Eighty-six years ago this week, the stock market hit its worst low. Today, with markets near all-time highs, things aren’t as different as you might think.

Then, as now, companies and investors were engaged in a massive power struggle. Then, companies were worth far more than investors thought -- and would do almost anything to keep investors from unlocking the hidden value. Today, companies may be worth less than investors think -- and are equally intent on preventing investors from noticing.

On...