mikeon88

以上是巴菲特的持股，
老巴的持股我們也會想買，
祂買的價格跟盈再表淑價差不多，
我的持股老巴也會買，
足見我的方法跟巴菲特很接近。

The above are Mr. Buffett's holdings, and we like to invest in the same stocks. The price at which he purchased these stocks is similar to the cheap price listed in On's table. Interestingly, he also bought some of the stocks that I own, indicating that my investment approach is quite similar to that of Mr. Buffett.

看了老巴的持股，請問有何感想？
都是耳熟能詳的龍頭股，
鐵路公司、雀巢奶粉、富國銀行，都至少聽過。
同學會不會突然有個衝動，
想打電話跟巴菲特報名當祂的接班人？
買這種公司誰不會？
而且還可以跟老巴說不用花5分鐘，
只要15秒即可，因有盈再表。
屆時借祂按比較快。

After reviewing Mr. Buffett's holdings, how do you feel? These are all well-known, leading stocks, such as railway companies, Nestle milk powder, and Wells Fargo Bank, which most people have at least heard of. Does this make you feel excited and eager to call Buffett to be his successor? We all know the kind of companies he likes. Moreover, you can tell Buffett that he doesn't need to take 5 minutes to make a decision; if he checks On's table, it will only take him 15 seconds.

同學有無赫然發現全世界的股票都會玩了！
第一堂跟各位保證，
給我2天，就可以把您變成巴菲特，
讓您全世界的股票都會玩，
現在是不是達成了。
不僅台股，美、中、英、瑞士等股都會玩了，
盈再表按得出來的49國股票都會玩了。

Do you now feel confident in your ability to invest in stocks around the world? In the first lesson, I promised that in two days, you would be able to learn how to invest like Buffett and play stocks all over the world. Now, I have fulfilled that promise. Thanks to On's table, you can now invest in stocks not only in Taiwan but also in the US, China, Britain, Switzerland, and 49 other countries.

mikeon88

講稿 13/21：IRR
Lecture 13/21 IRR



選股有三大條件：
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 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 theory is explained in detail in Lecture 16/21.

mikeon88

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分析師時學到的觀念，
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.

一次性利益即財報上之異常利益
底下說明請搭配Excel版盈再表設定之公式閱讀

One-time profits is Unusual Income reported in financial statements.
Please compare the formula setup in the Excel version of On's table with the explanation provided below.

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

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]

mikeon88

有了常利之後， 即可用過去5年常利來推算預期常利
只取過去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 from the past 5 years to calculate the expected recurring profits.
Only the past 5 years are considered, as profits from earlier years are not relevant.
This year refers to the past 4 quarters.

取近5年之中位數 (median)
取近2年之平均數 (average)
近5年指包含今年之過去5年；近2年亦然

1. 預期常利＝近2年平均x0.7＋近5年中位數x0.3
2. 近2年平均大於2倍近5年中位數時，預期常利＝近2年平均x0.9＋近5年中位數x0.1

Take the median of the recent 5 years.
Take the average of the recent 2 years.
The recent 5 years includes the current year and the 4 preceding years; the same applies to the recent 2 years.

1. Expected Recurring Net Profit = (Recent 2-Year Average × 0.7) + (Recent 5-Year Median × 0.3)
2. If the Recent 2-Year Average is more than twice the Recent 5-Year Median, then:
Expected Recurring Net Profit = (Recent 2-Year Average × 0.9) + (Recent 5-Year Median × 0.1)

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.

mikeon88

股價反映常利，而非淨利，
GSK是明顯例子，
用淨利算GSK股價是貴的。

Stock prices are based on recurring profit rather than net profit, which is exemplified by GSK. Using net profit to calculate GSK's stock price would be expensive.



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.

mikeon88

我們要用股息折現公式(IRR)來算投資報酬率，
買進價等未來8年股息和賣出價的折現值，
所謂折現值是除以1+r的幾次方，
r = 平均報酬率，
用這個價格買進，持有未來8年，平均每年報酬率 r。

The internal rate of return (IRR) is utilized for computing the return on investment. The purchase price is determined by discounting the value of dividends and the selling price over the next 8 years. The discounted value is then divided by the power of 1+r, where r denotes the average rate of return. One should purchase the asset at this price and hold it for the next 8 years, earning an average annual rate of return r.

