The sight picture should look like the round bead is snugged into the U or lowest part of the V, without hiding any of the bead with the rear sight. With this sight picture, the point of impact should be on the top edge of the bead at the range for which you've sighted it with the ammunition you intend to hunt with (and this should be your "stopping" load, in the case of a dangerous game rifle).
Sight pictures are a relative thing, being quite subjective and depending greatly on the shooter doing the aiming - hence, it should not alarm that your rifle is not shooting where you aim. In this case, it is a simple matter to file in the rear sight, though this may take the better part of an afternoon. Disregard all the highbrow hooey about fine rifles being "regulated"; they are "on" for the one doing the shooting and that's it. Get some small files and have at the rear sight slowly, while at the range. File the rear sight in the direction you want the shots to go - in your case, down. When you're done, polish a bit w/ emery cloth and stones, use one of the touch up bluing products on your work (it won't show much).
Even on a dangerous game rifle, I don't want the rifle sighted much less than 100 yards. This will admittedly depend on the caliber and intended use. On a .458 or similar, 100 yards would be my choice; on a .375, I'd prefer about 150 yards. The big thing here is not to sight in too far out such that your tragectory remains fairly close to line of sight (you'll not have to worry over mid range misses). Don't hedge your bet and file down only part way, thinking you'll just hold low. Nobody holds low in a tight spot, nor do they take a fine bead - nearly everybody will tend to shoot high.
Hope this is useful.
