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What is the difference between this index, and the S&P 500, other than price?

The S&P 500 Index is a list of stocks, selected by Standard and Poor's. It is not available for purchase and it incurs no management or trading costs. It pays no dividends.

The Vanguard Index 500 fund, OTOH, is a mutual fund that invests in the 500 companies listed in the S&P 500 list. Its purpose is to track that index, which it does with great and improving accuacy. It incurs some management and trading costs, something like 19¢ per $100 per year. You can buy this, unlike the Index itself, and it pays dividends. The difference in price is not significant. You can reasonably expect that when the S&P 500 Index gains x% one day, the Vanguard Index 500 fund will also gain x% that day. Any occasional slight discrepancy in percentage results is probably due to accumulating dividends that will be distributed quarterly or to the management fee.

Does this mean it is ONLY available through Vanguard, and I can't purchase it through my discount broker?

I don't know about your discount broker. My broker is Charles Schwab. Although I do not use this particular service, Schwab will buy Vanguard Index 500 fund for me or sell it, for a small commission. The fee is a percentage of the trade but is capped at around $150 even for a million dollar trade. I use this service: Schwab holds VFINX for me in both tax-sheltered and taxable accounts at no charge and no commission -- I bought them at Vanguard and then transferred custody to Schwab. There is no cost for this; specifically, there is no cost for initiating these transactions, none for transfering the mutual fund shares to Schwab's custody, and none for Schwab maintaining them in my account, reinvesting the dividends, and providing regular monthly reports. Works for me.

Chips, inveterate indexer

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