這條公式是投資學上最重要的公式，
不管做任何投資都用它來算報酬率，
股票、債券、房子、黃金、保險…均適用。
花1千萬元買一幢房子，租出去每年可收10萬元租金，
第8年以1,200萬元賣掉，8年下來年平均報酬率即 r。

This formula is considered the most crucial in investment science. Regardless of the investment type, it can be applied to calculate the rate of return. This includes stocks, bonds, houses, gold, insurance, and more. For instance, suppose a house costs $10 million to purchase, with an annual rent of $100,000. If sold for $12 million in the eighth year, the average annual rate of return after eight years would be denoted as r.

折現公式源自底下觀念：
100元投資 1 年變120，這句話寫成數學式子如何表示？
100(1+r) = 120

The IRR is based on the fundamental concept of an investment of $100 transforming into $120 in one year. This sentence can be expressed in mathematical formula as: 100(1+r) = 120.



把100改成「買」，120改為「息1＋賣」
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)



再來，100元投資2年變120，這句話如何用式子表示？
100(1+r)^2 = 120

Next, investment of $100 will change to $120 in 2 years.
How to express this sentence in a formula ?
100(1+r)^2 = 120



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

mikeon88

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.

mikeon88

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.

mikeon88

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.

mikeon88

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.



根據前述預期常利計算方法得出預期ROE 21%
EPS 3.9＝ROE 21% x NAV 18.7

Based on the aforementioned expected recurring net profit calculation method, the expected ROE is 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.

純息率A ＝今年股息/去年常利
配息率B ＝(今年股息+今年庫藏股 )/去年常利
混合率C ＝(純息率A＋配息率B)/2

混合率C採純息率A與配息率B之平均 C=(A+B)/2，
因若單用純息率A來算會高估預期報酬率；
單用配息率B又低估，
故取兩者平均C

Pure Dividend Yield A = This Year’s Dividends / Last Year’s Recurring Net Profit
Dividend Payout Ratio B = (This Year’s Dividends + This Year’s Share Buybacks) / Last Year’s Recurring Net Profit
Blended Ratio C = (Pure Dividend Yield A + Dividend Payout Ratio B) / 2

The Blended Ratio C is the average of Pure Dividend Yield A and Dividend Payout Ratio B,
i.e., C = (A + B) / 2.
Using only Pure Dividend Yield A would overestimate the expected return;
using only Dividend Payout Ratio B would underestimate it.
Therefore, the average of the two is taken as C.

過去配息率 ＝中位數(去年、前年、大前年混合率C)
取中間值為避免極端值。

Past Dividend Payout Ratio = Median of the Blended Ratio C from the past three years (i.e., last year, the year before last, three years ago).
The median is used to avoid the impact of outliers.

最後，預期配息率不得低於過去3年配息率之9成
若因資料缺漏無法計算，則預設預期配息率為65%
這是為保守起見，因在ROE固定下，配息率越低，IRR越高
=IFERROR(MAX((MEDIAN(V14,W14,X14)+W13)/2,MIN(F5:F7)*0.01*0.9),0.65)

Lastly, the expected dividend payout ratio should not fall below 90% of the dividend payout ratios in the past three years.
If the calculation cannot be performed due to missing data, the expected dividend payout ratio shall be set at the default value of 65%.
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



接下來依此類推，得到未來8年EPS和股息。

Following this, we can derive the EPS and dividends for the next 8 years accordingly.

mikeon88

還要算最後賣出價？
因已得出第8年EPS，乘以最終本益比即賣出價。
最終本益比？
股價最終應回歸到應有價值，
即一年定存利率6.7%的倒數本益比15倍，
抓保守一點12倍就好。

To calculate the final selling price, you can multiply the EPS from the 8th year by the final PER. What is the final PER? The final PER can be determined based on the assumption that the stock price will eventually return to its value. Specifically, the reciprocal of the 6.7% one-year time deposit rate multiplied by 15 times the PER provides a reasonable estimate. However, to be conservative, it may be better to use a multiple of 12 times the PER instead.



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 ?

mikeon88

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



10%不够好，因我們要求的淑價預期報酬率15%，
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.

IRR是投資學中必教的公式，
但真正用它作為買賣股票依據的人卻寥寥無幾，
甚至連投資學教授也很少實際應用。
原因在於學校的投資課程從未深入探討如何選定 IRR所需的關鍵參數，
而這恰恰是決定 IRR公式能否實用的核心所在。

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.



當ROE過高時，用 IRR計算預期報酬率，
結果往往會高得不切實際。
這並不是公式本身有誤，
而是因為在現實情況下，超高的ROE難以長期維持。

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.

當預期配息率過高，IRR計算出的預期報酬率卻可能低到不合理。
例如，UL的本益比僅23倍，但計算出的 IRR卻為-11%，顯然不合常理。

If the expected 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.





