Those who are not personality psychologists would probably believe that a “generalized outcome expectancy” could either be positive (i.e. “I usually expect things to go my way”) or negative. However, in personality psychology some researchers (e.g. doi:10.1016/S0191-8869(97)80009-8) do believe that one can have both positive and negative generalised expectations at the same time.
Let´s have a look at some dictionary, say this one. “generalized” gives “made general”, and “general” in turn has the first two entries “involving, applicable to, or affecting the whole” and “involving, relating to, or applicable to every member of a class, kind, or group”. I take this to mean that a generalized expectation is is something that involves all kinds of expectations; in the special context I am talking about this would be generally “expecting things to go my way” and not “generally expecting things not to go my way”.
Maybe I am wrong, but I think that either somebody (me or the authors of the paper cited, and there are many more who believe in the “partial independence of optimism and pessimism) does not understand the meaning of “generalized” or that word has a different meaning in personality psychology than in the usual language (whatever that may be…). The thing is, I fear that such misunderstandings are rather frequent in personality psychology: words are used but their meaning is in a hard-to-understand-way slightly different.