巴菲特致股東函 2022

 BERKSHIRE HATHAWAY INC.


To the Shareholders of Berkshire Hathaway Inc.:

致波克夏公司股東:

Charlie Munger, my long-time partner, and I have the job of managing the savings of a great number of individuals. We are grateful for their enduring trust, a relationship that often spans much of their adult lifetime. It is those dedicated savers that are forefront in my mind as I write this letter.

我和我的長期搭檔查理 · 孟格 (Charlie Munger),我們的工作就是管理大量股東的儲蓄,能獲得大家長久以來的信任,且這種信任往往能貫穿一生中的大部分時間,我感到非常榮幸。當我在寫這封信的時候,腦海中浮現的是那些專注的股東們。

A common belief is that people choose to save when young, expecting thereby to maintain their living standards after retirement. Any assets that remain at death, this theory says, will usually be left to their families or, possibly, to friends and philanthropy.

一般來說,人們的普遍觀念是,年輕時進行儲蓄,希望以此維持退休後的生活水平。去世後,遺留的所有資產通常會留給家人,也可能是朋友或慈善機構。


Our experience has differed. We believe Berkshire’s individual holders largely to be of the once-a-saver, always-a-saver variety. Though these people live well, they eventually dispense most of their funds to philanthropic organizations. These, in turn, redistribute the funds by expenditures intended to improve the lives of a great many people who are unrelated to the original benefactor. Sometimes, the results have been spectacular.

但我們的觀點有所不同,我們認為,波克夏的股東基本上是「儲蓄一次,儲蓄一輩子」的類型。儘管這些人生活優渥,但他們最終會將大部分資產捐獻給慈善機構。反過來,慈善機構又會用來改善許多與原始捐助者無關的人的生活,從而重新分配資金。有時,產生的結果是驚人的。

The disposition of money unmasks humans. Charlie and I watch with pleasure the vast flow of Berkshire-generated funds to public needs and, alongside, the infrequency with which our shareholders opt for look-at-me assets and dynasty-building.

一個人如何對待金錢,暴露了他是個怎樣的人。查理和我很高興地看到,波克夏產生的大量資金流向公眾需求,以及我們的股東很少關注波克夏資產和帝國建設。

Who wouldn’t enjoy working for shareholders like ours?

誰會不喜歡為我們這樣的股東工作呢?


What We Do

Charlie and I allocate your savings at Berkshire between two related forms of ownership. First, we invest in businesses that we control, usually buying 100% of each. Berkshire directs capital allocation at these subsidiaries and selects the CEOs who make day-by-day operating decisions. When large enterprises are being managed, both trust and rules are essential. Berkshire emphasizes the former to an unusual – some would say extreme – degree. Disappointments are inevitable. We are understanding about business mistakes; our tolerance for personal misconduct is zero.

查理和我將股東在波克夏的儲蓄分配成兩種相關的所有權形式。首先,投資於我們的全資控股企業,通常購買公司 100% 的股權。波克夏在這些子公司進行資本配置,並挑選負責日常營運決策的執行長。當管理大型企業時,信任和規則都是缺一不可的。

波克夏對前者的強調達到了不同尋常——以至於有人會說是極端的程度。失望是不可避免的,我們可以理解商業錯誤,但我們對個人不當行為的容忍度為零。


In our second category of ownership, we buy publicly-traded stocks through which we passively own pieces of businesses. Holding these investments, we have no say in management.

在我們的第二類所有權中,我們購買公開交易的股票,透過購買這些股票,我們被動地擁有部分業務。持有這些投資時,我們在管理方面沒有發言權。

Our goal in both forms of ownership is to make meaningful investments in businesses with both long-lasting favorable economic characteristics and trustworthy managers. Please note particularly that we own publicly-traded stocks based on our expectations about their long-term business performance, not because we view them as vehicles for adroit purchases and sales. That point is crucial: Charlie and I are not stock-pickers; we are business-pickers.

我們在這兩種所有權形式中的目標都是,對具有長期良好經濟特徵和值得信賴的管理者的企業進行有意義的投資。請特別注意,我們持有股票是基於我們對企業長期經營業績的預期,而不是將其視為熟練買賣的工具。這一點很關鍵:查理和我不是選股高手,我們是選擇商業模式的人。

Over the years, I have made many mistakes. Consequently, our extensive collection of businesses currently consists of a few enterprises that have truly extraordinary economics, many that enjoy very good economic characteristics, and a large group that are marginal. Along the way,other businesses in which I have invested have died, their products unwanted by the public.Capitalism has two sides: The system creates an ever-growing pile of losers while concurrently delivering a gusher of improved goods and services. Schumpeter called this phenomenon “creative
destruction.”

這些年來,我犯了很多錯誤。因此,我們廣泛的業務集合目前包括少數真正具有非凡經濟效益的企業,許多企業具有非常好的經濟特徵,以及一群龐大的邊緣企業。

在這一過程中,我投資的其他企業已經消亡,它們的產品被公眾拋棄。資本主義具有兩面性:一方面製度造就了越來越多的失敗者,但同時也帶來了大量改進的商品和服務。熊彼特稱這種現象為「創造性破壞」(creative destruction)。

One advantage of our publicly-traded segment is that – episodically – it becomes easy to buy pieces of wonderful businesses at wonderful prices. It’s crucial to understand that stocks often trade at truly foolish prices, both high and low. “Efficient” markets exist only in textbooks. In truth, marketable stocks and bonds are baffling, their behavior usually understandable only in retrospect.

我們的公開交易部門的一個優勢是,偶爾可以很容易地以極好的價格買到非常優秀的企業。重要的是要明白,股票會不時地以愚蠢的價格交易,可能是高也可能是低。「有效市場」只存在於教科書中。事實上,有市場的股票和債券令人困惑,它們的行為通常只有在回顧時才能理解。

Controlled businesses are a different breed. They sometimes command ridiculously higher prices than justified but are almost never available at bargain valuations. Unless under duress, the owner of a controlled business gives no thought to selling at a panic-type valuation.

被控股企業是另一種類型,有時它們的價格比合理價格高得離譜,但幾乎永遠不會以低價出售。除非受到脅迫,否則控股企業的所有者不會考慮以恐慌性估值出售。
 
* * * * * * * * * * * *
At this point, a report card from me is appropriate: In 58 years of Berkshire management,most of my capital-allocation decisions have been no better than so-so. In some cases, also, bad moves by me have been rescued by very large doses of luck. (Remember our escapes from near-disasters at USAir and Salomon? I certainly do.)