針對上述問題，投資學課本教導我們採用二分法來處理：
當企業成長到某一階段後，轉為低成長。
然而這種做法過於主觀，
中期以後的成長率應調降至何種程度，不可知。

To address the above issue, investment textbooks teach us to use a binary approach:
if a company enters a low-growth phase after reaching a certain stage of development.
However, this approach is overly subjective,
as it is unclear how much the growth rate should be reduced in the mid to long term.

當 IRR算法出現不合理結果時，我主張改用本益比法，
以避免過多的人為主觀調整。
此方法不僅標準明確，而且普遍適用。

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倍之預期報酬率為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法切換為PER法
在計算預期報酬率時，
當 IRR法淑價與貴價之平均數
高出或低於20%PER法時，
視為 IRR法偏離合理範圍，應改以PER法作為估值依據。

Change point: from IRR to PER method
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.

全市場真正依據 IRR公式進行股票買賣的，
恐怕只有我們巴菲特班。
盈再表包含了還原股價、ROE、常利、盈再率、配息率、IRR、PER 法與換軌點等多項指標，
看似平凡卻蘊藏了本人獨門秘訣。
雖然已將這些設定全數公開於盈再表中，
但我相信大多數人仍難以完全理解，因為相當複雜。

Across the entire market, the only ones who truly buy and sell stocks based on the IRR formula are probably just our Buffett class. On's table includes several indicators such as adjusted stock price, ROE, recurring profit, PR%, 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.

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!

mikeon88

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.



3. 不過，實證結果...
2018/4 我買BRK.B時NAV 141美元
我的買價200元為NAV之141%，
4年抱下來共賺了71%，年複利15%，
顯見盈再表用淨利計算BRK預期報酬率方法比老巴的估算合理

3. Nevertheless, based on my personal experience, I bought BRK.B when its NAV was $141 in April 2018. My purchase price of $200 represented 141% of the NAV at that time. After holding the stock for 4 years, I have achieved a total return of 71%, which translates to a compound annual return of 15%. It is clear that BRK's expected return based on net profit is more reasonable than Mr. Buffett's estimate.

mikeon88

貴了要賣掉，績效才會最好，
否則只能得到中等績效。

If it is expensive, you should sell it to achieve optimal performance. Otherwise, you will only be able to achieve moderate performance.

2011年中碳股價173元，預期報酬率1% ，
接近貴了，我把它賣掉。
若貴了的中碳不賣續抱到2017年12月，
6年7個月過去了才回到當初我賣的價格，
白抱了6年7個月！

In 2011, I purchased China Steel Chemical stock at NT$173 with an expected return of 1%. As it seemed relatively expensive at the time, I made the decision to sell it. Looking back, had I held onto the stock until December 2017, it would have taken 6 years and 7 months for it to reach the original price at which I sold it. This means that I would have lost 6 years and 7 months for nothing!

價值投資是便宜買，貴了賣，
有2招，工夫別只學一半。
台灣人有句話「會賣股票的才是師父！」

Value investing means buying cheap and selling pricey. There are two skills to this strategy, so it's essential not to learn only one half. In Taiwan, people often say, "The true master is the one who knows how to sell stocks!"



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 a stock is expensive, it's crucial to sell it; otherwise, holding onto it will yield no benefits. On the other hand, just because a stock is cheap doesn't mean you shouldn't consider selling it. Also, high dividends should not be the sole reason for holding onto a stock as a retirement fund, as passive income can also be earned by selling the stock at an opportune time. These common misconceptions about stock investing are incorrect.

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 reached an all-time high of $89, which was considered very expensive. If you had held onto the stock until 2010, its price would not have returned to $89, even after 12 years. It's futile to hold onto expensive stocks, even if they have high ROE and dividend payouts. Some people believe that Mr. Buffett never sells stocks, but he actually does. If you look at the 1998 annual report, you will see that Buffett's holdings, including Coca-Cola, American Express (AXP), Gillette razors, and even Berkshire's own stock, had become expensive. He knew that selling the large amount of shares he held on the market would not be practical. Instead, he conducted a stock swap merger, which involved merging the expensive Berkshire stocks with cheaper general reinsurance swaps. This was essentially a way of selling stocks. Similarly, I exchanged my expensive China Steel Chemical stocks for New Taiwan dollars.



老巴心裡在想什麼看祂的動作便知，騙不了人的，
若祂拿股票去換股合併，表示祂認定祂的股票貴了。
用現金去收購則持股便宜。

Mr. Buffett's actions reveal his true thoughts, and he cannot deceive others. When he exchanges shares for shares in a merger, it indicates that he considers the Berkshire shares to be expensive. It's more cost-effective to purchase stocks with cash instead.

