第一ROE要穩定，
第二要能配得出現金，
最近一年盈再率小於80%，
最近3年配息率大於40%。
第三大條件不會變的公司，
產品不會變、
產業地位不會變的龍頭股，
想3秒鐘就理解的公司，
懂得挑不會變的公司巴菲特神功大概就練成了。
There are three primary criteria for selecting stocks. Firstly, the company's ROE must remain stable. Secondly, the company should have high dividends, which means that the dividend payout ratio in the last three years should be over 40%, and the current dividend should be less than 80% of last year's PR%. The third and final criterion is that the company should have durability. Its products should be irreplaceable, and it should be a leading company in an industry with a stable status. Ideally, the company should be easily understandable within three seconds. If you can identify a durable company, you possess Buffett's investment skills.
選好股之後接下來就等便宜買，抱到貴才賣，
底下介紹貴淑價怎麼算。
股價不是亂漲的，沿著ROE所定義的價值線上下擺動，
所謂價值線是中間那條線，又稱合理價，
即跟正常時期定存利率6.7%一樣報酬的價格，
因做任何投資都是跟定存利率做比較。
股票不是買在合理價，因股票有風險要求的報酬較高，
必須比定存6.7%高1倍以上才會買，即15%以上才夠便宜。
Once you have selected stocks, you should wait to purchase them at a cheap price and then sell them when they become more expensive. The following explains how to determine what is considered cheap and expensive. Stock prices do not fluctuate randomly. Instead, they move up and down along the value line, which is determined by the company's ROE. The value line is the middle line, also known as the fair price, which is equivalent to the 1-year time deposit rate of 6.7% during normal periods. When considering investments, it is important to compare them with the interest rate. Stocks are riskier than deposits and require a higher discount. Therefore, stocks should not be purchased at the fair price. To be considered cheap enough, the price should be at least 15% higher than the 1-year time deposit rate of 6.7%.
同學問貴淑價應跟隨利率調整嗎？
理論上要，但一連動即變成要去預測利率升降？
這是不可知的，
我2013年買VALE和AESAY時，
並不知巴西利率3年後會從7%劇升到15%。
Students may ask whether the cheap and expensive prices should be adjusted with interest rates. Theoretically, yes. However, once the prices are linked to interest rates, we would have to predict the rise and fall of interest rates, which is unpredictable. For example, when I bought VALE and AESAY in 2013, I had no way of knowing that interest rates in Brazil would rise sharply from 7% to 15% in three years.
而且同一市場，各類股本益比差距也很大，
如美股2016年初AMZN本益比176倍，石油股卻僅2倍。
若要跟著利率調整本益比如何調呢？
Furthermore, there is a significant difference in the PER among various sectors in the same market. For instance, in early 2016, the PER of Amazon.com (AMZN) was 176 times, while the oil industry's PER was only 2 times. It is not clear how to adjust the PER based on interest rates.
比較可行的辦法是以正常時期利率6.7%為準，
再搭配GDP來加減，
GDP理論在講稿16/21詳述。
A more practical approach is to base the calculation on a 6.7% interest rate during a normal period and adjust it according to the GDP. The GDP theorem is explained in detail in Lecture 16/21.
講稿4/21曾證明只要高ROE，便宜買，報酬率就會最大，
現在就用ROE和買進價來算報酬率，
ROE由常利，經常淨利算得，
During Lecture 4/21, it was demonstrated that the greatest investment return can be achieved when both the Return on ROE is high and the purchase price is cheap. We can calculate the expected return by using the ROE and purchase price. The ROE is determined by recurring net profit.
常利 = 淨利 – 一次性利益
recurring net = net profit - one-time profits
一次性利益如賣土地和賣股票
內在價值隱含經常的概念，每年都發生的利益才算數。
有些公司在獲利不佳時會賣土地來美化帳面，必須扣除。
One-time profits include gains from the disposal of land and stocks. The concept of intrinsic value implies that only profits that occur consistently each year are considered. Some companies may sell land to improve their financial statements when they experience poor profits, but these gains must be deducted as they are not recurring.
一次性利益才須扣掉，而非業外(投資收入)，
波克夏、鴻海、台達電、巨大都是投資收入比率高的公司，
若投資收入比重高就不好這些偉大公司都會被排除掉。
Non-operating profits, such as investment income, will not be deducted as only one-time profits are considered. Companies such as Berkshire Hathaway, Hon Hai Precision Industry, Delta Electronics, and Giant Manufacturing, which have high investment income, would be eliminated if investment income were deducted. These are all great companies.
鴻海、巨大為何投資收入多？
因為透過轉投資去海外設廠，它們的投資收入仍屬本業。
對於公司的獲利我們在意的是有無經常性，
至於來自投資收入無所謂，
而財報不透明看合併報表即可。
Hon Hai Precision Industry and Giant Manufacturing have high investment income because they establish overseas factories through subsidiaries. Their investment income is considered part of their operating business. When evaluating a company's profit, what matters is whether it is recurring, including investment income. If you suspect that a company's financial report is not transparent, it is recommended to review the consolidated statement.
牽涉到淨利的指標，ROE、盈再率、EPS、大於5億元
都改用常利來算。
金融股只扣賣資產，因投資屬本業。
Indicators related to net profit, such as ROE, PR%, EPS, and net profit over NT$500 million, will be adjusted to reflect recurring net profit. Financial stocks only deduct gains from the disposal of assets, as gains from the sale of stocks are considered part of their operating business.
常利的觀念源自我在怡富證券當研究員時學到的觀念，
restated earnings(重編淨利) 即常利
reported earnings(報表淨利) 為稅後淨利
restated = reported - 處分利得
國外也有recurring earnings類似的講法。
The concept of recurring net profit originated from my experience as an analyst at Jardine Fleming. Restated earnings are equivalent to recurring net profit, while reported earnings refer to net profit. Restated earnings are calculated by subtracting disposal gains from reported earnings. Similar terminology, such as recurring earnings, is used in other foreign securities firms.