在這一點上,我的成績單是合適的:在波克夏 58 年的管理中,我的大部分資本配置決策都不過馬馬虎虎。此外,在某些情況下,我沒走好的棋也靠著很大的運氣得以挽救。(還記得我們在美國航空和所羅門公司險些發生的災難中逃生的故事嗎?我當然記得。)

Our satisfactory results have been the product of about a dozen truly good decisions – that would be about one every five years – and a sometimes-forgotten advantage that favors long-term investors such as Berkshire. Let’s take a peek behind the curtain.

我們令人滿意的結果是十幾個真正睿智決定的產物——大約每五年一個——以及一個有時被遺忘的優勢,它有利於像波克夏這樣的長期投資人。讓我們來窺探一下幕後的情況。

The Secret Sauce

In August 1994 – yes, 1994 – Berkshire completed its seven-year purchase of the 400 million shares of Coca-Cola we now own. The total cost was $1.3 billion – then a very meaningful sum at Berkshire.

1994 年 8 月——是的,1994 年——波克夏完成了為期 7 年的收購,購買了我們現在擁有的 4 億股可口可樂股票,總成本為 13 億美元——這對波克夏來說是一筆非常大的數目。

The cash dividend we received from Coke in 1994 was $75 million. By 2022, the dividend had increased to $704 million. Growth occurred every year, just as certain as birthdays. All Charlie and I were required to do was cash Coke’s quarterly dividend checks. We expect that those checks are highly likely to grow.

1994 年我們從可口可樂公司收到的現金股利為 7500 萬美元,到 2022 年,股利增加到 7.04 億美元。這樣的增長每年都在發生,就像生日一樣確定。我和查理所要做的就是兌現可口可樂的季度股利支票。我們預計這筆金額很可能會增加。

American Express is much the same story. Berkshire’s purchases of Amex were essentially completed in 1995 and, coincidentally, also cost $1.3 billion. Annual dividends received from this investment have grown from $41 million to $302 million. Those checks, too, seem highly likely to increase.

美國運通的情況大致相同。波克夏對美國運通的收購基本上在 1995 年完成,巧合的是,也花費了 13 億美元。從這項投資中獲得的年度股利已從 4100 萬美元增長到 3.02 億美元。這筆金額似乎也很有可能增加。

These dividend gains, though pleasing, are far from spectacular. But they bring with them important gains in stock prices. At yearend, our Coke investment was valued at $25 billion while Amex was recorded at $22 billion. Each holding now accounts for roughly 5% of Berkshire’s net worth, akin to its weighting long ago.

這些股利收益雖然令人高興,但遠非壯觀。但它們推動了股價的重要上漲。今年(2022 年)底,我們對可口可樂的投資價值為 250 億美元,而美國運通的投資價值為 220 億美元。現在這兩隻股票約占波克夏淨資產的 5%,與很久以前的權重相當。

Assume, for a moment, I had made a similarly-sized investment mistake in the 1990s, one that flat-lined and simply retained its $1.3 billion value in 2022. (An example would be a high-grade 30-year bond.) That disappointing investment would now represent an insignificant 0.3% of Berkshire’s net worth and would be delivering to us an unchanged $80 million or so of annual income.

假設我在上世紀 90 年代犯了一個類似規模的投資錯誤,這筆投資在 2022 年仍然價值 13 億美元 (比如 30 年期高等級債券)。這筆令人失望的投資現在只佔波克夏淨資產的微不足道的 0.3%,但仍將為我們帶來大約 8000 萬美元的年收入。

The lesson for investors: The weeds wither away in significance as the flowers bloom. Over time, it takes just a few winners to work wonders. And, yes, it helps to start early and live into your 90s as well.

給投資人的教訓:野草會在鮮花盛開的時候枯萎 (The weeds wither away in significance as the flowers bloom.),這同樣意義重大。隨著時間推移,只需少數勝利就能創造奇蹟。而且,是的,早點開始也有幫助,還能幫助你活到 90 多歲。

The Past Year in Brief

Berkshire had a good year in 2022. The company’s operating earnings – our term for income calculated using Generally Accepted Accounting Principles (“GAAP”), exclusive of capital gains or losses from equity holdings – set a record at $30.8 billion. Charlie and I focus on this operational figure and urge you to do so as well. The GAAP figure, absent our adjustment, fluctuates wildly and capriciously at every reporting date. Note its acrobatic behavior in 2022,which is in no way unusual:

波克夏在 2022 年表現不錯。公司調整後的營業利益——我們使用公認會計原則 (GAAP),不包括持有股票的資本利得——創下了 308 億美元的歷史新高。查理和我專注於這個實際數字,並建議你也這樣做。不過,如果沒有我們的調整,GAAP 數據在每個報告日都會劇烈波動。請注意它在 2022 年的波動,這並不罕見:

                                                                                           Earnings in $ billions
  2022 Quarter          “Operating Earnings”           GAAP Earnings We are Required to Report
              1                             7.0                                                         5.5
              2                             9.3                                                        (43.8)
              3                             7.8                                                         (2.7)
              4                             6.7                                                         18.2

The GAAP earnings are 100% misleading when viewed quarterly or even annually. Capital gains, to be sure, have been hugely important to Berkshire over past decades, and we expect them to be meaningfully positive in future decades. But their quarter-by-quarter gyrations, regularly and mindlessly headlined by media, totally misinform investors.

按季甚至按年查看 GAAP 利益具有 100% 的誤導性。可以肯定的是,在過去幾十年裡,資本利得對波克夏來說非常重要,我們預估在未來幾十年裡,資本利得將顯著增加。但是,媒體經常無意識地報導它們每個季度的波動,這完全誤導投資人。

A second positive development for Berkshire last year was our purchase of Alleghany Corporation, a property-casualty insurer captained by Joe Brandon. I’ve worked with Joe in the past, and he understands both Berkshire and insurance. Alleghany delivers special value to us because Berkshire’s unmatched financial strength allows its insurance subsidiaries to follow valuable and enduring investment strategies unavailable to virtually all competitors.

波克夏去年的第二個積極進展是我們收購了由喬 · 布蘭登 (Joe Brandon) 擔任董事長的財產意外保險公司 Alleghany Corporation。我過去曾與喬共事,他對波克夏和保險都很了解。Alleghany 為我們帶來特殊的價值,因為波克夏無與倫比的財務實力使其保險子公司能夠採用幾乎所有競爭對手都無法遵循的、有價值且持久的投資策略。

Aided by Alleghany, our insurance float increased during 2022 from $147 billion to $164 billion. With disciplined underwriting, these funds have a decent chance of being cost-free over time. Since purchasing our first property-casualty insurer in 1967, Berkshire’s float has increased 8,000-fold through acquisitions, operations and innovations. Though not recognized in our financial statements, this float has been an extraordinary asset for Berkshire. New shareholders can get an understanding of its value by reading our annually updated explanation of float on page A-2.

