TIP773：系统与简易数学如何塑造更佳投资——与Kyle Grieve对话

关键在于，虽然我喜欢算法且它们很有帮助，但只有使用它们的人采取行动时，算法才真正有效。

The point here is that while I love algorithms and they are helpful, they're only valid when the person using them takes action.

如果算法告诉你采取行动，而你却忽视行动部分，那么这个算法就成了毫无实际应用价值的模型。

If you have an algorithm telling you to take an action, but you're ignoring the action part, then the algorithm becomes a model with zero world applicability.

所以如果你创建投资算法来改善决策，请确保你真正在使用它们。

So if you create algorithms for investing to improve your decision making, make sure that you're actually using them.

查理·芒格曾说过，人生的秘密算法就是多做有效的事。

Charlie Munger once said, the secret algorithm to life is doing more of what's working.

因此我想借此机会分享一些我认为行之有效的生活经验。

So I wanted to take this chance to share with you a little bit on my life, which I think is working.

这些经验虽不多，但显然影响深远。

And it's not a few things, but obviously they have large impacts.

第一件事就是花时间陪伴家人，尤其是我的儿子。

So the first thing is just spending time with my family and especially my son.

其次是关于投资，即要兼顾长期和短期的投资机会。

And next is looking at investing, which is to invest in a mix of long term and short term opportunities.

这对我来说效果非常好。

That's also working really well for me.

我注意到另一个带来巨大改变的事情，就是尽可能经常地练习感恩。

Another thing that I've noticed has made a huge difference is practicing gratitude as often as possible.

另一件我不断努力的事情，就是让自己一天比一天更友善。

Another thing that I constantly trying to work on is becoming a kinder and kinder person each and every day.

显然还有工作与生活的平衡问题，虽然我的工作要求很高，但幸运的是我能在做好工作的同时优化自己的幸福感。

And obviously to do with kind of work life balance, While I obviously have this job that is pretty demanding, I'm lucky enough that I can kind of optimize myself for happiness while also being good at my job.

最后一点就是自我关爱，包括身体、情绪和心理三个层面的全面照顾。

And the last point here is just self care, you know, and that's physical, emotional, psychological, taking care of all three of those things.

因为如果你不照顾好这些方面，基本上很难在生活的任何领域获得成功。

Because I feel like if you don't take care of them, it's really hard to thrive in basically any area of your life.

正如沃伦·巴菲特在给伯克希尔·哈撒韦股东的最后一封信中所写：伟大不是通过积累巨额财富、获得大量关注或掌握政府大权来实现的。

So Warren Buffett in his final letter to Berkshire Hathaway shareholders wrote, greatness does not come about through accumulating great amounts of money, great amounts of publicity, or great power in government.

当你以千百种方式帮助他人时，你就是在帮助整个世界。

When you help someone in any thousands of ways, you help the world.

善良无需成本，却无价珍贵。

Kindness is costless, but also priceless.

无论你是否信仰宗教，黄金法则作为行为指南都难以超越。

Whether you are religious or not, it's hard to beat the golden rule as a guide to behavior.

我认为沃伦的内在评分卡和遵循黄金法则的能力，帮助他找到了属于自己的美好生活算法。

Now I think Warren's internal scorecard and ability to live by the golden rule helped him find his own algorithm for a great life.

虽然巴菲特眼中的美好生活可能与我——或许也与大多数听众——不尽相同，但这并不重要。

And while a great life in Buffett's eyes might not be the exact same for me and probably the majority of other listeners here, that's not really what matters.

重要的是回归查理的观点：多做对你个人有效的事。

What matters is going back to what Charlie stated and doing more of what works specifically for you.

在投资领域，我认为长期成功的算法就是专注于现金流。

For investing, the long term algorithm for success, I think, is to just focus on cash flow.

如果一家企业未来能产生不断增长的现金流，其股价表现很可能也会非常出色。

If a business generates increasing cash flow in the future, chances are its share price is also gonna perform incredibly well.

这就是我重点关注的领域。

This is where I put a lot of my focus.

请注意我说的是现金流而非自由现金流，因为我投资了大量拥有众多再投资机会的企业。

Note that I said cash flow and not free cash flow because I invest in many, many businesses that have a ton of reinvestment opportunities.

现金流量表中的投资活动部分经常被新收购项目填得满满当当。

The cash from investing part of the cash flow statement is often filled to the brim with new acquisitions.