一次性利益包括
1. 異常利益
2. 異常稅額
3. 暴增驟減
One-time profits include
1. Unusual income
2. Tax abnormalities
3. Unusual high and low
1. 異常利益
台股 : 土地+投資+其他+租金+補助+停業
土地 = [處分不動產、廠房及設備利益或損生]
投資 = [處分投資利益或損失]
其他 = [其他收入-其他] - [其他利益及損失-其他] + [其他營業收入-其他] - [其他業外收入(支出)]
租金 = [租金收入] + [業外租金收入(支出)]
補助 = [補助收益]
停業 = [停業單位損益]
感謝徐廣福桑指認上述會計科目
1. Unusual income
Taiwan Stocks: Land + Investment + Others + Rent + Subsidy + Discountinued Operations
Land = [Disposal gains or loss on real property, plant and equipment]
Investment = [Disposal gains or loss on investment]
Other = [Other income-other]-[Other income and losses-other] + [Other operating income-other]-[Other non-operating income (expense)]
Rent = [Rental Income] + [Non-operating Rental Income (Expenses)]
Subsidy = [subsidy income]
Discountinued Operations = [Income or Loss from Discountinued Operations]
Thanks to Guangfu Siu for identifying the above accounting accounts
美股：[unusual expense]，包含
賣土地和賣股票、停業損失、商譽、持股漲跌
商譽：4Q18 KHC提列154億美元商譽減損
持股漲跌：4Q18 波克夏認列354億美元持股跌價損失
US stocks: [unusual expense] including
Sale of land and stocks, Income or Loss from Discountinued Operations, goodwill, capital gain or loss on stock holdings
Goodwill: 4Q18 KHC withdraws $15.4 billion in goodwill impairment
Capital gain or loss on shareholding: 4Q18 Berkshire recognizes $35.4 billion of capital loss in holdings
港股：[特殊項目]+[出售資產]
中股：[非流动资产处置损失]+[其中:非流动资产处置损失]
Hong Kong Stocks: [Special Items] + [Sale of Assets]
China Stocks: [loss on disposal of non-current assets] + [including: loss on disposal of non-current assets]
2. 稅率異常也會影響常利的推估，
4Q17 川普稅改造成波克夏ROE由6%暴增為16%，
該現象非美股獨有，其它國家亦然，如RBGLY，
因此常利須再扣除異常稅額：
2. Abnormal tax rates can also impact the estimation of recurring net profit. For example, in the fourth quarter of 2017, Trump's tax reform caused Berkshire Hathaway's ROE to increase from 6% to 16%. This situation is not unique to US stocks, as seen in other countries like Reckitt Benckiser (RBGLY). Therefore, abnormal tax must be deducted from recurring net profit.
當稅率大於相鄰稅率1.2倍或小於0.8倍時，
異常稅額＝淨利 - 稅前x(1-相鄰稅率)
Abnormal tax is calculated when the tax rate is 1.2 times greater or 0.8 times less than the adjacent tax rate.
Abnormal tax amount = net profit - pre-tax x (1-adjacent tax rate)
相鄰稅率採percentile(相近3年稅率, 0.5)，
相鄰稅率上下限訂為35%和0，否則取上期相鄰稅率。
稅前虧損時，不調整異常稅額
The adjacent tax rate is determined by using a percentile of the tax rate for the previous three years (0.5). If the tax rate exceeds the upper limit of 35% or falls below the lower limit of 0%, the adjacent tax rate from the previous period will be used instead. If the company incurs a loss before tax, the abnormal tax amount is not adjusted.
3. 一次性利益除列在異常利益之外，
也藏在各會計科目，導至常利暴增或驟減，例如：
2018/12 UL 出售業務利益列於營利，導致營利暴增
2018/12 FMS 業外收入暴增
2018/9 NWL 常利暴增查不出原因
3. One-time income is considered unusual income and can be hidden in various accounts, leading to unusual high and low in recurring profits. For example, in December 2018, Unilever's (UL) sale of business benefits was recorded in their operating profit, resulting in a surge in operating profit. Similarly, in December 2018, Fresenius Medical Care (FMS) reported a surge in non-operating income. In September 2018, Newell Brands (NWL) experienced a sudden surge in recurring net profit, for which no clear explanation was found.
驟減：常利把最差換成次差
過去5年常利把最差換成次差，以防一年驟減逆轉淑貴
次差 = percentile(前5年常利, 0.3)
In case of a unusual low in recurring profit, the worst result is replaced with the second worst result from the past five years. This is done to avoid expensive stocks turning from cheap to expensive due to a sharp decline in profit in a given year.
The second worst recurring profit = percentile (the first 5 years of recurring profit, 0.3)
暴增A：營收未大增，但常利率暴增
若該年營收小於去年營收x1.15
且常利率大於percentile(前5年常利率, 0.7)x1.3
則暴增 = 常利 - 營收 x percentile(前5年常利率, 0.7)
常利率 =常利 / 營收
感謝陳坤良同學指導
Unusual high A：
In case of a unusual high in recurring profit despite a lack of significant sales growth, the following criteria are used:
If the sales for the year are less than 1.15 times the sales of the previous year,
and recurring profit margin is greater than percentile (the first 5 years recurring profit margin, 0.7) x 1.3
then unusual high = recurring profit - sales x percentile (the first 5 years of recurring profit margin, 0.7)
recurring profit margin = recurring profit/sales
Special thanks to Curry for providing guidance.
暴增B：常利暴增3倍，把最佳換成次佳
次佳 = percentile(前5年常利, 0.7)
感謝陳坤良同學指導
Unusual high B：
If the recurring profit has increased by three times, then the best recurring profit will be replaced with the second best
Second best of recurring profit = percentile (the first 5 years of recurring profit, 0.7)
Thanks Curry for instruction.
有了常利之後， 即可用前5年常利來推算預期常利
只取前5年因年代更久遠的獲利不具參考意義
其中今年為過去4季
After obtaining the recurring profits, we will use the recurring profits of the previous five years to calculate the expected recurring profits.
Only profits from the first five years are considered, as profits from earlier years are not relevant for reference. For this year, we will use the profits of the past four quarters.
暴增驟減只局限在後2年常利，
前3年則由底下「特別高、特別低」來處理。
The unusual high and low are confined to the recurring benefits of the last two years. The first three years are dealt with based on "exceptionally high" or "exceptionally low" below.
前3年常利：
取percentile(第一年:第三年, 0.7)
取percentile(第一年:第三年, 0.3)
後2年常利採簡單平均
Recurring profits for the first 3 years:
Take percentile (first year: third year, 0.7)
Take percentile (first year: third year, 0.3)
Simple average for the last 2 years
先處理某一年常利特別高或特別低之特別狀況
若後2年平均常利為正
特別高，percentile(前3年, 0.7)大於後2年平均之2倍，
如長榮(2603)
2019年 983
2020年 24,186
2021年 334,250
2022年 44,177
2023年 44,177
Firstly, address exceptional scenarios where the recurring profit for a specific year is unusually high or low.
