How many stocks should be bought in Taiwan's stock market to construct a well-diversified portfolio﹖Such a simple issue has been ignored by Taiwan's financial scholars for a long time. We examine the above issue and find that the number of stocks an investor needs to buy is far less than the number suggested by the traditional wisdom. Using 3 month, 6 month and 1 year as the investment horizon, this note finds that an investor needs only 4-5 stocks to reach the risk level specified by Bird and Tippett. Although there exists an identity relationship between portfolio variance and the number of stocks, an investor still needs to develop different investment strategies in different market structures. The number of Taiwan's stocks constitute a well-diversified portfolio is far less than the traditional suggestion is a living proof.