在 Alleghany 的幫助下,我們的保險浮存金在 2022 年從 1470 億美元增加到 1640 億美元。透過嚴格的承銷,隨著時間的推移,這些款項有相當大的機會實現零成本。自 1967 年收購第一家財產意外險公司以來,藉由收購、營運和創新,波克夏的浮存金增長 8000 倍。雖然在我們的財務報表中沒有得到證實,但這筆浮存金對波克夏來說是一筆非凡的資產。新股東可以透過閱讀 A-2 文件,看到我們每年更新的浮存金解釋,來了解其價值。

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A very minor gain in per-share intrinsic value took place in 2022 through Berkshire share repurchases as well as similar moves at Apple and American Express, both significant investees of ours. At Berkshire, we directly increased your interest in our unique collection of businesses by repurchasing 1.2% of the company’s outstanding shares. At Apple and Amex, repurchases increased Berkshire’s ownership a bit without any cost to us.

2022 年,由於波克夏與我們重倉的蘋果、美國運通公司都回購股票,波克夏的每股內在價值略微增長。在波克夏,透過對公司已發行股份的 1.2% 進行回購,我們直接提高了您在我們獨特的持倉組合中的權益。蘋果和美國運通的回購也提高波克夏的持股比例,而我們沒有增加任何成本。

The math isn’t complicated: When the share count goes down, your interest in our many businesses goes up. Every small bit helps if repurchases are made at value-accretive prices. Just as surely, when a company overpays for repurchases, the continuing shareholders lose. At such times, gains flow only to the selling shareholders and to the friendly, but expensive, investment banker who recommended the foolish purchases.

這裡的計算並不復雜:當股本數量減少時,您持有的眾多企業中的股權佔比就會增加。如果回購價格低於公司內在價值,那麼每一分錢回購對股東都有益處。當然,若公司以過高價格回購股票,繼續持有的股東會遭受損失。在這種時候,收益只會流向拋售股票的投資人,以及那些熱情推薦愚蠢購買行為但卻收費高昂的投資銀行家。

Gains from value-accretive repurchases, it should be emphasized, benefit all owners – in every respect. Imagine, if you will, three fully-informed shareholders of a local auto dealership, one of whom manages the business. Imagine, further, that one of the passive owners wishes to sell his interest back to the company at a price attractive to the two continuing shareholders. When completed, has this transaction harmed anyone? Is the manager somehow favored over the continuing passive owners? Has the public been hurt?

值得強調的是,如果回購價格低於公司內在價值,那麼公司所有股東將全面受益。如果您願意,可以思考下面的例子:一家當地汽車經銷商有三個完全知情的股東,其中一個負責企業管理。進一步想像一下,其中一位消極的股東,希望將他的權益賣回給公司,而且價格對另外兩位繼續持有的股東有吸引力。

交易完成後,是否對任何人的利益造成傷害?經理是否比持續消極的股東更受青睞?公眾是否受到傷害?

When you are told that all repurchases are harmful to shareholders or to the country, or particularly beneficial to CEOs, you are listening to either an economic illiterate or a silver-tongued demagogue (characters that are not mutually exclusive).

當有人告訴你,所有的回購行為都對股東或國家有害,或者對執行長特別有利時,那麼你要不是在聽一個經濟文盲說話,就是在聽一個能言善辯的煽動家說話 (這兩個角色並不互斥)。


Almost endless details of Berkshire’s 2022 operations are laid out on pages K-33 – K-66. Charlie and I, along with many Berkshire shareholders, enjoy poring over the many facts and figures laid out in that section. These pages are not, however, required reading. There are many Berkshire centimillionaires and, yes, billionaires who have never studied our financial figures. They simply know that Charlie and I – along with our families and close friends – continue to have very significant investments in Berkshire, and they trust us to treat their money as we do our own.

波克夏 2022 年的所有營運細節幾乎概述於 K-33 到 K-66 頁上。孟格和我,以及許多波克夏股東,都喜歡仔細研究這部分列出的諸多事實和數據。不過,這幾頁也不是必讀的。波克夏有很多百萬富翁,沒錯,還有一些億萬富豪,他們從來沒有研究過我們的財務數據。

他們只是知道,孟格和我——以及我們的家人和親密的朋友— —繼續在波克夏有大量投資,他們相信我們會像對待自己的錢一樣對待他們的錢。

And that is a promise we can make.

這也是我們可以做出的承諾。

* * * * * * * * * * * *

Finally, an important warning: Even the operating earnings figure that we favor can easilybe manipulated by managers who wish to do so. Such tampering is often thought of as sophisticated
by CEOs, directors and their advisors. Reporters and analysts embrace its existence as well. Beating “expectations” is heralded as a managerial triumph.

最後,一個重要的警告:財務報表中的「營運利益」是我們非常關注的,但這些數字很容易經理人操縱,只要他們想要這樣做。通常,執行長、董事和他們的顧問們也認為,這種篡改行為是久經世故的。記者和分析師也把這一行為當做家常便飯。畢竟,打破「預期」也是管理上的一次勝利。

That activity is disgusting. It requires no talent to manipulate numbers: Only a deep desire to deceive is required. “Bold imaginative accounting,” as a CEO once described his deception to me, has become one of the shames of capitalism.

(不過,)這種行為真的很噁心。操縱數字不需要天賦,只需要強烈的欺騙慾望。一位執行官曾對我說,「大膽而富有想像力的會計(Bold imaginative accounting)」已經成為資本主義的恥辱之一。

58 Years – and a Few Figures

In 1965, Berkshire was a one-trick pony, the owner of a venerable – but doomed – New England textile operation. With that business on a death march, Berkshire needed an immediate fresh start. Looking back, I was slow to recognize the severity of its problems.

1965 年,波克夏還只是一匹「只懂一種戲法的小馬」(即業務組成簡單),擁有一家歷史悠久、但注定要倒閉的新英格蘭紡織企業。隨著這項業務走向死亡,波克夏需要立即有一個新的開始。回過頭來看,我當時遲遲沒有意識到問題的嚴重性。

And then came a stroke of good luck: National Indemnity became available in 1967, and we shifted our resources toward insurance and other non-textile operations.

