As the other answer to this question suggests, we must construct a character sketch of Portia's father based on conjecture and inference, as he is dead before the play begins. While the other answer to this question is perfectly correct, I do think there's an alternative character sketch that we could create based on the casket test.
It's probable that Portia's father devised the casket test in order to prevent unworthy men from marrying her. Let's consider the nature of the test itself, though: doesn't it seem a little controlling (and slightly eccentric) to devise an intricate puzzle for your daughter's suitors to solve? Indeed, if we seriously consider the casket puzzle, it begins to seem very controlling indeed, as Portia's father is essentially ensuring his daughter will marry the kind of man he thinks is appropriate. This kind of controlling personality was probably not strange for fathers of...
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Shakespeare's day (men had significant power over women, and fathers more or less directed their daughters' lives), but it nonetheless seems part of Portia's father's personality.
Another aspect of the casket puzzle is that any suitor who fails in his attempt to solve the riddle must remain a bachelor (i.e. single) for the rest of his life. In devising such an addendum to the challenge, Portia's father seems to have a very sinister sense of humor, and we can easily imagine him deriving a grim sense of satisfaction from each failed attempt.
In short, while we can see Portia's father as a benign and caring figure, it's also possible to devise an alternative character sketch. Indeed, if we carefully consider the casket puzzle, we can easily see Portia's father as a controlling parent with a strangely twisted sense of humor.