Does the price of undervalued stock fall when general market decline

Here is our question, does the price of undervalued stock fall when general market decline? If you bought some undervalued stocks, and the general stock market, like the S&P 500 index, is expected is decline, will your undervalued securities fall down along with the general market?

Warren Buffett, the legendary value investor, said yes as early as in 1958.

In Buffett Partnership Letter, February 6, 1958, Buffett said,

My view of the general market level is that it is priced above intrinsic value. This view relates to blue-chip securities. This view, if accurate, carries with it the possibility of a substantial decline in all stock prices, both undervalued and otherwise.

In January 24, 1962 letter to his partners, he reaffirmed his view,

The generals [generally undervalued stocks] tend to behave market-wise very much in sympathy with the Dow. Just because something is cheap does not mean it is not going to go down. During abrupt downward movements in the market, this segment may very well go down percentage-wise just as much as the Dow. Over a period of years, I believe the generals will outperform the Dow, and during sharply advancing years like 1961, this is the section of our portfolio that turns in the best results. It is, of course, also the most vulnerable in a declining market.

Because stocks, even the undervalued ones, would fall market-wise with the general market level, it is important for the value investors to be prepared for their unfavorable short term price volatility.