One stock fell 12.64%, the index fell 0.38%: the arithmetic
Alphabet fell 12.64% and Amazon 4.25% on October 29, 2026; the S&P 500 fell 0.38%. The recovery, concentration and volatility arithmetic for a household.
- What happened
- On October 29, 2026 Alphabet fell 12.64% and Amazon 4.25%, while the S&P 500 (SPY proxy) fell 0.38% and closed 1.2% below its high. Alphabet's 20-day realised volatility was 49.1% annualised; the index's was 10.1%.
- Why
- A loss and the gain needed to undo it are not symmetric: recovering from −L requires 1 ÷ (1 − L) − 1. A 0.38% loss needs 0.38% back; a 12.64% loss needs 14.47%; a 29.5% drawdown needs 41.8%. How much of that lands on a household depends on position size.
- The numbers that matter
- 14.47%Gain needed to recover from Alphabet's −12.64% on Oct 29, 2026 (calculation)41.8%Gain needed to recover from Alphabet's −29.5% drawdown from its high (calculation)0.64% vs 3.09%Typical daily move implied by 10.1% (S&P 500) and 49.1% (Alphabet) annualised 20-day realised vol4.88%One-month, one-standard-deviation S&P 500 move implied by a VIX of 16.91 on Oct 28, 2026
- Why it matters
- A $100,000 portfolio with 5% in a stock that falls 12.64% loses $993; with 50% in it, $6,510. The recovery gain needed rises from 1.0% to 7.0%.
- What happens next
- The Market Memory pages update after each close; the figures here are as of the October 29, 2026 close for the S&P 500, Alphabet and Amazon and the October 28, 2026 close for the Nasdaq and VIX.
The index's one-day loss needs 0.38% back. Alphabet's one-day loss needs 14.47%, and its drawdown from the high needs 41.8%.
| S&P 500, one day (−0.38%) | 0.4% |
|---|---|
| S&P 500, from high (−1.2%) | 1.2% |
| Amazon, one day (−4.25%) | 4.4% |
| Alphabet, one day (−12.64%) | 14.5% |
| Amazon, from high (−14.2%) | 16.6% |
| Alphabet, from high (−29.5%) | 41.8% |
On October 29, 2026 Alphabet lost 12.64% of its value in one session. Amazon lost 4.25%. The S&P 500, measured through the SPY proxy on the site's Market Memory page, lost 0.38%, a move smaller than about six in ten of its daily moves since 1993. Two of the largest companies in the index fell hard, and the index barely registered it.
That gap is the subject of this piece. It is not about why Alphabet fell. It is about three pieces of arithmetic that decide what such a day does to a household: how much gain a loss requires to undo, how position size scales a single stock's move, and what the volatility figures on the Market Memory pages mean in dollars per day.
What happened, in percentages only
The site's Market Memory page for Alphabet records a −12.64% move on October 29, 2026, in the 99.9th percentile of its daily moves since 2004: 6 of 5,583 sessions have been this large or larger. Its drawdown from its high is −29.5%, its 20-day trend −16.1%, and its 20-day realised volatility 49.1% annualised. The Amazon page records −4.25% the same day (87.4th percentile since 1997), a drawdown from high of −14.2% and 20-day realised volatility of 36.3%. The S&P 500 page (SPY proxy) records −0.38%, a 39.3rd-percentile move, a drawdown from high of −1.2%, a 20-day trend of +0.7% and 20-day realised volatility of 10.1%. Each page carries the caveat that this is historical context, not a forecast.
The Nasdaq Composite page, whose latest data date is October 28, 2026, shows a +0.27% move that day, a drawdown from high of −3.8%, a 20-day trend of −1.2% and 20-day realised volatility of 18.0%. The VIX page shows a close of 16.91 on October 28, 2026, down 3.48% from 17.52, with a 20-day trend of +3.5%. Both pages state the same caveat: historical market behaviour does not predict future results.