If the average recurring profit for the next two years is positive.
For instances of exceptionally high recurring profit, if the percentile (the first 3 years, 0.7) exceeds twice the average of the last 2 years, consider Evergreen (2603) as an example:
2019: 983
2020: 24,186
2021: 334,250
2022: 44,177
2023: 44,177
特別低，percentile(前3年, 0.3)小於後2年平均之0.1，
如2501.T 札幌啤酒
2019年 6,792
2020年 (17,139)
2021年 12,218
2022年 6,650
2023年 7,068
When the recurring profit is exceptionally low, with the the percentile (the first 3 years, 0.3) falling below 0.1 times the average of the last 2 years, take for example Sapporo Brewery Co., Ltd. (2501.T):
2019: 6,792
2020: (17,139)
2021: 12,218
2022: 6,650
2023: 7,068
以上特別高和特別低之預期常利 = 後2年平均
The expected recurring profits for the above exceptionally high and low, are based on the average of the last 2 years.
再來處理底下狀況：
當常利往上，後2年平均大於percentile(前3年, 0.7)時，
預期常利 = 0.3xpercentile(前3年, 0.7) + 0.7x後2年平均
Handle the following scenario next:
When recurring profits increase, and the average of the last 2 years exceeds the percentile (previous three years, 0.7),
Expected recurring profit = 0.3 x percentile (previous three years, 0.7) + 0.7 x average over the last two years
當常利往下，後2年平均小於0.8xpercentile(前3年, 0.3)時，
預期常利 = 0.3xpercentile(前3年, 0.3) + 0.7x後2年平均
When recurring profit decline, the average of the last 2 years is less than percentile (the first 3 years, 0.3),
expected recurring profit = 0.3xpercentile (the first 3 years, 0.3) + 0.7x the average of the last 2 years
當常利持平時，
預期常利 = 0.55xpercentile(前3年, 0.3) + 0.45x後2年平均
When recurring profit is flat,
expected recurring profit = 0.55xpercentile (the first 3 years, 0.3) + 0.45x the average of the last 2 years
預期ROE = 預期常利 / 去年淨值
用預期常利來求預期ROE，而非直接拿過去5年ROE來平均，
因為ROE平均法當淨值變動大時會失準，
如買回庫藏股和大額現金增資。
Expected ROE = expected recurring profit / last year's net assets
Instead of directly averaging the ROEs of the past 5 years, we use the expected recurring profit to calculate the expected ROE. This is because the average ROE method can be inaccurate when there are significant changes in net assets, such as a buyback of treasury shares or a large amount of rights issue.
用預期常利求得的預期ROE，
非指公司未來獲利僅為預期常利，而是將按預期ROE進行，
隨著淨值增加未來獲利仍會成長。
Obtaining expected ROE through expected recurring profit does not imply that the company's future profits will be limited to expected recurring profit. Instead, they will be achieved through the expected ROE. As net assets increase, future profits will continue to grow.
若覺得內定預期常利不合理可手動調整，
如景氣循環股在景氣谷底或公司一時變不好時，
請自行將正常時期常利代入。
If you find the default expected recurring profit to be unreasonable, you can manually adjust it. For instance, during the bottom of the business cycle of cyclical stocks or when the company's performance deteriorates for a while, you can substitute the recurring profit during a normal period by yourself.
可是以常利來算卻是便宜的，
股價跌到此就跌不下了，
顯示股價反映常利，而非淨利。
However, using recurring profit to calculate GSK's stock price is cheap. The stock price cannot fall below the cheap price, indicating that the stock price reflects recurring profit rather than net profit.
即得 買(1+r) = 息1＋賣
移項，買=息1/(1+r) ＋ 賣/(1+r)......(1式)
Change 100 to "buy" and 120 to "dividend1 + sell"
then buy (1+r) = dividend 1 + sell
Transfer item, buy = dividend 1/(1+r) + sell/(1+r)......(Formula 1)
把100改成「買」，120改為「息2＋賣」
得 買=息2/(1+r)^2＋ 賣/(1+r)^2......(2式)
Change 100 to "buy" and 120 to "dividend2 + sell"
Get buy=dividend2/(1+r)^2＋ sell/(1+r)^2......(Formula 2)
買股票的狀況是：
買了股票，第1年配息1，第2年配息2及股票賣出，
其實是1式和2式的綜合：
買了股票 ＝ 買
第1年配息1 ＝ 息1/(1+r)
第2年配息2 ＝ 息2/(1+r)^2
股票賣出 ＝ 賣/(1+r)^2
所以 買 = 息1/(1+r)+息2/(1+r)^2+...+賣/(1+r)^2
The status of buying stocks is:
I bought the stock, the first year dividend1, the second year dividend2 and the stock sold,
It is actually a combination of Formula 1 and Formula 2:
Stock bought = buy
First year dividend1 = dividend1/(1+r)
Second year dividend2 = dividend2/(1+r)^2
Stock sold = sell/(1+r)^2
So buy = dividend1/(1+r)+dividend2/(1+r)^2+...+sell/(1+r)^2
這裡有3個問題：
1. 股息有無再投入買股？
有人把折現公式兩邊乘以(1+r)^8，展開之後式子變成
買(1 + r)^8 = 息1(1+r)^7 + 息2(1+r)^6 + ……
乍看之下每年配出來的股息好像有再投入買股？
股息折現公式的股息並未再投入。
There are 3 questions here:
1. Are dividends reinvested in stock purchases ?
Someone multiplies both sides of discount formula by (1+r)^8, and the formula becomes
Buy (1 + r)^8 = dividend1(1+r)^7 + dividend2(1+r)^6 + ……
At first glance, it seems that dividends paid out every year have been invested in buying shares ?
Dividends of dividend discount formula are not reinvested.
底下式子才是有再投入，
股息再投入買股，則分子為0，
最後賣出價將不只 1 股而是好幾股
The formula below is used for reinvesting dividends. If dividends are used to purchase shares, the numerator will be 0. The final selling price will not be for a single share but for multiple shares.
謝謝陳新元桑指導。
Thanks to Sinyuen Chen for his instruction.
2. 股子呢，擺在哪裏？
股子和母股全歸到最後的賣出價，賣 = 母股+子股。
2. Where are the stock dividends?
The stock dividends, along with the parent stock, are both factored into the final selling price. Therefore, the selling price equals the sum of the parent stock and the stock dividends.