这显然会抑制现金流的增长。

So this obviously serves to depress cash flow.

所以如果仅用这个数字筛选，我投资组合中的许多公司看起来可能并没有产生太多现金。

So if you screened using just that number, many names in my portfolio might not look like they are generating too much cash.

这就是为什么我喜欢使用诸如巴菲特的'所有者收益'这类指标，它能帮助显示企业在投资增长前实际产生了多少现金。

This is why I like using metrics such as, you know, Buffett's owners earnings, which helps to show how much cash the actual business is producing before investing in growth.

当我以这种方式审视我的投资组合时，可以清晰地看到我的企业产生了大量现金，而且我认为它们未来多年很可能会持续增加现金生成量。

When I look at my portfolio that way, I can clearly see that my businesses generate a ton of cash, and I think they're likely to grow that amount of cash that they generate many years into the future.

因此，如果你考察任何股价上涨的企业并观察其经营现金流，我可以向你保证它的现金流很可能已大幅增长。

So if you examine any business whose share price is appreciated and look at its operating cash flow, I can guarantee you that it has probably increased substantially.

只要看看'七巨头'就明白了。

So just look at the magnificent seven.

这七家优秀企业的十年平均经营现金流增长率超过27%。

The average cash from operation ten year keggers on those seven great businesses is over 27%.

以这样的复合增长率计算，即使保持固定倍数，一家公司十年后的价值预期可达11倍。

At that compounding rate with just a fixed multiple, a company can expect its value to be an 11 x over just ten years.

我在这个播客中多次强调：如果你持有一家能够持续多年复合增长经营现金流的企业，选择卖出将是个非常非常重大的错误。

Now I've said this many times on this podcast, but if you have a business that is capable of compounding its operating cash flow for many years into the future, you're making a very, very big error if you decide to sell it.

我会继续重申这个观点，因为我认为每个投资者都需要理解这点——包括我自己。

And I'm gonna continue saying it as I think every investor needs to understand it, including myself.

但关于算法有这样一个问题：

But here's the thing about algorithms.

即便在我刚讨论的现金流算法中，期间也可能发生各种变数。

Even in the cash flow algorithm that I just discussed, things happen in the meantime.

如果一家公司十年间保持27%的现金流复合增长，十年后其价值将显著提升。

Over ten years, if a company compounds cash flow at 27%, it's gonna be worth significantly more ten years later.

但在任何特定年份，任何事情都可能发生。

But in any given year, anything can happen.

这就是临界质量作为思维模型发挥作用的地方。

This is where critical mass comes into play as a mental model.

你看，如果你在过去十年持有像特斯拉这样的公司，想要充分享受其现金复利能力，你就必须经历四次40%或更大幅度的股价回调。

So you you see, if you were to own something like Tesla during the past ten years to get the full benefits of its ability to compound cash, you would have had to hold shares through four separate 40% or greater drawdowns.

但对于理解临界质量、能看到特斯拉全面大幅提升利润率并将持续改善的投资者来说，特斯拉成为了他们的必胜投资。

But for investors who did understand critical mass and could see that Tesla had drastically improved margins across the board and would continue to do so, Tesla became an absolute slam dunk investment for them.

那么究竟什么是临界质量？

So what exactly is critical mass?

它是系统中足够多的参与者或支持资源汇聚的临界点，使系统转变为能够自我维持或获得极大增长动力的状态。

It's a point in the system where enough participants or supporting resources converge, allowing the system to shift into becoming a self sustaining or having radically increased momentum.

使系统能够自我维持或获得极大增长动力。

Allowing the system to become self sustaining or have radically increased momentum.

如果你读过马尔科姆·格拉德威尔的《引爆点》，你就走对路了。

If you ever read Malcolm Gladwell's tipping point, you're on the right path.

那么，在评估企业时我们如何利用临界质量这个概念呢？

Now, how can we leverage critical mass when considering a business?

从多个方面来说。

In many ways.

第一种方法是关注临界点来运用它。

The first way is to use it by focusing on threshold.

如果你试图做出改变并需要多人支持你的行动，实际上并不需要所有人都来帮你达成目标。

If you're trying to make a change and need several people to support your journey, you don't necessarily need everyone to actually get you to where you need to go.

你只需要足够数量的人来推动系统转变即可。

You only need the right amount of people just to flip the system.