Losses and gains are not symmetric
A loss of L, expressed as a fraction, leaves 1 − L of the original. To return to 1, the remainder must grow by 1 ÷ (1 − L) − 1. For small losses the required gain is almost the same as the loss. For large losses it is not. This is the arithmetic of drawdowns, and the site's loss-recovery tool runs it for any figure.
Applying 1 ÷ (1 − L) − 1: a −0.38% loss needs 0.38% (1 ÷ 0.9962 = 1.0038). A −1.2% drawdown needs 1.22%. A −3.8% drawdown needs 3.95%. A −4.25% loss needs 4.44%. A −12.64% loss needs 14.47% (1 ÷ 0.8736 = 1.1447). A −14.2% drawdown needs 16.55%. A −29.5% drawdown needs 41.84% (1 ÷ 0.705 = 1.4184). Inputs are the October 29, 2026 figures for the S&P 500, Alphabet and Amazon and the October 28, 2026 figure for the Nasdaq.
| Series | Loss | Data date | Gain to recover |
|---|---|---|---|
| S&P 500 (SPY proxy), one day | −0.38% | Oct 29, 2026 | 0.38% |
| S&P 500 (SPY proxy), from high | −1.2% | Oct 29, 2026 | 1.22% |
| Nasdaq Composite, from high | −3.8% | Oct 28, 2026 | 3.95% |
| Amazon, one day | −4.25% | Oct 29, 2026 | 4.44% |
| Alphabet, one day | −12.64% | Oct 29, 2026 | 14.47% |
| Amazon, from high | −14.2% | Oct 29, 2026 | 16.55% |
| Alphabet, from high | −29.5% | Oct 29, 2026 | 41.84% |
Between −0.38% and −4.25% the required gain is within a fifth of a percentage point of the loss. At −12.64% the gap is 1.83 points. At −29.5% it is 12.3 points: the stock must rise by more than two-fifths to regain a loss of less than one-third. Nothing here says whether that happens. The Market Memory page lists only two analogue days for Alphabet, March 16, 2020 and September 29, 2008, with three-month outcomes of +32.41% and −21.94%: two cases in opposite directions, historical context and not a pattern.
What a single position does to a portfolio
The index shrugged because Alphabet and Amazon are two holdings among roughly 500, weighted by market capitalisation, and most of the others did something else that day. A household's exposure is set by its own weights. Take a $100,000 portfolio and assume the non-Alphabet part moved with the S&P 500 proxy, −0.38%, on October 29, 2026. That is a simplification: a real portfolio holds whatever it holds.
At 5%: $5,000 × 12.64% = $632 lost on the stock, $95,000 × 0.38% = $361 on the rest, total $993, or 0.99% of the portfolio. At 20%: $20,000 × 12.64% = $2,528, plus $80,000 × 0.38% = $304, total $2,832, or 2.83%. At 50%: $50,000 × 12.64% = $6,320, plus $50,000 × 0.38% = $190, total $6,510, or 6.51%. The index proxy alone lost $380 per $100,000; Alphabet alone lost $12,640.
Using 1 ÷ (1 − L) − 1 on the portfolio losses: 0.99% needs 1.00%; 2.83% needs 2.91%; 6.51% needs 6.96%. The single-stock holder needs 14.47%. The 50% holder's required gain is about 18 times the index holder's 0.38%, from one session.
| Weight in Alphabet | Loss on Alphabet | Loss on the rest (−0.38%) | Total loss | Gain to recover |
|---|---|---|---|---|
| 0% (index proxy only) | $0 | $380 | $380 (0.38%) | 0.38% |
| 5% | $632 | $361 | $993 (0.99%) | 1.00% |
| 20% | $2,528 | $304 | $2,832 (2.83%) | 2.91% |
| 50% | $6,320 | $190 | $6,510 (6.51%) | 6.96% |
| 100% | $12,640 | $0 | $12,640 (12.64%) | 14.47% |
This is the mechanism behind diversification and position sizing. Diversification does not stop a stock from falling 12.64%. It changes the multiplier between that move and the household's balance, from 1.0 at a 100% weight to 0.05 at a 5% weight.
