How to achieve a 15% long-term annualized return? Prerequisites: 1. "Long-term" means at least 10 years. 2. The target company's P/E ratio will eventually revert to a reasonable P/E ratio of 25. 3. You are within your circle of competence and can select companies with a 0-15% annualized net profit growth rate over the next 10 years. 4. You are not capable of selecting companies with a long-term annualized return higher than 12%. Substituting these prerequisites into the formula, you can calculate the return. g is the long-term annualized net profit growth rate, r is the long-term annualized return, and PE is the purchase P/E ratio to achieve r at the corresponding g. The data in the table makes the conclusion clear. For companies with a growth rate of 0-15%, it's impossible to achieve a 15% annualized return if you buy in with a PE ratio ≥ 16. Only companies with extremely high growth rates (>20%) and extremely low PE ratios (medium-growth companies), or both, can truly achieve a 20% annualized return. High P/E ratios coupled with moderate growth rates create a long-term return trap. This can be summarized in one sentence: Buy companies with a P/E ratio not exceeding X times, whose annualized net profit growth rate over the next 10 years will be no less than X%. This is the guiding principle and methodology for achieving a 15% annualized return over the long term. To put this into practice, you must first understand the two underlying prerequisites: 1. The company you want to buy is within your circle of competence. 2. X cannot exceed 15. The first point is easy to understand. If you don't understand the company, any P/E ratio you use is likely to be wrong. The second point, why can't X exceed 15? Because companies with an annualized net profit growth rate of no less than 15% for 10 consecutive years account for no more than 5% of all listed companies. If you think you can consistently select companies with an annualized net profit growth rate exceeding 15% over the next 10 years, this is extremely difficult, a low-probability event, which will significantly increase investment risk and could ultimately lead to substantial losses. Smart investors often underestimate their stock-picking abilities. Buffett generally avoids buying companies with a P/E ratio exceeding 15 because his company selection process implicitly assumes that, in the long run, he cannot consistently identify companies with an annualized net profit growth rate exceeding 15% over the next 10 years. Accepting this implicit assumption is crucial. Once you do, you'll formulate your strategy accordingly, making it easier to achieve decent long-term annualized returns. Personally, even for the top-tier companies, I only dare to assign a maximum of 10% annualized net profit growth rate over the next 10 years. Therefore, the highest P/E ratio I assign to top-tier companies is only 10. This applies to companies like Kweichow Moutai, Tencent, and Apple. Why can Buffett buy into some companies he favors at a maximum P/E ratio of 13-14, while I only dare to buy into companies I favor at a maximum P/E ratio of 12? Because I acknowledge that my company-picking ability is inferior to Buffett's, requiring a lower P/E ratio and a larger margin of safety. Returning to the initial question, how can one achieve a 15% annualized return over the long term? Within your circle of competence, if you believe a company's annualized net profit growth rate will reach 15% over the next 10 years, buy it when the target company's PE ratio is ≤12. Within your circle of competence, if you believe a company's annualized net profit growth rate will reach 12% over the next 10 years, buy it when the target company's PE ratio is ≤12. Within your circle of competence, if you believe a company's annualized net profit growth rate will reach 10% over the next 10 years, buy it when the target company's PE ratio is ≤10. Within your circle of competence, if you believe a company's annualized net profit growth rate will reach 7% over the next 10 years, buy it when the target company's PE ratio is ≤7. In short, buy companies with a projected annualized net profit growth rate of at least X% over the next 10 years at a PE ratio not exceeding X. Continue in this way, and you may achieve a long-term annualized return of 20% (I can't guarantee this; it also depends on patience and luck).