在马尔科姆·格拉德威尔《引爆点》的优秀续作《引爆点的复仇》中，他提到了这个神奇的三分之一法则。

So in Malcolm Gladwell's excellent follow-up to the tipping point, the revenge of the tipping point, he mentions this magic third.

因此如果你能改变某件事物的三分之一，比如董事会代表权，通常就能达到所需的引爆点。

So if you can change a third of something, such as board representation, you can often reach the tipping point that you need.

作为董事会成员，假设是一个九人董事会，如果你想推动变革，要么需要说服至少两名现有董事支持你，要么用认同你观点的新成员替换两名董事。

So as a board member, let's say a nine person board, if you want to make a change, you need to either sway two or more people onto your side who are already on the board or replace two of those members with new members who agree with you.

我知道自己进入董事会的可能性很低，所以与其专注于改变企业，我更倾向于寻找那些已有合适人选、只需持续优化业务的企业。

Now, I know the likelihood of me being on a board is quite low, so instead of focusing so much on making changes to a business, I prefer finding businesses where the right people are already in place and they just need to continue to improve the business.

因此我喜欢寻找杠杆点。

So I like to look for leverage points.

如果你知道一家公司正在积累现金，并有大量资金可以高回报率地部署，那么我就知道这家企业最终可能达到临界规模。

If you know a company is accumulating cash and has a large runway to deploy that cash at high rates of return, then I know the business could eventually reach a critical mass.

对于连续收购者来说，这可能意味着他们最初只有一个人专门负责并购机会。

For a serial acquirer, that might mean that they start with one person who just looks at M and A opportunities.

但随着时间的推移，他们可以建立一个系统，将业务分解为小单元，这些小单元也能发现越来越多的并购机会，从而形成一个非常可持续的系统，就像Constellation Software或Bergmann and Bevy那样。

But over time, they can create a system where the business gets broken down into small units, which can also find more and more m and a opportunities, which creates a very sustainable system, something like a Constellation Software or a Bergmann and Bevy.

另一个需要考虑的因素是时间。

Another consideration is time.

临界规模对一家企业来说近在咫尺，对另一家却只是白日梦。

Critical mass is around the corner for one business while being just a pipe dream for another.

在考虑投资时，牢记这一点至关重要。

It's essential to keep this in mind when considering your investments.

现在我倾向于寻找那些不仅能以可观速度增长收入，还能提高利润率的公司。

Now I like to look for companies that can not only grow their top line at a decent clip, but also improve margins.

这将使企业通过经营杠杆效应，实现比收入增长更快的现金流增长。

This will allow the business to grow cash even faster than the revenue due to operating leverage.

但有时这种经营杠杆效应可能需要一段时间才能真正显现出来。

But sometimes that operating leverage can take some time to actually show itself.

如果我错误地认为一家公司现在就有经营杠杆效应，但实际上在未来几个季度甚至几年内都不会看到显著效果，这就为投资者创造了一个极易失望的环境。

And if I mistakenly believe that a company has operating leverage now, but in reality won't see it in meaningful amounts for the next few quarters or even years, that creates an environment where investors are very likely to be disappointed.

临界质量的另一个有趣特点是它可以被逆转。

Another interesting aspect of critical mass is that it can be reversed.

因此，如果达到临界质量所需的投入减少到一定程度，它就可以退出临界质量状态。

So if an input required for critical mass is reduced enough, then it can exit the critical mass state.

我经常在商业中看到这种情况，尤其是在小型企业中。

I often see this in businesses, especially in smaller companies.

比如一家企业可能创造出一款爆款新产品，深受客户喜爱。

So a business might create a hit new product that its customers absolutely love.

然而，如果该企业没有竞争优势，那么竞争对手就可能纷纷涌现，复制产品，并以相同或更低的价格销售，使原产品的优势完全丧失。

However, if the business does not have a competitive advantage, then competition can come out of the woodworks, replicate the product, sell it for, you know, the same or lower prices and render the original product's advantage completely obsolete.

我曾拥有一家名为'大麻资本'的大麻公司。

So I once owned a cannabis company called Cannabis Capital.

这家企业曾生产过一种香烟形状的大麻产品，在短期内为公司创造了大量收入和利润。

This business had these cigarette shaped cannabis products that produce a lot of revenue and profits for the business for a very short time.