What 10.1% and 49.1% volatility mean per day
The Market Memory pages report 20-day realised volatility annualised: a daily standard deviation multiplied by the square root of 252 trading days, which is 15.87. Dividing by 15.87 reverses it into a typical daily move.
10.1% ÷ 15.87 = 0.64% per day for the S&P 500 proxy. 49.1% ÷ 15.87 = 3.09% per day for Alphabet. 36.3% ÷ 15.87 = 2.29% for Amazon. 18.0% ÷ 15.87 = 1.13% for the Nasdaq Composite (October 28, 2026 data). Each is one standard deviation of daily returns over the 20 trading days to the data date. Alphabet's −12.64% was roughly four of its own daily standard deviations, and the realised figure already includes that day.
A one-standard-deviation day moves $100,000 in the index proxy by about $640 and $100,000 in Alphabet by about $3,090, on the 20-day figures to October 29, 2026. Realised volatility describes the recent past, and volatility is not the same thing as risk: a series can be calm before a large move and noisy without one. But it sets the size of a typical day, and a 49.1%-volatility stock carries roughly five times the daily swing of the index proxy.
The VIX is the market's implied volatility of the S&P 500 over the next 30 days, quoted annualised. Dividing by the square root of 12 (3.464) converts it to a one-month figure: 16.91 ÷ 3.464 = 4.88%. On the October 28, 2026 close, that is the one-month move option prices treated as one standard deviation, not a prediction of direction. The site's VIX arithmetic piece walks through the conversion and its limits. Realised volatility on the S&P 500 proxy over the prior 20 days, 10.1%, sat below the VIX's 16.91.
What it means for your money
The three calculations above are the ones a household can redo with its own numbers.
- The recovery gap. For any position, take the loss from the high as a fraction and compute 1 ÷ (1 − L) − 1. To October 29, 2026, the S&P 500 proxy needs 1.22% to regain its high; Alphabet needs 41.84%. The loss-recovery tool does this for any figure.
- The weight multiplier. A stock's move reaches the household balance multiplied by its weight. At 5% a −12.64% day cost $993 on $100,000; at 50% it cost $6,510. The same multiplier applies on up days.
- The daily swing. Divide the annualised realised volatility by 15.87 for a typical daily move, and multiply by the dollars held. 10.1% gives $64 per $10,000 per day on the index proxy; 49.1% gives $309 per $10,000 on Alphabet, on the 20-day figures to October 29, 2026. A household that finds a $3,000 day on $100,000 unsettling has learned something about its weights; see loss aversion.
None of this says what to hold. The index fell 0.38% on a day two of its largest members fell 12.64% and 4.25% because an index is the weighted sum of everything in it. A portfolio is the weighted sum of what a household owns, and the weights are the only part of the arithmetic the household controls. Readers who sold at a loss in a taxable account can find the wash-sale mechanics in the tax-loss harvesting piece.
Sources
- Market Memory: S&P 500 (SPY proxy), latest close October 29, 2026Wealth Signal NYC Market Memory · Oct 30, 2026 · Secondary source
- Market Memory: Nasdaq Composite, latest close October 28, 2026Wealth Signal NYC Market Memory · Oct 30, 2026 · Secondary source
- Market Memory: VIX, latest close October 28, 2026Wealth Signal NYC Market Memory · Oct 30, 2026 · Secondary source
- Market Memory: Alphabet (GOOGL), latest close October 29, 2026Wealth Signal NYC Market Memory · Oct 30, 2026 · Secondary source
- Market Memory: Amazon (AMZN), latest close October 29, 2026Wealth Signal NYC Market Memory · Oct 30, 2026 · Secondary source
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