US Index Check — Same 500 Stocks, Two Weights, Two LinesS&P 500SP_DLY:SPXHappyLittleTradesFirst, four rules. 1. The market is always right. 2. Every price is already set. 3. Every view is a quantum view — stay flexible, keep every state open. 4. All evolution comes through repetition. Only two hard terms in this post. Cap-weighted means the biggest companies get the biggest share; equal-weighted means all 500 get the same share. The stocks are identical — only the weights differ. And effective number of bets counts not how many lines are on your list, but how many genuinely different decisions are on it. Two indexes hold the same 500 stocks. Overlay the two lines on one screen and they have separated. This post is about what that gap says — and how, once you know, the sentence "I'm diversified across US stocks" changes. Every measurement here is weekly bars, 520 weeks, ten years. What this post does ① — how the same 500 stocks separate when only the weights change: size and speed ② — the effective number of bets in four baskets, and where the names and the measurements disagree ③ — testing "in a crisis they all fall together" against a control — and what actually drives the index ④ — before you buy: which weighting your index ETF uses, and how many bets your list really holds ⑤ — after you buy: what to confirm, and what to measure to tell which weighting the regime favors — plus today's 5-minute check ④ and ⑤ are the point. ①–③ exist so you can do ④ and ⑤. And up front: ⑤ is not a table of which one to buy. It is a set of rulers. The answer comes out of your own measuring. What to look for in this chart — the broad-market index. This one chart is the baseline; every number below comes from the same weekly window as this screen. ① Same stocks, two lines In one sentence. Week to week they are almost one body; stacked over ten years they separate, and the gap is widening faster. The weekly-return correlation between the two indexes is 0.935. Nearly one body. Stack ten years and the cumulative paths diverge. Cumulative log difference over the same 519 weeks: +0.3176 A 0.935 correlation with a diverging cumulative path looks odd. It is not. If the two tilt slightly different ways every week, those small tilts accumulate over a decade. The standard deviation of the weekly difference is only 0.90%. That 0.90% is what piled up. Now the part that matters more. Cut the gap into halves: First half (about 5 years): +0.1104 Second half (about 5 years): +0.2072 The separation is accelerating. The second five years is nearly double the first. And one more thing. The cap-weighted side has smaller weekly swings (2.39% vs 2.55%). More concentrated, yet quieter. The opposite of the "concentration equals volatility" intuition. What to look for in this chart — the same 500 stocks at equal weights. Overlay it on the chart above and find where the two lines separate and where they converge. That single view is the most useful thing in this post. ② Length of the list vs number of bets In one sentence. The names say four, ten, seven; the measurement says 1.12, 1.54, 1.81 — and the order of the names and the order of the measurements disagree. Several baskets, one yardstick. N_eff = N / ( 1 + (N − 1) × r ) N is the length of the list; r is the average pairwise correlation. Same 520 weeks, same method. Basket · N · avg pair corr · min · max · N_eff Major US indexes · 4 · 0.854 · 0.743 · 0.945 · 1.12 Sector funds · 10 · 0.609 · 0.312 · 0.877 · 1.54 Largest by market cap · 7 · 0.478 · 0.270 · 0.645 · 1.81 Next tier of large caps · 5 · 0.376 · 0.112 · 0.739 · 2.00 Top 7 + next 5 · 12 · 0.385 · 0.112 · 0.739 · 2.29 Read the first line first. Four major US indexes are 1.12 effective bets. Large cap, tech, blue chip, small cap — four names, one decision. The lowest pair is 0.743, so even the two least similar are quite similar. Now the second and third lines. I did not expect this result. Sector funds, 10 of them: N_eff 1.54 Largest by market cap, 7 of them: N_eff 1.81 Splitting into ten sectors gives you fewer effective bets than holding the seven biggest stocks. That runs against intuition. Sector funds carry the label "diversified"; individual mega caps carry the label "concentrated." Measured, the labels are backwards. A plausible reason: each sector fund holds dozens to hundreds of names, so company-specific movement is already averaged away. What remains is the market as a whole, and that is why ten of them resemble each other. Individual giants still carry their own business and circumstances. That is my guess; the table above is the measurement. I am keeping the two separate. And do not read this as "so individual stocks are better." 1.81 is still 1.81 out of seven. Nothing in this post says one thing is better than another. What it says is that what the names claim and what the measurement shows are different things. What to look for in this chart — the tech-heavy index. Eyeball how often it moves the same direction as the broad index above at the same time. That overlap is why four major indexes came out as 1.12 bets in the table. ③ "In a crisis they all fall together" has never been tested In one sentence. In the worst 52 weeks, 6.33 of the seven fell together — but in the best 52 weeks, 6.33 of the seven rose together, and a fake market with nothing happening produces 6.35. Take the 52 weeks when the market fell the most and count how many of the top seven fell in the same week. Worst 52 weeks: average 6.33 of 7 down More than six of seven went down together. Stop here and you get "in a crisis even the giants become one block." Now look at the other side. Best 52 weeks: average 6.33 of 7 up Identical to the decimal. They do not cluster only on the way down. They cluster the same way on the way up. The crisis narrative has nowhere to stand. To confirm, I attached a control. Build a fake market with the correlation structure fixed at its full-period value. No crises, no correlation spike in bad weeks. Run the identical procedure 600 times. Metric · observed · null median · 5–95% band · p Count down · 6.33 · 6.35 · 6.12 – 6.58 · 56.5% Dead center of the band. The observed value is slightly below the null median. So "in the worst weeks six of seven fell together" is true — and says nothing about crises. Gather things with a 0.478 correlation, select the worst weeks, and that is what you get by construction. Last, what the index's weekly movement is actually attached to. Index ↔ average of 10 sectors: correlation 0.942, explanatory power 0.888 Index ↔ equal-weighted version: correlation 0.935, explanatory power 0.875 Index ↔ average of top 7: correlation 0.827, explanatory power 0.684 All three are high. But the top seven alone explain only 0.684. The rest comes from outside them. This connects back to ①. Cumulatively, cap-weighted and equal-weighted separate; week to week, they are 0.935, almost the same. The same two series read as "nearly identical" or "very different" depending on the time scale you look through. Both are true. What matters is knowing which one you are looking at. ④ Before you buy — which weighting, and how many In one sentence. Check two things before picking an index product and half of this post is done — which weighting it uses, and how many effective bets your list holds. 1 Weighting method — page one of the product document. Cap-weighted or equal-weighted. The same index name often exists in both versions. 2 Top-10 share — if cap-weighted, what percent of the index the ten largest names are. That is the concentration. 3 Effective bets — get your list's average pairwise correlation r and put it into N / (1 + (N − 1) × r). 4 The gap between the lines — plot cap-weighted ÷ equal-weighted once. Is it widening now, or converging? All four are free to know before you buy. Learn them after, and you have already paid. Number 3 in particular shows in numbers that adding names does not add bets. In the table in ②, adding the next five large caps to the top seven — twelve names — moved the effective count from 1.81 to 2.29. Five names bought 0.48 of a bet. ⑤ After you buy — what to confirm, and what decides which weighting is favored In one sentence. The two weightings move in opposite directions in some regimes. Which one is favored is decided not by taste but by three axes. Three things to confirm first. 1 Direction of the ratio — cap-weighted ÷ equal-weighted. Rising means a few names are carrying it; falling means the move is spreading. 2 Correlation holding — is the 0.935 weekly correlation intact? If it breaks, the two versions have become different markets. 3 Your effective count — if the list changed, count again. Adding names is not adding bets (see the twelve-name example in ④). What to look for in this chart — the breadth line itself: cap-weighted ÷ equal-weighted, drawn by typing the ratio SPY/RSP straight into TradingView's symbol box. Rising means a few names are carrying the index; falling means the move is spreading. One line answers item 2 every week. Then the axes for which weighting is favored. This is not a recommendation for either version. Put anything on these three axes and the favored and unfavored sides separate within the same regime. Axis 1 Is concentration being rewarded in this regime? When a handful of giant companies capture most of the profit, cap-weighted leads. The reverse favors equal-weighted. The ratio in item 1 makes the call: rising means concentration, falling means dispersion. Axis 2 Which way are rates going? Giant growth companies with far-out cash flows swing more with rates. Cap-weighted holds more of them. The sign flips between rising-rate and falling-rate regimes. Axis 3 How much swing can you carry? The concentrated side had smaller weekly swings (2.39% vs 2.55%). The opposite of the intuition. "Diversified means safer" needs to be re-measured against that number. Using it is simple. Write +, 0, or − on each axis for the current regime. If all three point the same way, that version is attached to this regime. If they conflict, the version is moving for a reason this post does not explain — and then it is not a weighting story. Today's 5-minute check All of it takes a few minutes on TradingView. One — two lines. Overlay the cap-weighted index and its equal-weighted version, weekly. Mark where they separate and where they converge, and look at the first five years and the second five years separately. The numbers in ① become visible. Two — effective bets. Write down what you hold, get the average pairwise correlation from weekly log returns, and put it into the one-line formula. Write the answer next to the length of the list. Compare with the table in ②. Three — demand a control. When you meet the claim "in a crisis they all fall together," ask: what does the same calculation return on data where nothing happens? Including this post's ③ — which answers that question itself, and the answer is "rejected," so that is what it says. Four — one ratio. Plot cap-weighted ÷ equal-weighted and watch whether it rises or falls when the index rises. Two rallies that look the same have different characters. Closing The names say diversified; the measurement sometimes says otherwise. Four major indexes were 1.12 effective bets. Ten sector funds were 1.54, and the seven largest stocks were 1.81. The order of the names and the order of the measurements disagree. And the same 500 stocks, with only the weights changed, separated over ten years. That gap is still widening. An honest limit. These numbers are one window — 520 weekly bars. Cut a different decade and the sizes may change, and whether the disagreeing order holds is something to re-measure then. Read this as a fact about this window, not a law. Which version to hold is not mine to decide. But before deciding, you can count how many you are actually holding. The formula is one line, and the charts are two. Count it yourself, and judge it yourself. So the last question is a single one. What was your list's effective number of bets? You already know the length of the list. Write the two numbers side by side and you will know which one you have been counting. For education and record only. Not a recommendation to buy or sell.