2016年報老巴公開澄清無所謂的永恆持股這回事，
之前寫巴菲特傳記的書都稱祂「Buy and Hold」。
老巴說掌控經營權事業(controlled business)不會賣，
因整個被祂買下來了，可能都下市了，無股價可言，
如那家鐵路股和潤滑油公司。
可是只持有部份股權的流通證券(marketable securities)
則會賣，因仍有股價，就有貴淑，
這種說法跟我的淑買貴賣就一致了。

In his 2016 annual report, Mr. Buffett explicitly stated that there are no permanent holdings. This is contrary to what some previous books on Buffett's biography suggest, which advocate for a "buy and hold" strategy. Buffett clarified that he would not sell controlled businesses because he has acquired the entire company, and some of these companies may not have a stock price or have already been delisted, such as railway and lubricant companies. However, he would sell securities that only hold a portion of the equity because there are still stock quotes and the prices may be either cheap or expensive. His statement aligns with my trading strategy of buying cheap and selling pricey.

mikeon88

億豐窗簾股價最高漲到408元，
盈再表算的貴價僅260元，
同學據此質疑盈再表不準？

Nien Made's share price increased to NT$408, but according to On's calculations, the fair price should be only NT$260. Based on this, a student questioned the accuracy of On's analysis.



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計算錯誤。

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.



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.



股票由便宜到貴或貴到便宜的時間很長
往往長達5-6年甚至10幾年
人的眼光又看不了太遠
中碳在2009年之後才漲上來，
之前好幾年一直在便宜價以下，
同學一直在問中碳怎麼都不會變貴？
2014年漲到200元同學又問怎麼都不便宜？

The time it takes for a stock to go from cheap to expensive or from expensive to cheap is very long, often lasting 5-6 years or even more than a decade.
People’s vision can’t see that far ahead.
For example, China Steel Chemical only started rising after 2009, but for several years before that, it remained below a cheap price.
Students frequently asked why China Steel Chemical wasn’t getting expensive.
Then in 2014, when it climbed to NT$200, they began asking why it wasn’t getting cheaper.



太貴的股票不能買
往往是讓投資人躲過泡沫破裂的唯一方法
2025年的AI投資狂潮
科技大頭們拼命畫大餅
動輒上兆美元的投資計劃
媒體鋪天蓋地吹捧洗腦
舉世瘋狂沒人敢看不好
我們巴菲特班避掉這大泡沫靠的一招
就是股價太貴不要買
 
Never buy stocks that are too expensive. This is often the only way investors avoid being wiped out when a bubble bursts. In the AI investment mania of 2025, tech giants relentlessly sell grand visions,roll out trillion-dollar spending plans, and are amplified by nonstop media hype. The world falls into collective euphoria, and almost no one dares to be skeptical. The Buffett Class stayed clear of this massive bubble by sticking to one simple rule: never buy a stock that’s too expensive.

mikeon88

盈再表上有一張績效表用來記錄投資績效，
等於是考試的總分，
考上哪間學校以總分為準。

很多人問我這樣的問題：
1. 該投資股票或買房、債券、ETF...？
2. 能不能以投資為本業？
我都難以回答
因為欠缺關鍵數字
即你的績效表

The On's table includes a performance table that tracks investment results.
it’s like a report card, and the total score determines which school you get into.

Many people ask me questions such as:
Should I invest in stocks, real estate, bonds, or ETFs?
Can I make investing my full-time career?
I find these questions difficult to answer — because what’s missing is one crucial number:
your own performance table.

是你的績效表，不是我的
同樣用巴菲特方法投資
結果不一樣
你該怎麼做？
我的績效表沒有任何參考意義。
大家應確實記錄自己的績效，
在重大問題上才能做出正確決定

It’s your performance table, not mine.
Even if we both use Warren Buffett’s investment methods,
the results will still be different. What should you do? My performance results have no reference value for you.
Everyone should diligently track their own investment performance —
only then can you make the right decisions on major issues.

我的績效12.5年平均14%，
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

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，大人們竟弄不清錢該擺哪裡？

My average return over 12.5 years has been 14%.
In comparison, bond yields are around 3%, ETFs about 7%, and real estate roughly 5%.
It’s obvious where the money should go —
this is as basic as a kindergarten entrance exam question.