但隨後,我們就迎來了一次好運:1967 年,國民保險 (National Indemity) 成立,我們將資源轉向保險和其他非紡織業務。

Thus began our journey to 2023, a bumpy road involving a combination of continuous savings by our owners (that is, by their retaining earnings), the power of compounding, our avoidance of major mistakes and – most important of all – the American Tailwind. America would have done fine without Berkshire. The reverse is not true.

就這樣,我們開啟了通往 2023 年的旅程,這是一條崎嶇坎坷的道路,包括我們所有者不斷的儲蓄(即透過他們的留存收益)、複利的力量、避免重大錯誤,以及最重要——搭上「美國順風」(American Tailwind)。沒有波克夏,美國也會過得不錯。反之則不然。

Berkshire now enjoys major ownership in an unmatched collection of huge and diversified businesses. Let’s first look at the 5,000 or so publicly-held companies that trade daily on NASDAQ, the NYSE and related venues. Within this group is housed the members of the S&P 500 Index, an elite collection of large and well-known American companies.

現在,波克夏擁有「無與倫比的龐大和多元化業務」的主要所有權。讓我們先看看每天在納斯達克、紐約證券交易所和相關交易場所交易的大約 5000 家上市公司。在這一群體中,有標準普爾 500 指數的成員。標準普爾 500 指數是一個由大型知名美國公司組成的精英集合。

In aggregate, the 500 earned $1.8 trillion in 2021. I don’t yet have the final results for 2022.Using, therefore, the 2021 figures, only 128 of the 500 (including Berkshire itself) earned $3 billion or more. Indeed, 23 lost money.

總體而言,這 500 家上市公司在 2021 年賺了 1.8 萬億美元。目前我還沒有 2022 年的最終數據。因此,使用 2021 年的數據,這 500 家公司中只有 128 家(包括波克夏)賺了 30 億美元或更多。事實上,還有 23 家公司虧損。

At yearend 2022, Berkshire was the largest owner of eight of these giants: American Express, Bank of America, Chevron, Coca-Cola, HP Inc., Moody’s, Occidental Petroleum and Paramount Global.

截至 2022 年底,波克夏是其中八家巨頭的最大股東:美國運通、美國銀行、雪佛龍、可口可樂、惠普股份、穆迪、西方石油和派拉蒙全球。

In addition to those eight investees, Berkshire owns 100% of BNSF and 92% of BH Energy, each with earnings that exceed the $3 billion mark noted above ($5.9 billion at BNSF and $4.3 billion at BHE). Were these companies publicly-owned, they would replace two present members of the 500. All told, our ten controlled and non-controlled behemoths leave Berkshire more broadly aligned with the country’s economic future than is the case at any other U.S.company. (This calculation leaves aside “fiduciary” operations such as pension funds and investment companies.) In addition, Berkshire’s insurance operation, though conducted through many individually-managed subsidiaries, has a value comparable to BNSF or BHE.

除去 8 家標的外,波克夏還持有伯靈頓北方鐵路運輸公司(簡稱 BNSF)100% 的股份和波克夏能源公司(BHE)92% 的股份,每個公司的獲利都超過上述 30 億美元的標準(BNSF 為 59 億美元,BHE 為 43 億美元)。

如果這兩家公司公開上市,它們將被收錄進那 500 強公司中。總體而言,我們的控股和非控股的 10 家巨頭,使波克夏公司比任何其他美國公司都更廣泛地與本國的經濟未來保持一致。(這一計算不考慮退休基金和投資公司等「信託」業務。)

此外,波克夏的保險業務雖然經由許多單獨管理的子公司進行,但其價值與 BNSF 或波克夏能源相當。

As for the future, Berkshire will always hold a boatload of cash and U.S. Treasury bills along with a wide array of businesses. We will also avoid behavior that could result in any uncomfortable cash needs at inconvenient times, including financial panics and unprecedented insurance losses. Our CEO will always be the Chief Risk Officer – a task it is irresponsible to delegate. Additionally, our future CEOs will have a significant part of their net worth in Berkshire shares, bought with their own money. And yes, our shareholders will continue to save and prosper by retaining earnings.

至於未來,波克夏將始終持有大量現金和美國國債,以及其他各種更加廣泛業務。我們還將避免任何會在關鍵時刻導致現金流緊缺的魯莽行為,哪怕是在金融恐慌和前所未有的保險損失的時刻。

我們的執行長將永遠是風險長——儘管他(她)本不必承擔這項責任。此外,我們未來的執行長將有相當一部分的淨資產收益是用自己的錢購買波克夏股票而獲得的。是的,我們的股東將透過持續的獲得收益,確保儲蓄和繁榮。

At Berkshire, there will be no finish line.

波克夏,不會有終點線。

Some Surprising Facts About Federal Taxes

During the decade ending in 2021, the United States Treasury received about $32.3 trillion
in taxes while it spent $43.9 trillion.

在截至 2021 年的十年間,美國財政部的稅收為 32.3 萬億美元,而支出卻達到 43.9 萬億美元,出現了嚴重的財政赤字。

Though economists, politicians and many of the public have opinions about the consequences of that huge imbalance, Charlie and I plead ignorance and firmly believe that near-term economic and market forecasts are worse than useless. Our job is to manage Berkshire’s operations and finances in a manner that will achieve an acceptable result over time and that will preserve the company’s unmatched staying power when financial panics or severe worldwide recessions occur. Berkshire also offers some modest protection from runaway inflation, but this attribute is far from perfect. Huge and entrenched fiscal deficits have consequences.

眾多經濟學家、政治家及名人均對財政失衡的現狀發表了自己的看法,但查理和我卻自認對此知之甚少,但我們堅信如此龐大的財政赤字的糟糕的程度或許遠超市場所想。

我們負責管理波克夏的營運和財務,希望公司能長期維持比較高的收益,並在金融風險加劇及全球經濟出現衰退時依舊保持活力。

為了能避免持續高企的通脹問題,波克夏對沖了部分風險,來給投資人們提供一定保護,但這層保護遠非完美,美國財政如此龐大且根深蒂固的赤字會帶來嚴重後果。

The $32 trillion of revenue was garnered by the Treasury through individual income taxes (48%), social security and related receipts (34 1⁄2%), corporate income tax payments (8 1⁄2%) and a wide variety of lesser levies. Berkshire’s contribution via the corporate income tax was $32 billion during the decade, almost exactly a tenth of 1% of all money that the Treasury collected.