3. 為何要假設到8年？
同學看到8年就頭皮發麻，
說「我股票連8天都沒抱過，遑論8年！」
這條公式未強制要抱多久，只是算一個數字給大家參考。
任何投資理論都要時間夠長才會成立，
我的主張「高ROE，便宜買，保證能賺到大錢」
須在什麼前題下才成立？時間要夠長！
3. Why should we assume a period of 8 years?
The assumption of an 8-year period made some students uneasy and they exclaimed, "I haven't held stocks for 8 days, let alone 8 years!" However, it is important to note that this formula does not mandate any specific holding period but rather provides a reference point. Investment theories are typically based on sufficiently long assumptions. My proposition is to "buy cheap with a high ROE, and guarantee big returns." However, for this proposition to hold true, it must be established under certain prerequisites, with the most critical being a sufficiently long investment horizon.
持有時間要多長？
看還原股價，即便中碳，若僅回顧2年不保證賺錢，
近2年還原股價49-57元，不如歷史最高價95-96元高。
可是回顧5年以上則一定賺錢，
還原股價81-102元，遠高於歷史股價45-60元。
What is the optimal holding period? Examining the adjusted stock price of China Steel Chemical, it is not a guarantee of profit if we only consider the past 2 years. Over this period, the stock price has fluctuated between NT$49-NT$57, which is lower than the historical high of NT$95-NT$96. However, looking back over the past 5 years, it is likely to be profitable as the adjusted stock price has ranged from NT$81-NT$102, much higher than the historical stock price of NT$45-NT$60.
至於5年以上，同學問「為何不取6年、7年，卻挑8年？」
這就無法解釋了，
因整套算法是我當初在那個的時候突然想到，
就草草結束，褲子一拉，出來霹靂叭拉打起來，
當時兵荒馬亂沒想太多，反正8年就給它巴下去。
當這個盈再表是我發明的，又成為大師時，
就不用跟人解釋，
不然...大家都不要用啊！
愛因斯坦說 e = mc^2，他也沒解釋為何要平方啊，
為何不3次方、4次方？
我們同屬大師級的人物就不必解釋了。
難怪有同學罵我得了大頭症！
As for more than 5 years, students asked "Why not pick 6 or 7 years but 8 years ?" This is unexplainable. The whole algorithm was suddenly thought of when I sit there, it ended hastily, and I pulled up my pants, I came out and started fighting. At that time, I didn't think too much about it. Anyway, I gave it to it for 8 years. When I invented this On's table and became a investment master, I don’t have to explain to others. Otherwise...Don't everyone use it ! Einstein said that e = mc^2, and he didn’t explain why it should be squared. Why not 3rd, 4th power ? We both are masters, so there is no need to explain. No wonder some students scolded me for macrocephaly !
後來同學拿1991年報上巴菲特舉的例子要我算給他看，
這答案2,500萬元是怎麼算出來的？
我代入盈再表上IRR的計算表，結果與老巴的答案相同，
該表的年數就是8年，顯見老巴也用8年在算。
A student asked me to demonstrate how Mr. Buffett calculated the answer of $25 million, using an example cited in his 1991 annual report. I used the IRR calculation in On's table and substituted the numbers from the example. The result I obtained was the same as Buffett's. It's worth noting that the table covers an eight-year period, which is consistent with the timeframe used by Buffett.
4. 折現公式指的是股息，而非自由現金流量，
若是用自由現金流量來算，
則擴廠增加資本支出，自由現金流量減少，
內在價值反而下降，這就矛盾了。
擴廠應該可以賺更多的錢，增加內在價值。
4. IRR calculation pertains to dividends, not free cash flow. If calculated based on free cash flow, the increased capital expenditures for factory expansion may reduce free cash flow and lower its intrinsic value, which is a contradiction. The expansion of the factory should lead to higher earnings and an increase in intrinsic value.
5. 折現公式更不是指資產負債表上的現金，
未配出來的現金不屬於股東的報酬。
公司有現金100元，後來倒閉，股價歸0，股東一無所有。
若把100元配息出來，即便後來倒閉股價變成 0，
股東仍保有100元。
5. IRR is not related to cash on the balance sheet. Unallocated cash does not contribute to shareholders' returns. For instance, if a company has $100 in cash and goes bankrupt, with its stock price falling to zero, the shareholders will receive nothing. However, if the company distributes a dividend of $100, the shareholders will still retain the cash even if the stock price falls to zero after bankruptcy.
接下來計算未來8年的股息和最後賣出價，
首先要知道起始NAV 18.7＝去年淨值÷最新股數，
因股數抓最新的，遇到除權時貴淑價會跟著調整。
Firstly, we need to determine the starting NAV by dividing last year's net assets by the current number of shares, which is 18.7. As the number of shares is up to date, the stock price will be adjusted accordingly when ex-rights are encountered. Next, we can calculate the dividends and final selling price for the next 8 years.
這個例子用講稿14/21的取法得到預期ROE 21%。
EPS 3.9＝ROE 21% x NAV 18.7
In this example, we apply the method discussed in Lecture 14/21 to calculate an anticipated ROE of 21%.
EPS 3.9＝ROE 21% x NAV 18.7
要算的不是EPS，而是隔年配多少息？
股息 = EPS x 配息率，
需要算未來的預期配息率
The goal is not to calculate EPS but rather to determine the amount of dividends that will be paid out next year. This can be achieved by multiplying EPS by the dividend payout ratio. To do so, we must first calculate the anticipated dividend payout ratio.
預期配息率 = (過去配息率+(1-盈再率))/2
其中 0<1-盈再率<1
為何要跟1-盈再率平均？
因盈再率會影響未來的配息率，
盈再率高，未來配息率低。
Expected dividend payout ratio = (past dividend payout ratio + (1 - PR%))/2
Where 0<1 - PR%<1
Why do we need to calculate the average of 1 - PR%? Because PR% can impact the future dividend payout ratio. Specifically, the higher the PR%, the lower the expected future dividend payout ratio.
過去配息率抓過去3年配息率取中位數，
3 個之中的那一個，取中間值為避免極端值。
The dividend payout ratio for the past three years is the median of the three ratios. The median is the middle value and is utilized to avoid extreme values.
過去3年配息率採純配息率與加計庫藏股配息率之平均，
因若單用純配息率來算會高估預期報酬率；
單用加計庫藏股又低估，
故取兩者平均。
The dividend payout ratio for the past three years is calculated by averaging the pure dividend payout ratio and the payout ratio of added treasury stocks. Relying solely on the pure dividend payout ratio can lead to an overestimation of the expected return, while using only the payout ratio of added treasury stocks can undervalue it. Therefore, we take the average of the two to achieve a more accurate calculation.