When I was a child, I had to take a test to get into kindergarten.
The teacher showed me two building blocks, one large and one small,
and asked which one was heavier.
It’s essentially the same kind of question.
I’m genuinely amazed that so many adults still can’t figure out where to put their money.

績效表用XIRR來算，而非IRR，
因為IRR假定現金投入和提出時間固定
可是實際做投資卻是不固定

The performance table should use XIRR rather than IRR,
as IRR assumes cash inflows and outflows occur at fixed intervals,
while in real-world investing, the timing is often irregular.

XIRR是年化報酬率，
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%

XIRR is the annualized rate of return —
it represents the return from the first investment up to the current one.
A 12% XIRR in 2023 means that the average annual return from 2013 to now
has been 12% over the past 10 years.



[本金]僅在加錢或提錢時才需增減，平時不變
[股票]和[現金]依帳上顯示填入

[Principal] should only be adjusted when adding or withdrawing funds; otherwise, it remains unchanged.
[Stocks] and [Cash] should be recorded based on the account statement.

若持股不到1年，XIRR的報酬率將超高，
如買了某股當天漲停板賺了10%，
XIRR為(1+10%)^365-1，高得嚇人
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，經過驗算無誤

If a stock is held for less than one year, the XIRR return can appear extremely high.
For example, if a stock hits the daily limit and gains 10% on the purchase day,
the XIRR would be calculated as (1 + 10%)^365 - 1 — an astonishingly high number.

To adjust for this, use the following formula:
For holdings less than one year:
(1 + XIRR)^(days held / 365) - 1

This formula should be used regardless of whether the total return is positive or negative.
This adjustment method is my own original creation and has been verified for accuracy.

上表總獲利3,014萬元，本金2,660萬元，
有人認為我的績效是年複利8%。
他錯了，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，
應以投入年數來加權本金，即僅1,600萬元。

The total profit shown in the above table is NT$30.140 million, and the principal is NT$26.601 million.
Some people think my performance is an 8% annual compound return.
They are mistaken because they calculate performance using the ending principal.
My principal increased year by year, starting from NT$7 million, then NT$14 million, and so on.
The principal should be weighted by the number of years invested, which amounts to only NT$16 million.

若想了解近5年來績效，
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 want to understand the performance over the past five years,
the first year would be from 2017 to the present.
You can simply take half of the 10-year table.
At this time, the principal for 2017 should be adjusted to the combined stock and cash amount of 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 with a highly diversified portfolio, Mike-san managed to double his capital in five years,
consistently achieving an annual return of at least 10%–20%.
Even in 2022, when the market reversed compared to 2021, he still saw an 8.5% gain.

He reduced his equity exposure at the 2021 GDP peak (from 99% to 85%)
and increased it again at the 2022 GDP trough (from 85% back to 99%).
This was a flawless application of the GDP theory Mike-san developed.
His outstanding performance is truly admirable.

用XIRR來算平均績效有一個問題
在不同期間下，
5年平均報酬率12%與8年平均報酬率10%，
誰的成績較好？
我提出一個指標，與巴菲特的距離，
以巴爺爺過去50年平均報酬率20%為基準。
 1.2^50 ≈ 9,100 倍
您過去9.6年的平均報酬率為11%，
與巴菲特的距離為93 ，
數值越小代表表現越接近巴菲特，表現優秀。

There is an issue when using XIRR to calculate average performance:
Over different periods, which is better — a 12% average annual return over 5 years or a 10% average annual return over 8 years？
I propose an indicator called the "Distance from Buffett,"
using Buffett’s average 20% annual return over the past 50 years as a benchmark.
1.2^50 ≈ 9,100 times growth.
If your average return over the past 9.6 years is 11%,
your distance from Buffett is 93.
The smaller the number, the closer your performance is to Buffett’s, indicating better performance.

計算方式如下：
差距A (時間差)：
 A = 1.2^(50 − 9.6)，再開平方根得A^0.5 ≈ 40
 開根號是為了避免數字過大，保持計算穩定

差距B (報酬率差)：
 (1 + 11%)^B = 9,100，解得 B ≈ 87 年

與巴菲特的距離：
距離 = 100 × (A^0.5 × B) ÷ 3,701
   其中，3,701 是參考一組基準值計算得出：
   3,701 = (1.2^(50 − 8 ))^0.5 × log(9100,1+12%)，
代表「以12%年報酬率、投資8年」所對應的比較基準。

特別感謝江文宏桑協助指導差距B 的公式設計。

Gap A (time difference):
 A = 1.2^(50 − 9.6), then take the square root to get A^0.5 ≈ 40
 The square root is used to keep the numbers manageable and maintain calculation stability.

