does a more risky stock necessarily ean a higher return on average
than a less risky one?

Baznichols --

No.  Performance of individual stocks cannot be predicted.

Motley Fool, an investment site, has had lots of fun analyzing a small
group of poor performers in "Dogs of the Dow" and "Pigs of the Dow." 
What this year's "pigs" show is that individual securities are too
variable to predict returns:
Motley Fool
"Pigs of the Dow Get Slaughtered" (Durrell, Jan. 13, 2006)
http://www.fool.com/news/commentary/2006/commentary06011309.htm

However, Modern Portfolio Theory says that a group or portfolio of
risky stocks -- if properly diversified -- will return a higher
average return.  It also says that managers within those higher risk
corporations should be investing in higher risk/higher return projects
and not putting the company's money in "safe" investments like real
estate:
Wikipedia
"Modern Portfolio Theory"
http://en.wikipedia.org/wiki/Modern_Portfolio_Theory

Of course, Motley Fool's group of "dogs" and "pigs" are a portfolio. 
But they're small portfolios, dominated by weak performance of one or
two stocks.  It's a generally accepted rule-of-thumb that about 10
stocks give an investor good statistical diversification.

For further research, I might suggest the following Google search strategy:
"modern portfolio theory" "individual stocks"
"modern portfolio theory" individual stocks

Best regards,

Omnivorous-GA

I would answer that in general yes.  (don't listen to that last guy)
You have to define risk in some way, and a lot of finance people do
that with beta.
http://www.investopedia.com/terms/b/beta.asp

A stock that has a beta of 2 is suppose to be twice as volatile as the
market.  So if the market goes up 10% one year, the stock will go up
20%.  However, the converse for this stock is also true, when the
market tanks, the stock double-tanks.
But since you can count on the markets generating positive returns
over the long haul, a portfolio of higher beta stocks should generate
even higher returns.  Most financial planners and investment advisors
structure their recommended portfolio allocations based on this --
younger people get risker portfolios (that is more stocks and with
higher betas) and older people get safer portfolios (less stocks,
lower beta stocks, and more bonds).

Baznichols --

While Wolf-GA is correct to introduce the concept of beta, they've
flunked finance 101.

Much of the answer here depends on interpreting "higher return on
average".  Will a mix of stocks produce a higher return "on average"? 
Yes, if properly diversified -- but only because you've lumped it in
with others of similar risk category.

But company-specific risks are different from systematic risks.  Beta
gives you a way to manage systematic risk; indeed that's what it
measures:
http://www.12manage.com/methods_capm.html

You can diversify it and manage it.  You can't manage company-specific
risk (though bond ratings, Value Line and others try to do it).  So,
will a risky stock return more than a less risky one?  No way to tell.

In fact, if your investments are all in "similar beta" companies in a
declining industry, returns will be lower than average.

Best regards,

Omnivorous-GA

I think this guy I'm jarring with may have taken Finance 101 but has
yet to set up his first Ameritrade account.

"You can't manage company-specific risk (though bond ratings, Value
Line and others try to do it)."

Options are a tool to do that.  

"So, will a risky stock return more than a less risky one?  No way to tell."

This also cannot be proven.  There are trading wizards out there who
clean up in the markets -- academic research supports this.  But I
guarantee that you are not going to get any insight for $5, and
certainly not from some know-it-all with a copy of his finance book on
Google Answers.