Wall Street’s Big Media bulls have had a great run. Stocks for the group of companies that includes Disney, News Corp, Time Warner, CBS, Viacom, and Discovery have outpaced the overall market for more than three years. And just this year, the Dow Jones U.S. Media Index has appreciated 35% while the benchmark Standard & Poor’s 500 rose 15%. Yet I’ve been struck lately by the growing number of reasons to suspect that the joy ride is about to end. They started to crystallize for me today when I read Cowen and Co analyst Doug Creutz’s “State Of Big Media” report making the case to remain “moderately positive” about the sector. Like most of his analyses, it’s smart and identifies the important questions that the Street will want CEOs to address in the upcoming Q3 earnings season. But Creutz’s case for remaining optimistic is so meek that you’d think it was prepared by the guy who coached President Obama for his first debate with Mitt Romney.

Creutz starts by cautioning investors that media stocks have become expensive. The big companies that he covers trade for 14 times earnings, ahead of the S&P 500’s 13.3 times. That’s quite a change from last year when the stocks traded for 11.5 times their earnings, in line with the overall market. As a result, he says, “we think outperformance over the next 12 months is likely to be more modest than that enjoyed over the last few years.” On top of that, the analyst notes that his upbeat case assumes that the economy can “muddle through” the next year. He says that the “#1 risk to Big Media stocks, by a wide margin” is the possibility of a global downturn — which could be triggered if a European country defaults on its debt, or there’s no resolution in the U.S. to the rush off the so-called “fiscal cliff.”

On top of those warnings, Creutz says he’s merely “neutral” about the possibility that advertising will be strong, or that movie theaters will see a resurgence of box office sales. (Domestic sales remain “under pressure” while overseas “trends remain highly favorable, particularly for big-budget tentpole films,” he says.)

OK, so why should we be optimistic? Creutz basically asks investors to take his side in some highly debatable propositions.

For example, he’s  confident that Big Media’s pay TV networks “will continue to be able to increase rates at a healthy clip over at least the next two to three years.” Maybe so. But before you accept that, take a look at the powerful counterargument that Bernstein Research’s Craig Moffett makes, which I summarized last week. He says that the poorest 40% of the country is so financially stretched that it can’t afford to keep paying higher prices for TV, wireless phones and broadband. Creutz says cord cutting is not a meaningful threat because “we believe TV remains an ‘essential’ service for most Americans.” Yet I doubt that many investors would feel so sanguine if the penetration rate for pay TV households dropped from 85% to, say, 75%.

Creutz also is optimistic about programmers’ ability to generate additional revenue by selling shows overseas and to digital streaming companies such as Netflix and Amazon. The concern here is that those online sales could backfire. We still aren’t sure whether broadcasters’ falling ratings in the first few weeks of the new prime time season may be at least partly attributable to the growing number of people who watch videos online, where they aren’t counted. And there’s still a raging debate over whether Netflix played a big role in the huge ratings drop this past year at Nickelodeon.

Then there’s investors’ favorite reason for liking Big Media: Companies are giving cash back to them — repurchasing shares and increasing dividends — instead of using it to expand or buy other firms. Execs “appear reluctant to squander their hard-won credibility” with shareholders who need to see their investments pay off, Creutz says. But companies also may simply be giving away their seed corn. Legendary investor Warren Buffett said this year that “Continuing shareholders are hurt unless shares are purchased below intrinsic value. The first law of capital allocation – whether the money is slated for acquisitions or share repurchases – is that what is smart at one price is dumb at another.” With Big Media stocks now trading above the overall market at 14 times earnings, I’ll let you decide whether their capital allocation strategies are smart or dumb. Put another way, you can judge whether they reflect confidence in their own prospects as opposed to fear that, without a special incentive to stay, lots shareholders might soon decide to flee.