against a smaller capital base.
Investment Return and Risk Objectives FAQ
How do I build an endowment's return objective in the exam?
Compute the spending rate (payout ÷ assets), then stack it additively: spending + real growth target + fees − donations, in real terms. Add expected inflation for the nominal figure. Then classify it as absolute or relative and attach a risk objective. Markers reward the label and the correct signs (fees add, donations subtract) as much as the arithmetic.
What is the difference between an absolute and a relative objective?
Absolute means a stand-alone target — e.g. 'earn CPI + 5%' or 'preserve real capital while funding spending'. Relative means measured against a benchmark: passive managers try to match the benchmark, active managers try to beat it. The same distinction sorts the risk measures — standard deviation, VaR and drawdown are absolute; beta and tracking error are relative.
Why does a VaR number need both a horizon and a confidence level?
VaR is 'the loss you should not exceed with confidence c over horizon T'. Change either input and the number changes, so 'the VaR is $2m' is incomplete. Always quote both, e.g. 'the 1-day 99% VaR is $2m'. Forgetting one is a guaranteed mark-drop and a favourite exam trap.
When should I use continuously compounded returns instead of simple returns?
Use continuously compounded (log) returns for financial time series, because they add across periods — the course expects them there. Use the simple holding-period (gross) return for a single period. Mixing the two up, or using arithmetic where the course wants log, loses marks.
What makes a good benchmark?
It must pass five tests: unambiguous (known constituents and weights), investable (you can buy the constituents and a tracker exists), measurable (returns computable over the horizon), appropriate (matches the manager's style), and reflective of current investment opinion. Naming index types without these five is the classic incomplete answer.
How do ability and willingness combine into risk tolerance?
Ability is objective (horizon, wealth, liabilities); willingness is behavioural. When they conflict, the lower of the two normally governs — a keen but low-ability investor is still constrained by ability. The manager's job is to reconcile them: educate the willingness up, or constrain the risk down.
Exam move
Topic 1 is tested on both assessments, so prepare it two ways. For the closed-book mid-semester test (no formula sheet), memorise and drill the core calculations until they are automatic: the endowment spending stack (spending rate = NCF / W0, then + real growth + fees − donations), the perpetual W0 = NCF / r versus the finite-horizon annuity, and the log return ln(Pt / Pt−1) versus the gross return. For the applied final (about 80% discussion), rehearse the labelling and justification answers: classify every objective as absolute or relative and match the correct risk measure (std dev/VaR/drawdown vs beta/tracking error), justify a benchmark against the five tests, and explain path dependence and the ability × willingness trade-off in words. Two reflexes bank easy marks — always state a VaR with both a horizon and a confidence level, and treat benchmark selection as a two-gate filter (apply the risk cap and the return floor separately, rejecting on the first failure).
