Most likely, the drawing is a record (rather than a preparatory study), made with the help of the studio, after a lost painting of the 1660s--which would explain the drawing's authentic signature upon a sheet with technical faults.
Signed with initials at lower left, in brown ink, "W.V.V.J". Numbered on the verso, at center, in graphite, "No. 5"; in the lower left corner, in brown ink, "262"; and at lower right corner, in broad pen and dark brown ink, "2".
Watermark: Countermark: Letters "PB" in a half-cartouche or "PBD" (similar to Churchill, nos. 6-7 and Heawood, no. 424A: 1654-79).
Velde, Willem van de, 1633-1707, Studio of.
Holford, Robert Stayner, 1808-1892, former owner.
Murray, Charles Fairfax, 1849-1919, former owner.
Morgan, J. Pierpont (John Pierpont), 1837-1913, former owner.
Collection J. Pierpont Morgan : Drawings by the Old Masters Formed by C. Fairfax Murray. London : Privately printed, 1905-1912, I, 147, repr.
Jane Shoaf Turner, with contributions by Felice Stampfle, Dutch Drawings in the Pierpont Morgan Library: Seventeenth to Nineteenth Centuries, New York, 2006, cat. no. 315.