根據數據來看,美國財政部的稅收包括個人所得稅(48%)、社會保障和相關收入 (34.5%)、企業所得稅支付 (8.5%) 和各種較小的徵收項目獲得了 32 萬億美元的收人。波克夏公司在這十年間藉由貢獻 320 億美元的所得稅,幾乎為財政部所有收入的千分之一。

And that means – brace yourself – had there been roughly 1,000 taxpayers in the U.S.matching Berkshire’s payments, no other businesses nor any of the country’s 131 million households would have needed to pay any taxes to the federal government. Not a dime.

這也意味著,美國僅需 1000 個波克夏實力相當的納稅企業,那麼其他企業和全國 1.31 億個家庭都不需要向聯邦政府支付任何稅收。

* * * * * * * * * * * *

Millions, billions, trillions – we all know the words, but the sums involved are almost impossible to comprehend. Let’s put physical dimensions to the numbers:

幾百萬、幾十化、幾萬億——我們都知道這些詞,但往往無法理解所涉及的龐大金額,讓我們給這些數字加上直觀的尺寸。

• If you convert $1 million into newly-printed $100 bills, you will have a stack that reaches your chest.

如果你把 100 萬美元兌換成新印製的 100 美元鈔票,你會有一疊達到你胸口高度的鈔票。

• Perform the same exercise with $1 billion – this is getting exciting! – and the stack reaches about 3⁄4 of a mile into the sky.

如果是 10 億美元——這時美元現金可以堆疊至 3/4 英里(約 1207 米)的天空。

• Finally, imagine piling up $32 billion, the total of Berkshire’s 2012-21 federal income tax payments. Now the stack grows to more than 21 miles in height, about three times the level at which commercial airplanes usually cruise.

最後想像 320 億美元,這也是波克夏在 2012 至 2021 年所繳納的所有聯邦所得稅,現在,這堆錢達到了超 21 英里以上(約 3.3 萬米)的高度,大約是商業飛機通常巡航高度的三倍。

When it comes to federal taxes, individuals who own Berkshire can unequivocally state “I gave at the office.”

因此,每次涉及到聯邦稅時,波克夏可以毫不含糊地表示「我們給了」。

* * * * * * * * * * * *

At Berkshire we hope and expect to pay much more in taxes during the next decade. We owe the country no less: America’s dynamism has made a huge contribution to whatever success Berkshire has achieved – a contribution Berkshire will always need. We count on the American Tailwind and, though it has been becalmed from time to time, its propelling force has always returned.

對於波克夏而言,我們希望且期待著在未來十年可以為美國繳納更多稅款,做出更大的貢獻。美國的經濟活力賦能了波克夏取得的所有成功。

I have been investing for 80 years – more than one-third of our country’s lifetime. Despite our citizens’ penchant – almost enthusiasm – for self-criticism and self-doubt, I have yet to see a time when it made sense to make a long-term bet against America. And I doubt very much that any reader of this letter will have a different experience in the future.

我已經做了 80 年的投資,超過美國建國時長的三分之一。儘管我們總是喜歡自我批評和懷疑,但我還沒在任何時候看到長期做空美國是有意義的。

Nothing Beats Having a Great Partner

Charlie and I think pretty much alike. But what it takes me a page to explain, he sums up in a sentence. His version, moreover, is always more clearly reasoned and also more artfully – some might add bluntly – stated.

查理 · 孟格和我的想法很相似,但我往往需要一頁紙來解釋的內容,他卻可以用一句話總結,且邏輯清晰,直抒胸臆。

Here are a few of his thoughts, many lifted from a very recent podcast:

以下是他的一些想法,很多都是從最近的 Podcast 中截取的:


• The world is full of foolish gamblers, and they will not do as well as the patient investor.

世界上有很多愚益的賭徒,他們遠不如有耐心的投資人。

• If you don’t see the world the way it is, it’s like judging something through a distorted lens.

當你還未看清世界的本來面目,便只能透過扭曲的鏡頭來判斷。

• All I want to know is where I’m going to die, so I’ll never go there. And a related thought:Early on, write your desired obituary – and then behave accordingly.

我想知道的是我將在哪裡死去,那我永遠不會去那裡。還有一個相關的想法:儘早寫下你想要的訃告——然後據此行事

• If you don’t care whether you are rational or not, you won’t work on it. Then you will stay
irrational and get lousy results.

如果你不關心自己是否理性,你就不會在這方面下功夫。那麼你就會一直不理性,得到最差的結果。

• Patience can be learned. Having a long attention span and the ability to concentrate on one
thing for a long time is a huge advantage.

耐心是可以學習的,擁有長時間的注意力且可以長時間集中於一件事的能力是巨大的優勢。

• You can learn a lot from dead people. Read of the deceased you admire and detest.

你可以從死去的人身上學到很多東西,閱讀你所崇拜和厭惡的死者的文章。

• Don’t bail away in a sinking boat if you can swim to one that is seaworthy.

如果你能游到一艘適航的船,就不要在下沉的船上跳走。

• A great company keeps working after you are not; a mediocre company won’t do that.

一個偉大的公司會在你不在之後繼續工作;一個平庸的公司則不會。

• Warren and I don’t focus on the froth of the market. We seek out good long-term investments and stubbornly hold them for a long time.

華倫和我不關注市場的泡沫,我們一直尋找長期投資機會,並堅持長期持有。

• Ben Graham said, “Day to day, the stock market is a voting machine; in the long term it’s a weighing machine.” If you keep making something more valuable, then some wise person is going to notice it and start buying.

本 · 葛拉漢(Ben Graham)曾說:「從短期看,市場是一台投票機,但從長遠來看,它是一台秤重機。如果你不斷地製造更有價值的東西,那麼一些聰明的人就會注意到它並開始購買,仔細權衡長期價值會比試圖猜測短期熱點更能創造出卓越的業績。」

• There is no such thing as a 100% sure thing when investing. Thus, the use of leverage is dangerous. A string of wonderful numbers times zero will always equal zero. Don’t count on getting rich twice.

投資是沒有 100% 的把握,因此,使用槓桿是危險的。一串美妙的數字乘以零,永遠等於零。不要指望一夜暴富。

• You don’t, however, need to own a lot of things in order to get rich.

然而,你不需要擁有很多東西就能致富。

• You have to keep learning if you want to become a great investor. When the world changes,
you must change.

如果你想成為一個偉大的投資人,你必須不斷學習。當世界發生變化時,你必須改變。

• Warren and I hated railroad stocks for decades, but the world changed and finally the country had four huge railroads of vital importance to the American economy. We were slow to recognize the change, but better late than never.