Gap B (return difference):
 (1 + 11%)^B = 9,100, solving for B gives approximately 87 years.

Distance from Buffett:
Distance = 100 × (A^0.5 × B) ÷ 3,701
Where 3,701 is a reference baseline calculated as:
 3,701 = (1.2^(50 − 8 ))^0.5 × log₍₉,₁₀₀₎ (1 + 12%)
This represents the comparison baseline for “12% annual return over 8 years.”

Special thanks to Mr. Wen-Hong Jiang for his guidance in designing the formula for Gap B.

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。
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

Building a portfolio that steadily aims for a 15% annual return is the most important step to becoming wealthy,
because having confidence in this portfolio means:
You’re willing to bet your entire capital — the principal will grow substantially over time.
You’re willing to hold it long-term without constantly moving in and out, allowing the power of compounding to work.
Large principal × long-term compounding = becoming wealthy.

mikeon88

講稿 14/21 殖利率陷阱
Lecture 14/21 Yield trap

IRR 股息折現公式是計算投資報酬率唯一正確的公式，
它完整的把未來的股息和賣出價考慮進來，
其它算報酬率的方法都是錯的。
這幾年流行的現金殖利率是錯的報酬率算法，
因只算到第一年的股息。
中碳2003年殖利率7%，
我8年抱下來賺6倍，IRR為 31%(註)，
現金殖利率7%離實際報酬率很遠。

The IRR formula is the correct method for calculating return on investment as it considers both future dividends and selling prices. Other methods are incorrect. The popular cash yield method used in recent years is flawed as it only accounts for the dividend in the first year. For example, China Steel Chemical had a yield of 7% in 2003, but this is far from the actual rate of return as I earned six times my initial investment over eight years, resulting in an IRR of 31%.(Note)

註：投資一檔股票不是純粹的單利或複利，
而是單複利綜合，
股息是單利，未配出來的為複利，
IRR包含單利和複利才是報酬率正確算法。

Note: Investing in a stock involves a combination of simple and compound interest, rather than just one or the other. Dividends represent simple interest, while unallocated dividends represent compound interest. Therefore, the correct method for calculating the rate of return is to use IRR, which accounts for both simple and compound interest.



股價反映IRR還是現金殖利率？
像200元的中碳貴嗎？
按盈再表清楚顯示貴了，
可是現金殖利率還有 4%(=8.3息/200)，還會以為便宜。

Does a stock's price reflect its IRR or cash dividend yield?
For example, Is the price of NT$200 per share of China Steel Chemical expensive?
On's table clearly shows that it is expensive, but some still consider it cheap because of the 4% cash yield (= 8.3 dividend / 200).



2011年中碳173元接近貴了賣掉之後我在討論區公告週知，
在其它社群上看到居然還有網友在感謝我
「感謝洪老前輩把中碳賣出來才能讓他買在180元」，
這位網友為何180元還會去買中碳，
正是誤信現金殖利率的結果。

In 2011, I sold China Steel Chemical at the expensive price of NT$173 and announced it on a discussion forum. I noticed that netizens in other investment clubs thanked me, saying "Thank you, Uncle On, for selling China Steel Chemical so that we can buy it for NT$180." However, this netizen's purchase of China Steel Chemical for NT$180 was the result of a misunderstanding of cash yield.

現金殖利率會受到配息率高低和買回庫藏股而扭曲，
無法正確評估貴淑。
配息率高，現金殖利率也高，進而高估貴淑價

Cash dividend yield can be distorted by high payout ratios or stock buybacks, making it unreliable for accurately assessing whether a stock is overpriced or undervalued.
The high payout ratio will drive up the cash dividend yield, which may lead to a higher estimation of the stock's value, whether cheap or expensive.



中碳是本人的成名代表作之一，
2003年最早發掘，在「選股魔法書」介紹，
上課時三不五時提一下，巴班同學都賺飽飽。

One of my famous success stories is China Steel Chemical. I discovered it in early 2003 and included it in my "Magic Book". I also mentioned it in my class on numerous occasions, and all my students who invested in it made a fortune.

mikeon88

一般人以為跑短線在賺價差，長期投資則收股息，
錯！無論短線和長期投資都在賺價差。
配息的同時股價也會減下來，仍未賺到息，
須等股價漲回去了，填息才是賺到。
我買中碳總共賺了6倍，包括股息的1 倍，
都是因為股價漲了6倍賺來的。

Most people believe that short-term trading is about profiting from price differences, while long-term investing focuses on earning dividends. This is incorrect ! In both short-term and long-term investing, the primary goal is to profit from price appreciation. When dividends are distributed, the stock price drops by the same amount, meaning you haven’t truly benefited from the dividend until the stock price recovers to its pre-dividend level. Only then can it be considered a real profit. I achieved a sixfold return from my investment in China Steel Chemical, with onefold coming from dividends. However, all the profits ultimately stemmed from the sixfold increase in the stock price.



