We have index for stock market, like S&P500, Nikkei 225, etc.
I wonder if we have any index for hedge funds, private equity or venture capital?
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I am not familiar with indexes for private equity or venture capital. For hedge funds, there are various indexes, with the best-regarded ones provided by HFR. They include an investable index.
I happen to believe these indexes, even the investable one, are of very limited use at best. Many hedge funds are closed, meaning they are not taking in new money. Others have exited the index through failure, meaning there is a strong survivorship bias.