最後，預期配息率不得低於過去3年配息率之9成，
這是為保守起見，因在ROE固定下，配息率越低，IRR越高
Lastly, the expected dividend payout ratio should not fall below 90% of the dividend payout ratios in the past three years. This is a conservative measure because, given a fixed ROE, a lower dividend payout ratio results in a higher IRR.
如此可算出預期配息率，
EPS 3.9 x 預期配息率90%＝3.51 隔年股息。
By following these steps, we can calculate the anticipated dividend payout ratio.
EPS 3.9 x expected dividend payout ratio of 90% = 3.51 dividends for the next year.
隔年NAV = 去年NAV + 去年EPS - 去年股息
Next year NAV = last year's NAV + last year's EPS - last year's dividend
有人問不同公司是否給予不同本益比？
因有些公司本益比就是比較高。
不要，本益比固定，比較基礎一致才能比較貴淑。
最終本益比設多少都沒關係，設成1萬倍也可以，
只要所有股票標準一致即可。
Is the PER different for each company? Yes, the PER can vary across different companies, and some companies may have higher PERs than others. However, a fixed PER can be used as a consistent basis for determining whether a stock is cheap or expensive. The actual value of the PER doesn't matter as long as it is the same for all stocks being compared, even if it is set at a high value like 10,000 times.
本益比高或低往往是十年河東，十年河西的事。
微軟在90年代本益比30倍，
2010年代則掉到10倍，因獨占地位受到Android 挑戰。
PER often changes every 10 years. For instance, Microsoft's PER was 30 times in the 1990s. However, in 2010, it dropped to 10 times due to the challenge posed by Android to its monopoly position.
請問以上計算過程有沒有問題？
通常這一段都不會有問題，而且還睡成一片。
計算過程聽不懂沒有關係，考試不會考，
只要會看最後答案即可，看預期報酬率多少？
Are there any issues with the above calculation process? Typically, this part is unproblematic, and it tends to put people to sleep. It is not necessary to understand the calculation process fully, as this is not typically tested on exams. You can simply focus on the final answer: what is the expected return?
未來8年股息和最後賣價算出來之後即可代入折現公式，
公式變成一元八次方方程式，
在國中因式分解教過如何解，
同學有興趣上來解解看嗎？國中數學而已。
不用自己解，Excel有一個函數IRR
可以算出預期報酬率 r = 10%。
Once the dividends for the next 8 years and the final selling price have been calculated, they can be substituted into the IRR equation. This formula can be transformed into a one-variable eighth power equation that can be solved using factorization, which is a math concept that students learn in junior high school. However, students do not necessarily need to solve it themselves, as Excel has an IRR function that can do the calculations. The expected return can be calculated as r = 10%.
IRR(-47.0買, 3.51息, 3.67息, …, 4.18息, (4.29息+58.7賣))
= 10% = r 預期報酬
IRR (-47.0 buy, 3.51 dividend, 3.67 dividend, …, 4.18 dividend, (4.29 dividend + 58.7 sell))
= 10% = r expected return
所對應淑價是多少？
代入NPV函數即得35元。
A 10% expected return is not sufficient, as a 15% expected return is required for a cheap price. What constitutes a cheap price is not specified. However, when the NPV function is substituted, the result is $35.
NPV(15%, 3.51息, 3.67息, …, 4.18息, (4.29息+58.7賣))
= 35.0 淑
股價跌到35元以下買，每年報酬率才有15%才夠便宜。
NPV(15%, 3.51 dividend, 3.67 dividend, …, 4.18 dividend, (4.29 dividend + 58.7 dividend))
= 35.0 S
If the stock price falls below $35, then buying it can be considered cheap enough, as long as it provides an annual rate of return of 15%.
何時賣？貴了，預期報酬率 0，
所對應貴價一樣代入NPV得出貴價86.1元。
NPV(0%, 3.51息, 3.67息, …, 4.18息, (4.29息+58.7賣))
= 86.1 貴
When should you sell a stock? You should sell when the stock becomes expensive, and the expected return drops to 0. An expensive price can be determined by substituting it into the NPV equation. For instance, a price of $86.1 is considered expensive.
NPV(0%, 3.51 dividend, 3.67 dividend, …, 4.18 dividend, (4.29 dividend + 58.7 dividend))
= 86.1 pricey
貴了就該賣掉，因貴了的預期報酬率為負，
表示再抱下去總報酬只會更少不會更多。
If the stock price is deemed pricey you should sell it because the expected return is negative. This means that if you hold on to the stock, the total reward will only decrease, rather than increase.
貴淑價於財報出爐和除權時會變動。
預期報酬率除息時將上升。
Cheap and pricey prices can change when financial reports are released or when ex-rights dates occur. The expected return is expected to rise on the ex-dividend date.
總算講完了，本章是整個課程最多數學的地方，
有位同學不敢置信一個人在馬桶上
竟然可以想出這麼複雜的計算，
一直問我在馬桶上待了多久？
馬桶和蘋果樹都是人類文明的搖籃啊！
In conclusion, I have finished my speech for this section. The mathematical content covered here is the most complex in the entire course. One student couldn't believe that someone would sit on the toilet and contemplate such complicated calculations, and kept asking me how long I had been sitting there. However, toilets and apple trees are the cradles of human civilization!
波克夏的估價是目前唯一的例外，
1. 為因應新會計準則，老巴把持股漲跌列為異常利益，
可是持股漲跌應是日常的事，非異常
故盈再表單就BRK，採用淨利而非常利，作為淑貴價的計算
如此ROE看起來較合理
Berkshire Hathaway's valuation calculation currently stands as the only exception.
1. In order to comply with new accounting standards, Mr. Buffett has classified the capital gains of his investment portfolio as exceptional interests. However, fluctuations in holdings are a routine matter and not exceptional. Therefore, the On's table employs net profit instead of recurring profit as the valuation calculation solely for BRK. This results in a more reasonable return on equity (ROE) calculation.
2. 2011年波克夏股價跌到淨值，
老巴即宣布買回庫藏股，生平第一次，且連買了2次，
顯示祂認定淨值是便宜價。
2013年報老巴明白指出波克夏內在價值＝淨值 x 120%，
便宜價是內在價值打8折，便宜價＝淨值。
2. In 2011, the stock price of Berkshire Hathaway fell to its NAV. Mr. Buffett announced that he would repurchase treasury stock for the first time in his life and buy it twice, indicating that he believed the NAV was undervalued.