十年來,華倫和我一直痛恨鐵路股,但世界發生了變化,美國終於擁有了四條對美國經濟至關重要的大型鐵路。我們遲遲沒有意識到這一變化,但遲到總比不到好。

• Finally, I will add two short sentences by Charlie that have been his decision-clinchers for decades: “Warren, think more about it. You’re smart and I’m right.”

最後,我要補充查理的兩句話,這句話是他幾十年來做決定的關鍵:「華倫,多考慮一下吧。你很聰明,但我是對的。」

And so it goes. I never have a phone call with Charlie without learning something. And,
while he makes me think, he also makes me laugh.

我和查理通話時,總能學到很多,而且他讓我思考時,也讓我發笑。

* * * * * * * * * * * *

I will add to Charlie’s list a rule of my own: Find a very smart high-grade
partner – preferably slightly older than you – and then listen very carefully to what he says.

我會在查理的名單上添加一條我自己的規則:找一個非常聰明的高級合作夥伴——最好比你年長一點,並認真地聽取他的意見。

A Family Gathering in Omaha

Charlie and I are shameless. Last year, at our first shareholder get-together in three years,we greeted you with our usual commercial hustle.

查理和我真是有點不知羞恥。去年,在我們三年來的第一次股東會上,我們一如既往地以繁忙的商業活動迎接大家。

From the opening bell, we went straight for your wallet. In short order, our See’s kiosk sold you eleven tons of nourishing peanut brittle and chocolates. In our P.T. Barnum pitch, we promised you longevity. After all, what else but candy from See’s could account for Charlie and me making it to 99 and 92?

開市鈴一響,我們就直奔你們的錢包。很快,我們的 See’s Candy 賣掉 11 噸富含營養的花生糖和巧克力。在我們 PT 巴納姆(注:一位著名的大騙子)式的演講裡,我們保證過吃它會長壽。畢竟,除了 See’s Candy,還有什麼可以解釋查理和我能活到 99 歲和 92 歲呢?

I know you can’t wait to hear the specifics of last year’s hustle.

我知道你們迫不及待地想聽去年聚會的細節。

On Friday, the doors were open from noon until 5 p.m., and our candy counters rang up 2,690 individual sales. On Saturday, See’s registered an additional 3,931 transactions between 7 a.m. and 4:30 p.m., despite the fact that 6 1⁄2 of the 9 1⁄2 operating hours occurred while our movie and the question-and-answer session were limiting commercial traffic.

我們從周五中午一直營業到下午 5 點,See’s Candy 店鋪紀錄 2690 筆交易。周六午 7 點到下午 4 點半,See’s Candy 店鋪又記錄了 3931 筆交易,這 9 個半小時裡有 6 個半小時是我們的電影放映和問答時間。

Do the math: See’s rang up about 10 sales per minute during its prime operating time (racking up $400,309 of volume during the two days), with all the goods purchased at a single location selling products that haven’t been materially altered in 101 years. What worked for See’s in the days of Henry Ford’s model T works now.

算一算:See’s Candy 店鋪在黃金時段每分鐘能賣掉 10 批糖果(兩天內累計銷售額達 40 萬美元),101 年以來,消費的模式沒有發生本質變化。在福特 T 型車時代賣 See’s Candy 的方法,今天一樣管用。

* * * * * * * * * * * *

Charlie, I, and the entire Berkshire bunch look forward to seeing you in Omaha onMay 5-6. We will have a good time and so will you.

查理、我和整個波克夏公司期待著在 5 月 5 日至 6 日在奧馬哈和你們見面。我們會玩得很開心,相信你也是。

February 25, 2023                                                                                            Warren E. Buffett
                                                                                                                          Chairman of the Board

2023 年 2 月 25 日                                                                                            華倫 ·E· 巴菲特 董事長


-----------------------------------------------------------

巴菲特和蒙格給年輕人的其他建議:

  1. 量入為出,除了房貸,不要有任何債務;
  2. 不要總是批評別人,不要用貶低別人的方式表達觀點;
  3. 不要做不善良的事,善良的人不會沒有朋友;
  4. 遠離有毒的環境和人,堅持終生學習、要有感恩心態。如果還是不成功,那就是運氣沒到。

信用交易成本精算(融資利息、借券費怎麼算)

 散戶心理圖 (GOOGLE)

散戶心理圖
信用交易的類型跟限制

  • 現金交易
    • 現金 → 股票買進
    • 現股 → 股票賣出
  • 信用交易
    • 融資 → 融資買進 → 融資賣出
    • 融劵 → 融劵賣出 → 融資買進
  • 當日沖銷
    • 先行融資買進一定數量股票 → 收盤前融劵賣出同樣數量的股票 → 軋平
    • 先行融劵賣出一定數量股票 → 收盤前融資買進同樣數量的股票 → 軋平


新手必會:信用交易成本精算(融資利息、借券費怎麼算)

  (1) 融資作多

融資作多成本 = 手續費 +證劵交易稅+ 融資金利息

以融資買進股票,只需要用到一半不到的錢, 好處是槓桿可以更大讓你槓上天, 壞處則是借錢當然要利息啊!(當然其實要顧慮的不只這點,融資須謹慎)
所以融資買進會比一般現股買賣多出一筆「融資金利息」做為成本。
融資的本意就是跟券商借錢來買股票,但你自己當然也要出一些,總不能全借;

可以融(借)幾成?
上市證券原則融資六成,上櫃證券原則融資五成;計算至千位,千位以下無條件捨去。

舉例來說:
要買進一張50元的股票本應花費5萬元,但你向券商融來6成,5萬的6成=3萬,也就是在買進股票的過程中,你跟券商借了3萬元作為融資金額。
借錢當然要利息,那麼這3萬元利息要怎麼算呢?
很簡單,就跟普天下所有借錢的利息公式雷同,融資金利息 = 融資金額 x 融資利率 x 天數/365
舉例說明:
青峰俠6/1融資買進股票一張,成交價位50元,6/9融資賣出,利息天數共8日,融資利率6%。簡單乘法如下:

融資金利息 = 融資金額 $3萬 X 融資利率 6% X (天數8/每年天數 365) = $39.45(四捨五入)


圖像說明了融資作多的三項成本:

融資作多成本 =
  • 手續費 -每股單價 X 張數 X 1.425 X 卷商折扣
  • +
  • 證劵交易稅 - 賣出金額 X 0.03%
  • +
  • 融資金利息 - 融資金額 X 融資利率 X (天數/365)

