La Bourse / Volume III / Nº III.10 / Quiz, reflection, essays

A watercolour of a broad tree with its roots reaching down into orange earth beneath a green canopy. — Plate III.10 · Quiz, reflection, essaysThe Deep Pantry.A reserve is not what you have. It is what you have already decided not to use.

ASSESSMENT · Chapter III.10 — Reserves and Resilience

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. Write the safety stock formula in full and say which of its two variance terms usually dominates.

safety stock = z · σ_DL, where σ_DL = sqrt(L·σ_d² + d²·σ_L²). The first term is demand variance over the lead time; the second is demand squared times lead-time variance. One mark for the expression, one for naming the lead-time term as the dominant one — in the chapter's 2022 case it is 96.34 percent of the variance, and it belongs to the supplier, not the buyer.

2. State the newsvendor's critical ratio and name the problem Edgeworth originally posed it for.

CR = Cu / (Cu + Co) — the cost of being short over the cost of being short plus the cost of holding one unnecessary unit. Edgeworth (1888) posed it for a bank's cash reserve. Full marks require both; the point of the question is that reserve theory and inventory theory are one theory.

3. What does Expected Shortfall measure that Value at Risk does not, and what did the Basel Committee do about it in 2019?

ES is the average of the losses beyond the threshold; VaR is only the threshold itself. BCBS (2019) replaced 99 percent VaR with 97.5 percent ES in the market risk framework.

4. Write the break-even return period and say how it is used.

T = (loss × recovery fraction) / annual carrying cost, an interval in years. Hold the reserve if an event of that size arrives more often than T. One mark for the formula, one for the direction of the inequality.

Four on application.

5. A colleague says: "Ecosystems show that resilience needs a ratio of ascendency to capacity of 0.368, so we should manage the firm to that." What are the three things wrong with the sentence?

First, 0.368 is where R = −a·ln a peaks, and that function was chosen for its shape, not derived from a measurement. Second, the peak is a plateau — within 10 percent of maximum, a runs from 0.216 to 0.544, a band 0.89 times a itself. Third, a depends on how the analyst draws the compartments: flow diversity on k equal compartments is ln k, so aggregation moves the denominator. Credit strongly any answer that keeps what survives: an interior optimum exists, and too much order is as fatal as too little.*

6. Your CFO proposes cutting the firm's committed undrawn revolver and holding the cash instead, "so we actually control it." Give the arithmetic and the counter-argument, on a $50m requirement.

Cash costs the ROIC-to-cash spread: at 12 and 2 percent, $50m × 10% = $5.0m a year. A 37.5bp commitment fee costs $0.188m — the option is 26.7 times cheaper. The CFO's instinct is nonetheless partly right: a facility is a promise correlated with the shock. In March 2020 corporates drew revolvers on the order of a quarter of a trillion dollars in weeks. The strong answer prices the facility at its reliability — at 70 percent availability it is still 18.7 times cheaper — and concludes "layer, not replace."

7. A supplier offers to hold your strategic stock on consignment for 6 percent of value a year. You currently carry it yourself at 25 percent. Beyond the saving, what is the second reason to take the offer, and what must you check?

On $50m the saving is $12.5m − $3.0m = $9.5m a year, 76 percent lower. The second reason is that under IFRS 15 title has not passed, so it does not consolidate into working capital or touch the leverage covenant. What to check: that the stock is genuinely segregated and callable, that the supplier's own credit can carry it, and that your incentive metrics do not still penalise the unit for holding it.

8. Your reserve has never been drawn in eleven years. Colleagues offer this as evidence it is well run. What is the stronger reading?

That the authority chain, the drill and the replenishment route are all untested, and the failure mode of an untested reserve is not emptiness — it is that nobody has the authority to open it in the eight hours when it would have mattered. Credit any answer naming an annual small-scale drawdown drill, and the Svalbard 2015 withdrawal or the 2022 SPR release as the reason a drawn reserve is more credible than an untouched one.

Two that require the arithmetic to be done.

9. A component is used at 800 units a week with a demand deviation of 200. Lead time is 10 weeks. Lead-time deviation rises from 1 week to 4 weeks and nothing else changes. At a 98 percent service level, what happens to safety stock? Show your working.