In the 2013 annual report, he clearly stated that Berkshire's intrinsic value = NAV x 120%.
Cheap price is 20% lower than intrinsic value, cheap price = NAV.
貴了要賣掉，不然將白抱，
不是持股成本很低就可以不賣，
更非高配息要來當退休金用，坐享被動收入就可不賣，
這通通錯誤！
If it’s pricey, you have to sell it, or you will hold it for nothing.
It’s not that you don’t have to sell if cost of holding shares is low.
It’s not that high dividends would be used as a pension, and you won’t sell it for passive income.
This is all wrong !
1998年可口可樂股價漲到最高89元，非常貴。
若不賣一路抱到2010年，
12年過去股價還原仍未回到89元，12年來白抱！
高ROE，高配息的公司，股價貴了不賣，仍然白抱。
有人說巴菲特不是沒賣嗎？
老巴不是沒賣，有賣！
1998年報上寫得很淸楚，
當年老巴的持股都紛紛變貴了，
不僅可口可樂貴了，連美國運通、吉列刮鬍刀，
甚至連波克夏也貴了。
巴菲特當然知道那麼多股票不可能在市場上抛售，
所以祂怎麼賣？
祂去換股合併，
祂拿貴了的波克夏股票去跟便宜的通用再保換股合併。
這樣不也等於在賣股票，
像我就是拿貴了的中碳去跟新台幣換股合併。
In 1998, Coca-Cola's stock price rose to a high of $89, which is very expensive.
If you hold the stock until 2010, its stock price will not return to $89 in 12 years.
If you don't sell stocks at an expensive price, it will be futile even for stocks with high ROE and high dividend payouts.
Some people say that Mr. Buffett did not sell.
Yes, he did sell it !
If you look at 1998 annual report, you will know.
At that time, Buffett's holdings became expensive,
not only Coca-Cola, but also American Express (AXP) and Gillette razors,
even Berkshire's stock is expensive.
Buffett certainly knows that the number of shares he holds is too large to sell on the market.
How did he sell ?
He conducted a stock swap merger, merging expensive Berkshire stocks with cheap general reinsurance swaps.
This is equivalent to selling stocks.
盈再表算的貴淑價，並非在抓股價高低點，
貴價不是最高價，便宜價亦非最低價。
股價漲到接近貴、剛好貴、非常貴都有可能，
漲到非常貴不代表盈再表貴價就算錯。
所以到了貴淑價之後何時該賣或買？
不可知也無標準答案，
請自己決定，別再問了。
The pricey and cheap prices calculated by On's table are not meant to identify the high and low points of stock prices. A pricey price is not necessarily the highest, and a cheap price is not necessarily the lowest. The stock price may rise to a level that is close to pricey, just hitting the pricey mark, or even reaching an extremely expensive level. However, reaching an extremely expensive level does not mean that On's table's pricey price calculation is incorrect.
So, when should one decide to sell or buy after reaching the pricey or cheap price? It is unknowable, and there is no standard answer. Please make your own decision and refrain from asking further questions.
很多事件的發生並非絕對，而是機率高低，
像「人性本善」這句話對不對？
大家不會單純答：對或錯，
而是「7成對，3成不對」，
這才是答案。
The occurrence of many events is not absolute but rather a matter of probability. Is the statement "Human nature is inherently good" correct? People won't simply answer "yes" or "no," but rather "70% correct, 30% incorrect"—that's the answer.
70%股票在淑貴價之間波動，
5%股票貴了還會更貴，
請問如何操作最好？
A. 遵守淑買貴賣
B. 貴了也不賣
70% of stock fluctuations occur between cheap and pricey prices, and 5% of stocks that are already expensive can become even more expensive. What is the best approach?
A. Follow the strategy of buying cheap and selling pricey.
B. Do not sell even when the stocks are expensive.
答案是A
Bloomberg做過這項統計，由底下圖可知，
1954-2014美股報酬率落於0-15%之間，
可見盈再表訂的貴淑價相當合適，
便宜價預期報酬率15%，本益比12倍，
貴價預期報酬率0%，本益比30倍。
The answer is A.
Bloomberg has conducted this analysis, as shown in the figure below. The study of U.S. stock returns between 1954 and 2014 indicates that the "pricey" and "cheap" prices established by On's table are quite suitable. The expected return for "pricey" prices is 0%, with a PER of 30 times, while the expected return for "cheap" prices is 15%, with a PER of 12 times.
再看Bloomberg的圖，
買的本益比越低報酬率越高
反之買的本益比高則報酬率低，
故得證：淑買貴賣，績效會最好
Upon closer examination of Bloomberg's analysis, it is evident that the lower the PER, the higher the expected return. Conversely, a high PER corresponds to a low rate of return. This supports the idea that a "buy cheap and sell pricey" strategy is likely to yield the best results.
多看幾張股價圖可更明瞭：
台達電若買在貴價之上，後來股價腰斬。
Let's examine a few more stock charts to illustrate the point more clearly. For instance, imagine purchasing shares of Delta Electronics at a price higher than the "pricey" price, only to see the price drop by half shortly thereafter.
美利達也是，
有人不信邪，以為股價只要會漲就可以追，
硬是買在貴價之上，後來也腰斬。
美利達在貴價以上長達2年，股價的時間觀非常漫長。
Merida (9914.TW) is another example of this phenomenon. Some investors ignore established principles and believe that as long as the stock price rises, they can buy at any price. However, if the purchase price is higher than the "pricey" price, and the price subsequently drops by half, significant losses can occur. In the case of Merida, its stock price has recently surpassed its pricey price in two years, indicating stock price horizon is very long.
中碳在2009年之後才漲上來，2009年一直在便宜價以下，
同學一直在問中碳怎麼都不會變貴？
後來漲到200元同學又問怎麼都不便宜？
China Steel Chemical's stock price only began to rise after 2009, having remained below the "cheap" price prior to that point. Some students may wonder why the stock did not become "pricey" once its price exceeded the "cheap" threshold. However, the stock eventually rose to NT$200, prompting other students to question why it did not fall back into the "cheap" category.
建立一個穩定趨向15%年報酬率的投資組合是成為有錢人最重要步驟，
因為對這個投資組合有信心：
1. 才敢押身家，本金滾起來才會大，如我在美股已有3,000萬元台幣。
2. 才願意長期一直擺著，不跑來跑去，這樣就有複利效果。
本金大 x 複利長 ＝ 有錢人
Achieving a 15% annual return gives you the confidence to invest a significant portion of your wealth for the long term.
