NEW YORK ( TheStreet) -- Private equity giant Apollo Global Management's ( APO) investment success in chemicals conglomerate LyondellBasell ( LYB) shows what big money private equity has discovered and what retail investors have yet to realize: Cyclical stocks can tell you the direction of corporate earnings but that doesn't mean they say anything about valuations. By looking at chemical giant LyondellBasell's continued recovery from bankruptcy and gains made by its private equity and hedge fund shareholders since an October 2010 initial public offering illustrate that confusion may abound about cyclical stock valuations. Be it steel manufacturer Alcoa ( AA), chemicals giant DuPont ( DD) or equipment maker Caterpillar ( CAT), cyclical's are rightfully seen by investors as leading indicators for corporate earnings and the overall economy. But as a read on the direction of stock market valuations, cyclical stocks may be the exact opposite. In fact, a look at the private equity and hedge fund score in LyondellBasell stands as proof of a crucial, but counterintuitive investing dynamic. While Apollo invested in LyondellBasell at peak valuation multiples, it also entered the company as it neared cyclical earnings lows after the onset of the Great Recession. Now, many expect that the opposite. In fact, after a string of blockbuster earnings quarters in a shaky economy, continued optimism on LyondellBasell's shares hinge on whether its multiple rises as earnings peak. The counterintuitive interplay between earnings and valuations is the key, after LyondellBasell reported better than expected second quarter earnings in late July. " We continue to believe that at 4.8x our 2013 EBITDA earnings before interest, taxes, depreciation and amortization forecast for the stock is reflecting more peak-like earnings despite the fact that we are below mid-cycle levels that should improve over the coming years," wrote Credit Suisse analyst John McNulty, in a note to clients after LyondellBasell's July 27 earnings. Apollo's entry point into LyondellBasell came as markets and the global economy turned from a boom to the biggest bust since the Great Depression. Saddled with a $30 billion in debt from a leveraged 2007 merger between Houston-based Lyondell and Basell of the Netherlands, a subsidiary of investing conglomerate Access Industries, the company quickly suffered from downturn and was forced into bankruptcy.