有位學生為了這個問題在電話上跟我盧了10分鐘，
問他「有沒有聽過賺了股息，賠了價差？」
一個平常只要股價跌就唉唉叫的人
現在突然忘記最重要的價差？
他還跟我嗆聲他是第一志願的學生，
讓我發現人碰到投資就變笨。
他說他是長期投資者「只在意股息，不管價差。」
「這樣好了，」我回「把你買的股票給我，我每年把股息匯給你。」
這時他才悻悻然掛上電話。

A student spent 10 minutes on the phone pestering me about this issue.
I asked him, "Have you ever heard of earning dividends but losing on capital gains?"
This is a guy who complains every time stock prices drop, yet now suddenly seems to have dismissed the importance of capital gains.
He even boasted about being a student at a top university, which made me realize how stupid people can become when it comes to investing.
He insisted he was a long-term investor, saying, "I only care about dividends and don't care about capital gains."
So, I replied, "Here’s an idea: hand over the stocks you bought, and I’ll send you the dividends every year."
It was only then that he grudgingly hung up the phone.

坊間一堆不良理財達人和雜誌都在誤導大家，
說只要把錢存到殖利率5%的股票，
累積到每年可以領200萬元股息時就財務自由了！
一個年輕人如獲至寶的分享給我這個觀念。
我回「這不是一句廢話嗎？
問題是這需要4千萬元本金，從何而來？」
同學說他的月薪才3萬多元。
我說「你讀的那些書刊沒教嗎？怎麼跑來問我？」

There are so many lousy financial experts and magazines misleading people, claiming that simply investing in stocks with a 5% yield and accumulating enough to earn NT$2 million in annual dividends will lead to financial freedom.
A young man excitedly shared this idea with me, as if he had discovered a hidden treasure.
I replied, "Isn't this nonsense ? The real question is, where do you get the NT$40 million in principal needed for that ?"
This student then mentioned that his monthly salary is just over NT$30,000.
I responded, "Didn’t the books and magazines you read explain that? Why are you asking me instead ?"

那些所謂的達人不懂裝懂，
還說只要高配息都不用賣，
不管多貴都可以買！
是嗎？
中碳若買在200元，後來跌到100元，
配息4元，要配25年息才解套！
一個人大概只有3個25年，
第一個25年在唸書，唸一些沒用的書，
第二個25年在工作，大部分人工作附加價值都不高。
時間過得很快，我僅剩最後一個25年，
若仍在這裡跟大家「高ROE，低盈再率」就悲哀了，
驚覺不對，應該要去做一些更有意義的事，
所以就宣布不教了。
中碳買在200元的人25年則在等解套，豈不更可悲？ !

Those so-called experts know nothing but pretend they do. They even claim that as long as the dividend is high, there's no need to sell, and you can buy no matter how expensive it gets ! Really ? For instance, if one bought China Steel Chemical at NT$200, and the price subsequently dropped to NT$100, with a dividend yield of NT$4, it would take 25 years to break even! A person probably only has three sets of 25 years. During the first 25 years, one learns from books that are often of little use. During the next 25 years, most people work in jobs with low added value. Time flies by quickly, and I only have my last 25 years left. It would be miserable  if I were still here teaching everyone about "high ROE, low P/E ratios". Realizing this, I decided to do something more meaningful and announced that I would no longer teach. How sad it is for those who bought China Steel Chemical at NT$200 and have been waiting for 25 years to break even !



2024年9月5日中碳跌回我2011年賣出的還原股價，
當年未隨著我賣掉的人白抱了，漫長的13年4個月。
證明股票貴了要賣績效才會好 ，
股票貴了還買，想當盤子嗎 ?
貴了也不賣，傻了嗎 ?

On September 5, 2024, China Steel Chemical's stock price returned to the adjusted level where I sold it back in 2011.
Those who chose not to sell when I did have been stuck holding the stock for a long 13 years and 4 months.
This clearly demonstrates that selling overpriced stocks is essential for achieving strong performance.
Buying overpriced stocks—are you setting yourself up to be taken advantage of?
Not selling when it's expensive? Are you a fool ?

mikeon88

2015年理專猛推南非幣，說利率高。
結果呢？賠了匯差。

In 2015, financial advisers strongly recommended investing in the South African currency, Rand, due to its high interest rates. The outcome? Investors suffered significant exchange losses.