1. Be bold in investing the majority of your wealth to maximize your principal.
2. Emphasize generating compound interest by abstaining from speculative trading.
Large principal x long compound interest = billionaire
A large principal combined with sustained compound interest can lead to significant wealth accumulation over time.
善用盈再表績效頁XIRR記錄自己的績效，以確定穩定性
台股若找不到100檔以上可好很久的公司，請來投資全世界。
To assess the stability of your investment performance, it's important to utilize XIRR in your performance sheet. If you find that there are not more than 100 companies in Taiwan that can maintain their success over the long term, consider expanding your investments to the global market by investing in US stocks.
有人看到上表，總獲利897萬元，本金2,190萬元，
認為我的績效是年複利6%。
他的算法錯了，因為用期末本金來算績效。
我的本金是由700萬元，1,400萬元，逐年增加，
應該以投入年數來加權本金，即僅1,600萬元。
績效計算公式不是總獲利/期末本金，
而是用年數加權本金的XIRR。
Someone reviewed the table above and noted that the total profit was NT$8.97 million with a principal of NT$21.9 million. They argued that my annual performance was a compounded 6%. However, their method was incorrect, as they used the period-end principal to calculate performance. In reality, my principal increased from NT$7 million to NT$14 million over the years. Therefore, the principal should be weighted by the number of years invested, which amounts to only NT$16 million. The correct performance appraisal formula is not the total profit divided by the period-end principal. Instead, it is XIRR, which is calculated based on the weighted principal over the number of years invested.
XIRR是年化報酬率，
若持股不到1年用XIRR算出來的報酬率將超高，
如買了某股當天漲停板賺了10%，
XIRR高得嚇人(1+10%)^365-1
此時須加以調整如下：
未滿 1 年 (1+XIRR)^(天數/365)-1
總獲利無論正負均用上式計算。
本調整公式係本人獨創，經過驗算應該無誤
XIRR is a metric used to determine the annualized rate of return on an investment. If you hold shares for less than a year, the rate of return calculated with XIRR can be extremely high. For example, if you bought a stock and earned 10% on the daily limit, the XIRR would be calculated as (1+10%)^365-1, resulting in a terribly high rate of return. However, in such cases, it's important to make adjustments to the XIRR calculation. For investments held for less than a year, the adjustment formula should be (1+XIRR)^(number of days/365)-1. This formula should be used to calculate total profit, regardless of whether it's positive or negative. This adjustment formula was created by Michael On and has been verified as correct.
加錢提錢：本金增減，現金增減
買賣股：本金不變，現金減增，股票增減
配息：本金不變，現金增
Adding money and withdrawing money: Principal changes, cash changes.
Buying and selling stocks: Principal remains unchanged, cash decreases or increases, stocks increase or decrease.
Dividends: Principal remains unchanged, cash increases.
我的績效表記錄了10年，
XIRR為自第一筆到本筆之投入報酬率。
2023年12%表示自2013年至今
10年平均績效為12%
My performance record spans over 10 years, with XIRR representing the return on investment from the first entry to the current one. The 12% in 2023 indicates the return from 2013 to the present. The average performance over the past 10 years is 12%.
若想了解近5年來績效，
即第一年為2017年至今的績效
可直接將10年表截半
此時2017年本金應改為股票+現金之24,778,950
而非17,775,983
If you wish to know the performance for the last 5 years, which includes from 2017 to the present, you can simply take the last half of the 10-year record.In this case, the initial principal in 2017 should be adjusted to include stocks and cash, totaling $24,778,950 instead of $17,775,983.
ArthurWang 2023-7-17 21:14
Mike-san在高度分散持股的情況下仍能在五年翻倍，
且每年創造至少10%-20%的穩定報酬率，
即便2022年巿場反轉對比2021年仍有8.5%成長。
在2021年GDP高點時減碼(持股比例99%->85%)，
並在2022年GDP低點回補(85%->99%)。
的確完美的實踐Mike-san創造的GDP理論，
完美績效令人嚮往。
Even in a highly diversified stockholding situation, Mike-san managed to double his investments in five years, consistently achieving annual returns of at least 10%-20%. Despite the market reversal in 2022 compared to 2021, there was still an impressive 8.5% growth.
In 2021, when the GDP reached its peak, Mike-san reduced his holdings (from 99% to 85%), and in 2022, during the GDP's low point, he made a comeback (increasing from 85% to 99%).
This perfect execution of Mike-san's GDP theory resulted in a remarkable performance that is truly admirable.
大家應確實記錄自己的績效才能做出正確的重大決策：
1. 該全力投資或買房、債券、ETF...？
2. 自己夠不夠格成為無業投資人？
Everyone should keep track of their performance honestly to make informed major decisions, such as:
1. Whether to fully invest or buy a house, bonds, ETFs, etc.
2. Whether they are qualified to become an unemployed investor.
mikeon88 2023-7-4 18:29
我的績效10.2年平均12%，
債券殖利率3%，ETF 7%，房地產5%，
錢該擺哪裡很清楚了，
這是幼稚園入學考題
My performance averaged 12% over 10.2 years, with bond yields at 3%, ETFs at 7%, and real estate at 5%. It's quite clear where to allocate the money. This is a question from a kindergarten admission test.
我小時上幼稚園入學要考試，
老師拿兩塊積木一大一小，
問我哪一個比較重？
跟上述問題一模一樣。
我非常驚訝，絕大多數大人弄不清錢該擺哪裡
When I was a child, I had to take an entrance exam for kindergarten. The teacher showed me two building blocks, one large and one small, and asked which one was heavier. It's the exact same question as above. I was surprised because the vast majority of adults struggle to figure out where to put their money.
IRR是投資學必教的公式，
可是卻少有人真正拿它來做為買賣股票依據，
連投資學教授也一樣沒在用，
因為學校投資課中不曾探討過如何選定IRR參數，
而這才是IRR公式可不可行的關鍵。
The IRR formula is a fundamental concept taught in investment courses. However, in practice, few investors use it to buy and sell stocks. Even professors who teach investment courses rarely use the IRR formula because the course curriculum often neglects to cover how to choose parameters, which is the key to making the IRR formula feasible.