不同券商所使用的融資利息都不一樣,但是其實都是滿高的, 若非短線有相當把握,融資利息將會吃掉一部份的獲利。

(2) 融券作空

融資作空成本 = 手續費 +證劵交易稅 + 借劵費

若要融券作空,則會多一筆借券費,為什麼要借券呢?
因為我們手上沒有股票可賣,所以要跟券商借;
大家知道借錄影帶都要花錢,借股票當然也是,這個租金就叫借券費。
既然手續費和證交稅你都會,在這裡我們把借券費搞清楚就OK了~
借券費如何計算其實非常單純:借券費=成交單價x股數x借券利率就OK了。

借劵費 = 成交單價 50元 X 股數 1000股 X 借劵利率 0.1% =50元

例如:以50元買進一張(等於1000股)股票,借券利率0.1%,則 要補充的一點是保證金的計算。

借東西通常是需要抵押品的, 所以我們要借股票,就得把股票價值的九成資金暫放在券商那裏,當作保證金,用以保證我們不會拿了股票就跑路。

我們先來算假設我想作空某股票,也就是融券賣出,需暫放多少保證金在券商那?
上市上櫃證券的融券保證金原則要押"九成";計算至百位,百位以下無條件進位。
融券保證金金額=成交單價x股數x融券成數
舉例說明:50.1元x1000股x0.9=45,090元,百位以下無條件進位故融券保證金=45,100元。
為什麼要介紹保證金呢?因為既然我們這份保證金放在券商那,券商就會補貼我們這些錢生的利息,但,非常微薄,幾乎可以不計。
到這裡,整個融券作空的成本你就懂囉!

融資作空成本 =
  • 手續費 -每股單價 X 張數 X 1.425 X 卷商折扣
  • +
  • 證劵交易稅 -賣出金額 X 0.03%
  • +
  • 借劵費 - 成交單價 X 股數 X 借劵費率
由於融券金利息實在太微薄了(52->50元的股票擺8天也不過2元新台幣...)公式卻有點長,文末有興趣學習的讀者可以再細究;

至此我們只要清楚融券做空的成本結構主要是 手續費+證交稅+借券費 就可以囉!

(3)股票當沖交易
當沖一般來說,如果是當沖作多就是資買後券賣,
當沖作空就是券賣後資買。
交易成本跟交易現股比較來說,多了借券費一門成本。
再次重新溫習一下借券費要如何計算:

借劵費 = 成交單價 50元 X 股數 1000股 X 借劵利率 0.1% =50元
然而有券商提供「當沖免借券費」服務, 各位交易人也可以跟自己的券商詢問是否能夠申請。
Tips:融券金利息公式
融券賣出利息如何計算:
  • 融券金利息公式=(擔保品價款+保證金)x融券利率x日期/365
  • 融券擔保品價款=(成交單價x成交股數)-手續費-交易稅-借券費
  • 舉例說明:(66.2元x1000股) -94元-198元-66元=65,842元;
  • 融券擔保品=65,842元
    • (註:手續費0.1425%、交易稅0.3%、借券費0.1%計之)
舉例說明:
  • 王先生6/1(三)融券賣出2330台積電一單位,成交價位52元, 6/9(四)融券買進2330台積電一單位,成交價位50元。
  • 融券利息為=(46800+51,718) X 0.1% X 8/365 = 2元(小數四捨五入)
  • 提醒你,還是要清楚瞭解自己下單券商的「手續費折數」、「是否擁有最低20元手續費限制」、 「融資利率」、「融券借券利率」 才算有做到精算成本!

理論基礎

景氣循環概述:

以景氣循環為出發點,經濟週期呈現有規律的波動,可分為四個階段:
  • 0~1
    • 「繁榮期」景氣高峰
  • 1~0
    • 「衰退期」
  • 0~(-1)
    • 「蕭條期」景氣谷底
  • (-1)~0
    • 「復甦期」
其中繁榮期與蕭條期是兩個主要階段,衰退期與復甦期則為兩個過渡性階段,各階段均有明顯之特徵可供辨識。

在不同階段中,投資者可藉由轉換不同種類之標的與投資比例的調整,達到景氣榮枯均可穩定獲利之目標。

四種階段的投資策略:
 特徵建議投資標的
繁榮期貨幣供給額持續成長
匯率持續強勢
股市持續強勢
經濟成長率遠高於平均值
企業獲利成長迅速
商品價格大幅上揚
短期利率走高
長期利率走高
通貨膨脹走高
股票
土地
房地產
衰退期貨幣供給額持續走弱
匯率相對疲軟
股市低迷
經濟成長率趨緩,並跌破長期平均值
企業獲利由高峰開始下降
商品價格由高峰開始下降
短期利率由高峰開始下降
長期利率由高峰開始下降
通貨膨脹由高峰開始下降

商品
貴金屬
硬資產

蕭條期貨幣供給額持續走弱,但隨著短期利率達到高峰後開始回升
匯率開始恢復強勢
股市由低點反轉向上
經濟成長率趨緩
企業獲利依舊不佳
商品價格處於低檔
短期利率持續下降
長期利率持續下降
通貨膨脹持續下降
現金
國庫券
復甦期貨幣供給額開始升高
匯率恢復強勢
股市開始上漲
經濟成長率走穩,但仍低於長期平均值
企業獲利走出谷底
商品價格持續走弱
短期利率持續走低
長期利率持續走低
通貨膨脹持續走低
股票
共同基金
ETF

凱利公式 (Kelly Formula)

兼具強固性的下注建議 

             凱利公式 (Kelly Formula)

~I. 公式介紹 ~
先簡單解釋一下何謂標題中提到的「強固」。該名詞為塔雷伯(Nassim Nicholas Taleb)所提出,意指不會有爆炸的危險。因為若使用凱利公式所建議的下注比例,最糟的狀況也只是損失下注金額,不會波及到其餘的本金。這跟某些大量舉債以產生穩定收益的投資方法是截然不同的(塔雷伯會將此類歸為「脆弱」)。
凱利公式最初發明的目的是用來處理通訊上的雜訊問題,但後來被愛德華·索普(Edward Oakley Thorp)應用在賭場的21點上,並且發揚光大。不過,賺大錢的代價就是被各家賭場視為眼中釘,並且禁止進入。於是索普轉戰剛萌芽的選擇權市場,並發明了最早的選擇權定價模型─布雷克-休斯模型(Black-Scholes Model),從市場中大賺一筆。但是由於索普從未發表此模型,因此後來該公式便以發表者費雪·布雷克(Fischer Black)及麥倫·休斯(Myron Scholes)來命名(順帶一提,麥倫後來爆炸了)。
凱利公式的樣貌如下:
其中
  • F* = 下注比例
  • b = 賠率 = 獲利金額 /虧損金額
  • p = 獲利機率
  • q =虧損機率
由於公式中含有一個扣除項目,因此只要勝率不是100%,基本上你的本金是不會全押上的(但若是穩贏的賭局,為何不全押?)。另外,仔細一看後,會發現該公式的分子其實是期望值。這也意味著,若賭局的期望值小於0的話,根本沒必要繼續玩下去(但若你是個純粹的賭徒則另當別論了)。
~II. 實戰應用 - 賭局與股市 ~
好了,在你認識了凱利公式後,該怎麼應用在實際賭局上呢?讓我們假設你找到了一個擲骰子的賽局,其規則如下:
碰到這樣的賭局,凱利公式會怎麼建議我們呢?我們試著將賭局條件帶進公式看看。
首先是公式參數:
 b = 獲利金額 /虧損金額 = 6/1 =6
P = 出現1點的機率 = 1/6 =16.67%
q = 出現其他點數機率 = 5/6 =83.33%