σ = sqrt(10 × 200² + 800² × 1²) = sqrt(400,000 + 640,000) = 1,019.8. At 98 percent, z = 2.0537, so safety stock is 2,094 units. With σ_L = 4: σ = sqrt(400,000 + 10,240,000) = 3,261.9, safety stock 6,699 units — a factor of 3.20×. Expected units short per cycle moves from 7.49 to 23.95 at the same z. The mark is for noticing that demand never changed: the buffer tripled because the supplier's variance tripled.

10. A disruption would cost your firm $24m. A proposed reserve would prevent about half of that and costs $900,000 a year to carry. Your incident log shows two such events in eighteen years. Does it clear, and by how much?

T = (24m × 0.50) / 0.9m = 12m / 0.9m = 13.3 years. The observed interval is 18 / 2 = 9.0 years. Nine is shorter than 13.3, so the reserve clears by a margin of 1.48×. The stronger answer states the sensitivity: at a 30 percent recovery fraction T becomes 8.0 years and the reserve no longer clears — so the recovery fraction, not the loss, is the number to defend.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

What is the reserve you keep in your own life that you have never costed? Money, time, a relationship you do not spend, an unfilled evening. What is it against — and when was it last drawn?

Where are you running at 99.99 percent service on something that deserves 95? What is the price you have been paying for that last point, in hours or in attention?

Think of a time you were caught short. Was it a demand surprise or a supply surprise? What does your honest answer say about where your own buffers should sit?

What capability of yours has been quietly maintained by someone else — a colleague, a partner, a habit — while you assumed it was simply there?

Recall a period when you carried far more reserve than you needed. What did it cost you, and would you know now how to tell that state from the safe one?

Where in your work is the tail fatter than you have assumed? Name the event you have been treating as unprecedented that has in fact happened more than once.

Which of your reserves is alive — it earns its keep in ordinary years — and which is dead, sitting still and costing the spread? What would it take to move one thing from the second list to the first?

Who pays for the reserves you benefit from and do not hold? Write the list. Then write what you would owe them if the accounting were honest.

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. The efficiency–resilience trade-off: real, or an artefact of dead capital? The chapter's arithmetic shows that the drag of a buffer collapses as the buffer's own return approaches the firm's — from a 47-year break-even ruin frequency at zero return to 187 years at 9 percent. Argue either that the trade-off is fundamental, as Ulanowicz's curve implies, or that it is largely an artefact of holding reserves in assets that do not produce. Use Ulanowicz et al. (2009) and one source on capital productivity or working-capital efficiency that the chapter does not cite.

2. Should strategic reserves be mandated? The chapter finds that reserves surviving at scale are mandated, mutualised or regenerative, and gives the EU's 2022 gas storage regulation and the SPR as mandated cases. Argue either that mandated commercial reserves are a legitimate correction of a genuine externality, or that they are a tax on producers that raises prices in ordinary years to insure against extraordinary ones. Use the 2022 gas storage regulation and at least one source on strategic stockpile performance the chapter does not cite.

3. Just-in-time on trial. Ohno's system produced measurable gains for four decades before 2020. Write the case for the prosecution — that JIT externalised its buffers and the 2020–22 record is the bill — and then the case for the defence, that the system's gains over forty years exceed a single decade's disruption cost and that the correct response is targeted dual-sourcing rather than general inventory. Use Ohno and Simchi-Levi et al. (2014), and at least one empirical study of inventory practice post-2022.

4. The correlated buffer. A living reserve — soil, retained skill, a maintained relationship — is cheap precisely because it is embedded in the system it insures, and vulnerable for the same reason. Argue whether the correlation disqualifies living reserves from the core of a resilience strategy, or whether the objection applies equally to every reserve a firm can actually control. Use the Rodale Farming Systems Trial or the OECD (2020) job-retention work, and one source on correlated risk or reinsurance that the chapter does not cite.

5. Ergodicity, ruin, and the ethics of the lean firm. The chapter computes that a 20 percent cash buffer pays only if ruin without it would occur more often than once in 56 years, and concedes that below that frequency the lean competitor wins. Peters (2019) argues that time-average and ensemble-average growth diverge precisely where ruin is absorbing. Argue either that the ensemble logic of capital markets correctly prices this — a diversified owner is indifferent to one firm's ruin — or that it systematically under-reserves the whole economy because no individual owner bears the correlated failure. Use Peters (2019) and one source on systemic risk or financial fragility that the chapter does not cite.