Pension funds need to pay out all the time, in good times and bad, so they also have a short term component to worry about it. And they do invest in index funds, but going all in into sp500 isn’t the same as diversifying. Here are some good responses:
Pension funds also have money flowing in. They invest more money in down markets than good ones because they need to ‘catch up’ in bad markets and can scale back in good ones. The risk is the company failing to keep up in a bad year.
Diversification is also a relative term. Compared to owning a single stock the sp500 is more diversified.
https://www.quora.com/Why-dont-pension-funds-university-endo...