Seven months of spending in a liquid fund prevents every Nifty sale in this simulation, the smallest tested reserve to do so. The result applies to the paper's main household when it loses all income in months 12 to 17. It answers a narrow question: when do equity sales reach zero? Reaching the goal and rebuilding the reserve require separate answers. Harini, Srihari and Gopavarapu keep those questions apart. A reader hunting for a rule of thumb may miss the distinction.
How the simulation works
The authors use historical returns in a deterministic simulation, without random draws. Equity follows the Nifty 50 Total Return Index; cash follows HDFC Liquid Fund Direct Growth. They multiply its NAV by 100 before the August 2015 face-value change to keep the unit switch from appearing as a return. The resulting history contains 144 monthly return pairs from January 2014 to December 2025. From these they form 85 overlapping 60-month windows. Neighbouring windows share 59 months. Testing reserves of 0, 3, 6, 7, 8, 9 and 12 months of spending under 45 scenarios produces 26,775 paths.
The main household has Rs600,000 initially, earns Rs60,000 a month and spends Rs40,000, with a goal of Rs2,000,000. Income, spending and the goal rise 5% a year in annual steps. The household divides its initial wealth between equity and the reserve. Cash-first, the paper's withdrawal rule, pays deficits from the liquid fund before selling equity; any remaining deficit becomes unmet spending. Surpluses replenish cash before funding equity purchases. Equity is never sold to refill the reserve.
Holding cash avoids equity sales during an income interruption. The price is the equity return forgone on that money. For full income loss in months 12 to 17, a six-month reserve reduces mean equity sales to fund spending from Rs250,000 to Rs5,777. Mean terminal wealth drops from Rs2,394,214 to Rs2,278,077, costing Rs116,137. The lowest-10% mean improves from Rs1,781,945 to Rs1,817,390, a gain of Rs35,445. Raising the reserve to twelve months lifts the tail mean to Rs1,833,878 and lowers the overall mean to Rs2,143,961.
What does seven months buy?
With a reserve labelled six months, 100.0% of windows still require equity sales. Spending rises at month-13, partway through the shock. The household therefore needs Rs250,000 against a Rs240,000 reserve. The remaining sale averages just Rs5,777, and only 3.5% of windows require it during a drawdown of 20% or more. At seven months, equity sales disappear from every window.
Every policy pays the bills in this scenario. All seven fund every rupee of planned spending, including the zero-reserve policy, which sells Rs250,000 of Nifty. Cash also carries a cost when income continues uninterrupted: the six-month reserve lowers mean terminal wealth by Rs135,852 even without a shock.
Change the shock and the threshold changes. For a 50% income loss, it falls to 3 months. Full losses beginning in months 12 and 24 push it to 12; moving the second loss to month 30 brings it back to 7. The interval between interruptions matters alongside their combined duration: 12 months of reserve versus 7.
Bills paid, reserves still empty
The headline finding on goal success depends on a test added after the authors saw the original results. This test requires terminal wealth to cover both the goal and a common six-month reserve, totalling Rs2,858,871. Applying it takes success for the six-month policy from 12.9% to 0%; for zero reserve, success falls from 28.2% to 4.7%. The paper explicitly discloses that the test followed inspection of the original results and was not preregistered. Its accounting makes sense. The same rupees cannot serve as both goal wealth and emergency cash.
At a 30-month goal, that six-month policy succeeds 95.3% of the time. With the same asset paths and policy, protected success falls to 43.5% at a 40-month goal and 0% at 50. The authors describe this as an accounting clarification. They say it implies neither new returns nor a statistically significant decline in success. The abstract nevertheless leads with the 12.9%-to-0% figure.
Recovery tells us more.
Households saving 5% or 10% of income cover the entire interruption: unmet spending occurs in 0.0% of windows. But neither rebuilds the reserve in any of the remaining 43 months, with restoration at 0.0% of windows. At a 20% saving share, every window restores the reserve, taking an average of 24.4 months. The one-earner profile already runs a 27.3% deficit before the shock arrives. Give it six months of reserve and a full income loss, and 60.0% of windows leave spending unmet. Mean terminal wealth is Rs25,840.
Cash-first depends on this history
The cleanest comparison fixes the initial allocation at six months of reserve and varies only the withdrawal order. For shocks beginning in months 12, 30 and 48, cash-first raises mean terminal wealth relative to proportional withdrawal by Rs16,232, Rs19,390 and Rs15,449. It wins in 68.2%, 74.1% and 65.9% of paired windows and avoids mean equity sales of Rs177,420 to Rs246,638. This test uses only the original household. Its six-month starting allocation stays fixed; withdrawal order is the only change.
The advantage comes from the same return history that makes cash expensive without a shock. The Rs135,852 no-shock cost implies that equity beat the liquid fund on average across these windows. By retaining more equity, cash-first benefits from that spread. In the abstract, the authors say their results "support conditional policy comparisons rather than a universal reserve recommendation or estimated future success probability." That is the appropriate scope. Traders should take it literally: the conditions consist of imposed cash flows and one 144-month history covering one index and one fund.
The main model makes little allowance for costs. It excludes taxes, exit loads and settlement delays, while treating equity as a fee-free index. The sole cost test applies a 1% annual equity drag. Six-month mean wealth then comes to Rs2,214,295, with total-wealth goal success of 4.7%. Tax on the capital gains in the zero-reserve household's Rs250,000 of sales would work against its mean-wealth advantage. The paper leaves that tax unpriced.
The tail measure is fragile too. Its lowest-10% mean takes the 8 worst outcomes among 85, adds the ninth at half weight, and divides by 8.5. Those outcomes come from heavily overlapping windows. The authors acknowledge the limitation, describing a finite-sample mean for the lowest 10% and making no claim about future tails. Each shock arrives at the same relative month in every window, whatever the market is doing. The authors explicitly state that they do not model dependence between job loss and equity markets. A reserve earns its keep in that joint scenario, yet the design never forces it to occur.
We could not rerun the study. Our data contains neither the Nifty 50 Total Return Index nor the HDFC Liquid Fund NAV history. Substituting US equity and cash ETFs would test a different sequence of returns.
Across these 85 windows, cash-first beat proportional withdrawal with a six-month reserve. The saving rate determined whether the reserve recovered. Forcing job losses to coincide with Nifty drawdowns, or rerunning with pre-2014 data, would help establish whether the Rs35,445 tail gain justifies holding cash or reflects 85 windows with almost complete overlap.