One of the worries for equity investors is that we might be in a scenario similar to what happened in 1994. Then, too, an increase in long-term interest rates took place, as can be seen below (Source: Yahoo Finance):
And it had consequences for the equity markets. Using the SPDR S&P500 (SPY) as a proxy, these consequences are easy to see. 1994 was a roller coaster of a year, though it did end up higher than it started if we include dividends (Source: Yahoo Finance).
Let's see the timing of the two moves, superimposed on each other (1-month rolling returns for SPY, 1-month rolling deltas for 10-year interest rates, Source: Yahoo Finance).
What we can gleam from this is that over 1994, the moves in interest rates were the main determinant for the moves in the equity market. Each peak in rates was followed by a valley in SPY returns, and the dynamics made for a roller coaster year. Eventually, however, the market seemed to get tired of following interest rates, for interest rates were nearly 35% higher at the end of 1994, with the 10-year bond going from 5.78% at the start of the year to 7.82%, yet the equity market as represented by SPY ended the year slightly higher than it started (including dividends).
Perhaps also tellingly
All the equity volatility in 1994 gave way to a powerful endless rally with low volatility during 1995 (Source: Yahoo Finance).
… Which was certainly helped by a massive contraction in interest rates (Source: Yahoo Finance).
However, I'd surmise that this would be considerably harder to happen today given the starting point, about which I've written on my article "Is This The Start Of A New Bull Market?"
One large difference today comes from the fact that even after a significant increase in long-term rates, the 10-year is at "just" 2.71%. While the Fed might constrain further upside, 2.71% presents a long-term picture that's a lot different from 1994's 7.82% at year-end.
What 1994 seems to teach us is that for a while, the long-term interest rates can be a driver of the equity market. If the same thing were to happen today, what would be expected would be continued volatility with the equity market going essentially nowhere, and with spikes in rates leading to short-term dips in the equity market. The market seemed to avoid one such dip on Friday, but it wouldn't be surprising if this week it choose to reconnect with the bond bearishness, as long as interest rates don't stage a significant (downward) recovery.
Looking into what happened right after 1994, however, one cannot exclude a significant equity rally if interest rates now drop for their new highs as long as these aren't accompanied by an all-too-obvious economic/earnings slowdown.
In short, the 1994 scenario would call for further volatility in the short term and possibly an equity rally after rates stabilize and head back down. However, with rates not being so high (2.71% in the 10-year), there's the chance that the move higher can be secular and thus that we won't get the massive equity rally which would follow rates peaking.
As a small aside, a much scarier scenario would be stocks following the 1987 precedent, where an increase in interest rates was possibly one of the triggers for a massive (and quick) slide in equities. During the slide, interest rates also fell, so a measure of switching from equities to bonds took place during the plunge.