I use a Stanley Hobby Plane from the hardware store for about 10 bucks. Does the same thing.
Mark the arrow with a sharpie or pen @3" then 6" and finally at 9" from the nock end of a nock tapered shaft. Make a circle ring around the shaft.
Set the plane to take extremely paper thin shavings. Start at the 3" mark and make one pass to the rear, turn the shaft a hair, or just under a 1/16", and make another cut, continue till you make passes all the way around to where the 1st cut started. Then go to the 6" mark and repeat, then finally to the 9" mark and proceed to make the cuts all the way back over the the 6 and 3" marks to the nock end. This will make a 11/32" shaft tail tapered to 5/16"
One you get the hang of it you will be glad you did not dump a 100bucks on the same plane with a arm and holder, much like the arm and holder you already own.... your arm. Only way I've ever done it.