買房的人都在算租金報酬率，說3%很不錯。
卻忘了房價會跌。
2013年跟大家警告房價會跌，沒人相信，
都以為房價是無敵的，不可能跌。
這世界哪有只漲不跌的商品，
若有的話世上就不會有窮人了，
我們祖先在漢朝買一幢房子到現在大家不都發了嗎？

Housing investors are calculating rental returns and considering 3% to be a good rate. However, they seem to overlook the possibility of house prices falling. In 2013, I warned others that house prices were likely to decline, but nobody believed me. They all thought that house prices were invulnerable and would never decrease. However, if such a commodity existed, nobody would be poor in the world. Our ancestors purchased houses during the Han Dynasty and passed them down to the next generation. Does that mean everyone is wealthy now?

很多人比較買房的報酬率
都是拿20年前買的屋子
跟現在的新房作比較
這是錯的
20年後已是舊屋扣掉折舊
沒那麼值錢了

Many people evaluate housing returns by comparing homes purchased 20 years ago with new ones today.
That’s a mistake — a 20-year-old house has already aged and depreciated, so it’s no longer as valuable.

最近又聽到怪論，理專慫恿客戶把房子拿去貸款，
說利率不到3%，拿來買高收益債的利率6%可以套利？
可以套利嗎？
用3%去套利6%的前提是6%的債券價格不跌才有，
可是高收債跟股市的漲跌同方向且同樣劇烈，
怎麼套利？

I recently came across a strange argument that bank advisors are encouraging customers to take out a mortgage on their homes at a 3% interest rate and invest in 6% high-yield bonds, claiming it as an arbitrage opportunity. But is it really an arbitrage opportunity? The premise of this strategy is based on the assumption that the price of 6% bonds will not decline, but high-yield bonds are known to fluctuate with the stock market and can be quite volatile. So, how can one actually arbitrage in this scenario?

以上種種問題俱是殖利率陷阱！
賺股息，賠了價差。

All of these issues can be yield traps: earning dividends while suffering capital losses.



為何高股息ETF的績效很差
因為不是只看股息還要看價差
貴淑價的計算不是殖利率
而是IRR或本益比
 
Why has the performance of high-dividend ETFs been so poor ?
Because it’s not just about dividends you also need to factor in capital gains. Whether a stock is cheap or expensive isn’t determined by its yield rate, but by its IRR or PE ratio.

除了股息之外4大條件都要面面俱到
1. 高ROE
2. 配得出現金，即高配息和低盈再率
3. 不會變的公司
4. 預期報酬率大於15%

Beyond dividend yield, four key conditions must also be met:
1. High ROE
2. The ability to consistently generate cash for dividends (i.e., high dividend payout ratio and low profit reinvestment rate)
3. A stable and enduring business
4. An expected return above 15%

只看殖利率等於瞎子摸象，
只摸到尾巴就以為大象是一條蛇，
當然畫虎不成反類犬

Focusing only on dividend yield is like a blind person feeling an elephant—touching just the tail and thinking the elephant is a snake. Naturally, you end up trying to draw a tiger but producing something more like a dog.

mikeon88

講稿15/21 GDP理論
Lecture 15/21 GDP Theory

便宜價僅表示股價便宜，
可是當大盤不好時，便宜還會更便宜。
2008年金融風暴許多股票跌到便宜價以下又再跌40%。
別以為選高ROE、高配息的股票，等到便宜才買，
就不會被斷頭，照樣會！

Cheap price only means that stock price is cheap, but during a market downturn, the prices can plummet even further. For instance, during the 2008 financial crisis, many stocks that were previously deemed cheap fell by an additional 40%. Relying solely on selecting stocks with high ROE and dividends and waiting for them to become cheap is not sufficient. It is still possible to experience a margin call with this approach.



從過去記錄發現，GDP年增率跟大盤指數高度相關，
底下這張圖從1990年以來到現在，是相當完整的一張圖。
若這個現象過去都成立就別懷疑這次會不準，
每逢大盤高點老是有同學質疑GDP理論不準。

Based on past records, it has been found that the annual GDP growth rate is highly correlated with the major stock indices. The chart below, which covers the period from 1990 to the present, is quite comprehensive. If this phenomenon has consistently held true in the past, there is no reason to doubt its accuracy this time. Whenever the stock market reaches a high point, some people inevitably question the validity of the GDP theory.