Theoretically, stock returns should keep pace with inflation. Ultimately, returns are tied to a company's ability to generate profits. If prices rise, companies should ideally be able to pass their higher costs on to their customers, and thus preserve their profit margins. Also, the debt in a company's books erodes with inflation because the firm pays back money it borrowed yesterday with today's devalued dollars (in other words, the fixed interest rate bonds earn is worth less in real terms after inflation). Thus, other things being constant, inflation alone shouldn't affect profit margins or stock returns.
Things get complicated in practice, however. Many empirical studies have shown a negative correlation between stock returns and inflation; in other words, stocks tend to do poorly when inflation is rising or is expected to be high. The academic explanation for this observation splits a couple of different ways. For one, an accelerating rate of inflation does make profits uncertain because it becomes trickier for companies to manage their costs and price their products. This causes stock investors to demand a bigger margin of safety, which depresses equity valuations. Another reason is that even if a company were to keep its profits intact, investors discount those future cash flows more steeply because of the perceived erosion in buying power of tomorrow's dollars. This line of reasoning implies that while stocks do poorly when inflation spikes, they are undervalued.
The 1970s serve as the classic example. Inflation ranged well over 7% in that decade, and stocks fared very poorly. When the inflation surge was tamed in the early 1980s, it laid the groundwork for a long bull market in equities.
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