Let me tell you all about it!
Interest rates are being held at zero by the Federal Reserve, using quantitative easing, in order to protect the economy from recession. Unfortunately, this has been necessary since 2008, and the Federal Reserve is continuing to postpone raising rates, i.e. monetary normalization, although it is increasingly difficult to justify.
...the entire public market is likely to go down—perhaps substantially—when interest rates materially move up, though that may be a long time away.
The Federal Reserve intended to keep interest rates low, in order to encourage businesses to invest in R&D, new ventures or make capital expenditures for plants, property, and equipment. The logic is that with interest rates so low, there is a strong disincentive to accumulate cash reserves, for both businesses and investors. For reasons that aren't entirely clear, businesses have not taken advantage of the ultra-low interest rate environment (the cheap money in your question) for building durable wealth, but instead, have been doing things like stock buybacks.
This recovery has been one of the weakest in U.S. economic history, and cannot seem to get past stagnant wages and persistently high unemployment.
In a world of 0 percent interest rates, people become pretty focused on finding new sources for fixed income.
Investors are chasing yield, which only drives speculative markets higher. Speculative markets include the stock market as well as venture capital. There are fewer sources of return on investment, despite easy credit for businesses due to extravagantly accommodating monetary policy.