The above exercise is very good if you wish to have arm vibrato, where the movement is coming from the elbow. Before you start, I like to give my students the choice of which type of vibrato they would like to learn: arm or wrist. Then they need to stick with it until it is perfected. If you want to learn both arm vibrato and wrist vibrato, you should wait a few years after mastering the first, before learning the second. I started with wrist vibrato when I was in middle school and didn’t learn arm until university.
If you would like to learn wrist vibrato, the movement is coming from bending the wrist and holding the elbow still. So, the above exercise will not work, because it’s imposible for your wrist to go all the way up the neck! Here’s what I like to do when teaching wrist:
1) Without the violin, hold your left hand in front of you so the back of your hand is against a wall. Bend your wrist back and fourth so that it is coming forward, like you’re waving at yourself. The wall is to prevent your hand from moving too far back.
2) Try the exaggerated wrist movement with the violin, but do not have any fingers down. Make sure you are not bending from the elbow or moving your hand too far back.
3) Get out a metronome or metronome app and select a very slow metronome speed (60-70). At this point, what I’m about to suggests works for both wrist and arm vibrato. One finger at a time, try rocking back and forth either at the metronome tick, or by 8th notes to the metronome tick. Make sure each of the two “notes” you are making is clear. That way it is a true, even sounding vibrato and not just a quiver. Then, gradually increase the metronome speed by a few ticks. Eventually over the course of several weeks you will have it at a speed where it becomes a true vibrato.