The relationship between stocks and bonds is difficult to speak about intelligently, unless you're prepared to define it in different ways depending on the time frames considered and the market moving variables in play. For instance, over short time frames, we tend to see more correlation between yields and stock prices. This is most in-line with the conventional wisdom of traders moving money out of one asset class and into the other (i.e. buying stocks and selling bonds). This conventional wisdom-based relationship would result in a chart of stock prices and bond yields moving in the same direction, as has been the case over the past few weeks.
The most notable exceptions to the conventional wisdom have occurred when quantitative easing has been up for debate. On most days in mid-2013 (when markets were coming to terms with the taper tantrum), the lines in the chart above would be moving in the opposite direction (meaning stocks and bonds were weakening/improving together) as each market benefited from the Fed's largesse.
Over longer time horizons, most market watchers are surprised to see that stocks and bonds don't follow each other at all, but instead tend to move in the opposite direction. One could argue that's a byproduct of a decades-long bond rally coupled with the fact that stocks should average positive growth over time.
Even then, there are many examples of yields and stocks moving in the same direction over longer time frames. This dynamic tends to play out when markets are uncertain about the near-term future and when "risk-on/off" is one of the key considerations. Arguably, the risk-on/off trade has been a key ingredient in 2017's movement. It was most recently seen heading into (and out of) the French election last Monday.
As the chart above shows, both stocks and bond yields were trending lower in linear fashion heading into the French election. They both broke out of those trends last Monday and they've both been sideways ever since. There's no rule that says they will continue to share the same technical cues, but at the very least, we can assume bonds are somewhat concerned by the possibility of stocks breaking back above 2017's highs and going on another bull run.
That's precisely the sort of thing that drives the "conventional wisdom" of stocks and bond yields moving together. In this case, a break into 2017 highs for stocks would likely result in a firm reentry into the 2017 trend for 10yr yields (2.315-2.615). There is no significant data on tap today to inform that trade, but data ramps up tomorrow and remains relevant through Friday's NFP and the final French election run-off this weekend.