1. decline your broker's suggestion.
2. follow your broker's advice, since that is what you are paying him for.
Choose the correct option.
You should decline. The implication of the broker's argument is that stocks that have declined will continue to decline and ones his firm recommends will increase in value. Since all brokers in his firm are giving the same advice to their clients, any value of that advice is already reflected in the prices of the stocks. Moreover, if stocks that fall in value are more likely to fall in the future than other stocks, their prices would have fallen even more than they did. Every time you buy or sell a stock your broker earns a commission---he has an interest in getting you to trade frequently.
It is important to realize here that stock prices fall as the result of a change in investors' evaluation of the future earnings of the firms in question. That new lower valuation of the future earnings reflects market participants' interpretation of all information available. Similarly, the prices of other stocks increase because market participants, based on all information available to them, revise their valuation of the future earnings from those firms upward.
Since new information about the future performance of all stocks is just as likely to be good as bad relative to what is now known, regardless of whether the stock price has gone up or down during the past, any stock price is just as likely to rise or fall as any other. If new information about a particular stock is more likely to be bad, investors will have bid its price downward to take this into account---if it is more likely to be good, they will have bid the stock's price upward.
So you can expect to gain by purchasing one particular stock or type of stock rather than another only if you have information about the future earnings of those stocks that the rest of the market does not have. Anything your broker tells you based on the analysis of the research department of his firm can't possibly be new information because the research report has been sent to every broker in the firm and its conclusions passed along, in turn, to every one of those brokers' clients, all over the world.