有了計算前提後,便可得出下注比例:
F* = p - ( q / b )
    =16.67 - (83.33 / 6 )
    =2.78%

上述推導所得出的2.78%就是最佳化的下注建議,該比例可在控制虧損金額的情況下,令財富達到最快的增長速度。以100元的本金而言,這場賭局最多只能下2元。上述案例因為報酬和勝率都相當不吸引人,因此凱利公式冷靜地叫你用微薄的比例下注就好。
想知道凱利公式怎麼發明出來及公式證明的讀者可以參考這裡(我個人是不會去做推演啦,就像學工程的人很少會去琢磨 e 的證明,反正會用就好了)。

由於凱利公式一般都是使用在明確金額的賽局上,但若想拿來應用在股市上的話,該怎麼辦?其實很簡單,只需要將賠率的計算須由損益金額改為本金的報酬率即可,如下:
舉例來說,若你辛苦做了許多研究,終於發現了一檔超值股票。你評估了一下後,列出你對它的看法:
於是在上述前提下,可得到公式參數:

b = 本金報酬率 / 本金虧損率 = 50% / 40% = 1.25
p = 獲利可能性 = 70 %
q =虧損可能性 = 30%
故便可求得:
F* = p - ( q / b )
    =0.7 - (0.3 / 1.25 )
    =0.7 - 0.24
    =46%
因此根據凱利公式的建議,你對該股票的最大下注比例便是46%。但是請注意,凱利公式只是個參考,沒必要每次都下到最大注。以本例而言,或許你只要下10%比例便可。在如此嚴格控制虧損金額的情況下,你的投資將可由「強固」昇華至「反脆弱」。
~III. 進階應用 - 多重可能結果的下注 ~
現在,我們可以讓股票的評估稍微複雜一點,以符合實際的狀況。上述例子中的你,重新評估後,決定修改列出你對該股票的看法:
  • 產生50%報酬的可能性: 40%
  • 產生20%報酬的可能性: 30%
  • 產生40%虧損的可能性: 29%
  • 產生100%虧損的可能性: 1%
對於這種多重可能的結果,該如何使用凱利公式呢?其實作法也是很簡單,首先要區分獲利和虧損的機率:
p = 獲利可能性 = 40% + 30% =70%
q = 虧損可能性 = 29% +  1% = 30%

接下來便是計算賠率。但須注意的是,在報酬和虧損率的部分,需用平均值來計算。計算如下:
平均報酬率 = 50%*40%+20%*30% / 40%+30% =0.37
平均虧損率 = 40%*29%+100%*1% / 29%+1% =0.42

因此可得出賠率:
b = 平均報酬率 / 平均虧損率 =37% / 42% =0.88

在公式前提都具備的情況下,便可開始計算下注比例。如下:
F* = p - ( q / b )
    =0.7 - (0.3 / 0.88 )
    =36%

因此上式最後得出的36%便是下注的建議值。

藉由多重可能結果的條件,可使評估過程更為平滑,不再只拘泥於大賺或大賠的下注比例。此公式推演在書中並未提到(書中甚至沒給公式),而也就是這部分困擾了我許久。
~IV. 投資組合控管 ~
學會單一個股的資金配置方法後,接下來便可以延伸至整體的投資組合。假設你辛苦做了許多研究,終於挑選出5檔令你滿意的股票。再經過評估與計算後,凱利公式對這5檔股票的下注比例如表1所示:
  • 股票      資金比例
  • 公司A        30%
  • 公司B        50%
  • 公司C        40%
  • 公司D        60%
  • 公司E        20%
  • 總計          200%
表1. 個別公司的下注建議

問題來了,下注資金總計為200%,已經超過本金了,那該怎麼辦?(千萬不要去舉債讓本金達到200%阿!)答案其實很簡單,只要將所有比例除以200%便可讓總計回復成100%了。於是經過調整後的資金配置如下:
  • 股票       資金比例       實際比率
  • 公司A       30%                15%
  • 公司B      50%                 25%
  • 公司C      40%                 20%
  • 公司D      60%                 30%
  • 公司E      20%                  10%
  • 總計         200%              100%
表2. 個別公司的實際下注建議
由於實際的資金配置已經剩下建議值的一半,再加上個別股票間的關聯性低(除非你5檔都選同一個產業的類股),因此你的投資組合在價格波動和風險上將可獲得有效地保障註1。
這邊補充一下,《下重注的本事:當道投資人的高勝算法則》書中的作者帕波萊(Mohnish Pabrai)在帕波萊基金管理上,一律設定為10%。他認為雖然這樣的配置並非最佳化,但卻可以處理預估表現的失誤。舉例來說,他發現他認為應該表現最好的股票卻常會輸給預估表現第三、第四好的股票。縱然這樣的報酬比不過將80%資金重壓在少數幾檔股票上,但整體而言仍可令他滿意(這傢伙的年化報酬有28%阿...)。

~V. 結論~
文章到這邊,相信各位已經學會基本的凱利公式及資金配置了。雖然你現在可能感覺有如神助,不過還是得記住,在股市之中,沒有什麼事情是確定的。須注意到,公式中的每一項參數都是由你自己評估後所訂出的。只要是主觀的參數設定,都很容易產生誤差。就像是本文的例子中,光是多出了兩項可能結果便會使下注比例降低10%。因此,一般狀況下,還是不要使用到最大下注比例,別對自己太有自信比較好。
註1:補充說明,這裡的波動性及風險低是建立在「個別股票間的關聯性低」的這個要點。事實上凱利公式並不確保波動率,它只在乎最終的結果。