Packaged food companies have faced two bouts of input cost inflation over the past six years. During the 2007-08 wave, companies were able to pass on those higher costs to consumers.
But during the spike in 2010-11, companies had less room to raise prices and instead cut back on advertising and promotional (A&P) spending to keep their operating margins from shrinking.
According to Wrede, cutting back on marketing was a popular tool at Kellogg, General Mills and Smucker.
Cost inflation is still working its way through the system, but isn't as bad as it was over the past few years. General Mills CEO Ken Powell told CNBC last month that inflation will be "very manageable" over the next 12 months and that it expected its product prices to remain stable.
But after a few years of reduced marketing spending, there is growing risk that companies will start to see volumes decline unless they beef up their ad budgets again.
Wrede is particularly worried about the volume outlook for General Mills and downgraded the stock to "underperform" from "hold" on Friday.
"The stock trades close to all-time highs and most of the year-to-date performance has been driven by multiple expansion, making it, in our view, more vulnerable to a potential valuation pullback for the sector," the analyst wrote.
Unlike Smucker's, which has announced plans to boost marketing spending, General Mills has not stated any plans for an increase, Wrede said. Kellogg is not as expensive as General Mills, hence not as much pressure on the stock, he added.
With General Mills' stock trading at a big premium to its five-year average, Wrede views the stock as overvalued given the deteriorating fundamentals. His new $44 price target implies about 12 percent downside.
For investors that still have an appetite for food stocks, Wrede has a "buy" rating on ConAgra.
"It's much cheaper than all of the other packaged food names," Wrede told CNBC. "It plans to grow earnings 10-plus percent per year for the next 10 years."
—By CNBC's Justin Menza. Follow him on Twitter