ROE超高時用IRR計算預期報酬率會高得離譜，
這不是公式錯誤，
而是在現實狀況下超高ROE不可能持續多年。
In situations where ROE is extremely high, the expected return calculated by the IRR formula will be unreasonably high. However, this is not a formula error. In reality, it is unlikely for an ultra-high ROE to persist over many years.
當預期配息率太高，IRR預期報酬率又偏低，
如UL的PER才23倍，IRR卻已是 -11%，這明顯不合理
If the expected dividend payout ratio is too high, the expected return calculated by the IRR formula may be unreasonably low. For instance, the PER for UL is only 23 times, yet the IRR's expected return is -11%, which is clearly an unreasonable figure.
這個方法流於主觀，
中期之後成長率調低多少無客觀標準，事實上也不可知。
Some professors use dichotomy to address the aforementioned problems by opting for low-growth strategies after a certain period of growth. However, this method is subjective and lacks an objective standard for determining how much the growth rate should be reduced after the mid-term. In fact, it is impossible to know for certain.
當IRR算法不合理時，我提出改用PER法來除去人為主觀調整的缺點，
既標準明確，且一體適用。
If the IRR formula yields unreasonable results, I suggest using the PER method instead to eliminate the drawbacks of subjective adjustments. The standards for using the PER method are clear and can be easily applied.
PER法：
我規定貴價本益比30倍，預期報酬率為0；
淑價預期報酬率15%
PER4倍漲到30倍，預期報酬率為(30/4)^(1/8)-1=28.6%
淑價x(1+15%)^8=預期EPSx30
貴價x(1+0%)^8=預期EPSx30
PER method:
I stipulate that for pricey price the PER is 30 times and expected return is 0;
for cheap price expected return 15%
PER increases from 4 times to 30 times, expected return is (30/4)^(1/8)-1=28.6%
cheap price x(1+15%)^8=expected EPSx30
pricey price x(1+0%)^8=expected EPSx30
換軌點：由IRR換成PER法
參考陳坤良同學建議，在預期報酬率的計算上
當淑價和貴價之平均，IRR法比PER法小20%或大20%
則由IRR法改為PER法
Change point: from IRR to PER method
As per Curry's recommendation, we will switch from using the IRR method to the PER method for calculating expected returns when the average of the cheap and pricey prices obtained by the IRR method deviates more than 20% from that obtained by the PER method.
全台灣只有巴菲特班確實按照IRR公式來買賣股票。
盈再表上的指標，還原股價、ROE、常利、盈再率、配息率、IRR、PER法、換軌點
看似尋常，其實都有本人獨門密訣。
如何設定完全公開在盈再表上，
可是我相信大部份人看不懂，因頗為複雜。
In Taiwan, only the Buffett Class invests in stocks based on the IRR formula. On's table includes several indicators such as adjusted stock price, ROE, recurring profit, PR%, dividend payout ratio, IRR, PER method, and change point. While these indicators may appear ordinary, each has its own secrets. On's table fully discloses how to set up these indicators, but they may be difficult for most people to comprehend due to their complexity.
最後，在盈再表績效頁上本人提出比較績效的辦法，
以巴爺爺50年平均20%為基準，
巴菲特 50 年平均 20% = 1.2^50 = 9,100
您 9.6 年平均 11% 與巴菲特距離 93 (越小越好)，成績優秀
9.6 年的差距A = 1.2^(50-9.6)，A^0.5 = 40
11% 的差距B (1+11%)^B = 9,100，B = 87年
與巴菲特距離 93 = 100x(A^0.5xB)/3,701
其中 3,701 = (1.2^(50-8))^0.5xlog(9100,1+12%)，8年平均12%
謝謝江文宏桑指導B
開根號為防數字變大
Lastly, I propose a method for comparing performance on On's table's performance sheet. This method involves comparing the performance to the 50-year average return of 20% achieved by the Buffett Class.
Mr. Buffett's 50-year average of 20% = 1.2^50 = 9,100
Your 9.6-year average of 11% distance from Buffett 93 (The smaller the better), Excellent !
9.6 years gap A = 1.2^(50-9.6)，A^0.5 = 40
11% gap B (1+11%)^B = 9,100，B = 87 yr
Distance from Buffett 93 = 100x(A^0.5xB)/3,701
where 3,701 = (1.2^(50-8)^0.5)xlog(9100,1+12%), 8-year average of 12
Thanks to Wenhong Jiang for his guidance in B.
The square root is used to prevent the number from becoming too large.
跟巴菲特比績效指標解決了一個千古難題，
5年平均賺12%跟8年平均賺10%可以相互比較誰好了。
Comparing performance with the Buffett indicator resolves a longstanding issue where an average of 12% over 5 years can be compared to an average of 10% over 8 years.
- 講稿 1/21：歡迎 (Lecture 1/21 Welcome)
- 講稿 2/21：知與不知 (Lecture 2/21 Knowable and unknowable)
- 講稿 3/21：巴六點 (Lecture 3/21 Buffett's Six Criteria)
- 講稿 4/21：物美價廉 (Lecture 4/21 Cheap and fine)
- 講稿 5/21：還原股價 (Lecture 5/21 Adjusted stock price)
- 講稿 6/21：高ROE (Lecture 6/21 High ROE)
- 講稿 7/21：配得出現金 (Lecture 7/21 High dividends)
- 講稿 8/21：會計 (Lecture 8/21 Accounting)
- 講稿 9/21：地雷股 (Lecture 9/21 Landmine stocks)
- 講稿 10/21：他們通通是錯的 (Lecture 10/21 They are all wrong)
- 講稿 11/21：不會變的公司 (Lecture 11/22 Durable)
- 講稿 12/21：多種果樹 (Lecture 12/21 Diversification)
- 講稿 13/21：IRR (Lecture 13/21 IRR)
- 講稿 14/21：現金殖利率的毒害 (Lecture 14/21 The poison of cash yield)
- 講稿15/21：GDP理論 (Lecture 15/21 GDP Theorem)
- 講稿 16/21：全世界都成立 (Lecture 16/21 Globally applicable)
- 講稿17/21：不要想太多 (Lecture 17/21 Do not think too much)
- 講稿 18/21：玩融資期貨選擇權是悲劇的開始 (Lecture 18/21 Margin trading, futures and options are the beginnings of a tragedy)
- 講稿 19/21：基金太貴，不做代操 (Lecture 19/21 Funds are too expensive, don’t manage other's funds)
- 講稿 20/21：股債不是蹺蹺板 (Lecture 20/21 Stock debt is not a seesaw)
- 講稿 21/21：技術分析 (Lecture 21/21 Technical analysis)
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