投资者——包括我自己在内——都将这一优势外推至未来。

And investors extrapolated that advantage into the future, myself included.

但遗憾的是，这种优势转瞬即逝。

But that advantage unfortunately was very short lived.

虽然产品热销时推动了业务增长，但企业却无法维持其临界规模。

And while it helped propel the business upward while they were selling well, the business was unable to sustain its critical mass.

一旦产品滞销，企业很快就失去了所有发展势头。

And once the product was no longer selling, the business quickly lost all of its momentum.

因此，临界质量理论对我最有用的场景，大概是在投资拐点型企业时。

So where I have the most use for critical mass is probably in my investing in inflection point businesses.

我完全可以把这类企业称为——你们懂的——临界质量型企业。

I could easily call these, you know, critical mass businesses.

我寻找转折点的原因在于，这通常是量化观察公司内部是否真正形成临界质量的有效方法。

The reason I look for inflection points is that it's often a quantitative way to observe that a critical mass is actually happening inside of a company.

对于我的转折点标准，我寻找的是连续两个季度实现正现金流或盈利的企业。

For my inflection points, I'm looking for a business with two consecutive quarters of positive cash flow or profits.

这意味着企业通常正处于运营杠杆开始发挥作用的阶段。

This means that the business is often at a point where operating leverage is coming into play.

许多过去拖累企业发展的支出，现在正助力企业提升利润水平。

And many of its past expenses, ended up being a drag on the business are now helping that business grow its bottom line.

因为随着时间的推移，增量收入会越来越显著地超过固定成本。

As much of the revenue that's incrementally added over time is much further above fixed costs.

但正如我之前提到的，失去临界质量是真实存在的风险，我必须持续密切监控。

However, as I mentioned earlier, falling out of critical mass is a real risk that I must continually monitor very closely.

企业经营很复杂，而要实现盈利则更加困难。

Business is complex and, you know, being a profitable business is even harder.

只有由最优秀管理团队运营的顶尖企业，才能持续获得盈利性的成功。

Only the very best companies managed by the best management teams will experience continued profitable success.

因此必须管理这种方法以应对潜在的下跌风险。

So the approach must be managed for potential downside risk.

我的做法是购买那些从未来角度看通常相当便宜的企业。

And I do this by buying businesses that are generally pretty cheap when looked at on a forward basis.

不幸的是，总存在下一年情况与我的投资论点不符的风险，这就是为什么这些头寸通常比我更有把握押注于更成熟、根基深厚的远程企业时要小。

Unfortunately, there's always the risk that what happens in the next year is not aligned with my thesis, which is why these positions are generally smaller than my higher conviction bets on more established and deep remote businesses.

所以我的整体投资目标，无论是投资于更明显成熟的业务还是不太明显的拐点业务，都只是为了找到复合增长型企业。

So my overall goal in investing, whether that's from investing in more obvious well established businesses or less obvious inflection point businesses is just to find compounders.

这很好地过渡到本期节目的数学环节。

This is an excellent transition to the mathematics segments of this episode.

复利是一个强大的概念，因为如果你理解它并能加以利用，你将获得惊人的回报。

Compounding is a powerful concept because if you get it and can set yourself up to take advantage of it, you're gonna reap some mind blowing rewards.

但如果你不理解它，你很容易成为复利的牺牲品，只是方向错了。

But if you don't understand it, you can easily fall prey to compounding, but in the wrong direction.

复利最显而易见的形式大概就是复利利息了。

The most visible form of compounding is just probably compound interest.

当你赚取利息并再投资时，你将在更高的本金基础上获得利息。

When you earn interest on money and reinvest it, you earn interest on an even higher amount.

随着时间推移，这个过程的持续使得资金增长的潜力简直令人难以置信。

As this process continues over time, the potential for that pile to grow is simply mind boggling.

我认为复利过程中很多困惑来自于那些不太明显的复利形式。

Where I think a lot of confusion comes from in the compounding process is from the less visible forms of compounding.

复利现象在我们身边无处不在。

Compounding happens all around us.

但由于短期内的变化几乎难以察觉，要理解复利的来源可能相当具有挑战性。

But because the changes in the short term are kind of imperceptible, it can be quite challenging to understand the sources of compounding.

我认为许多人对复利的误解实际上体现在他们的信用卡使用上。

Where I think many people misunderstanding compounding is actually in their credit cards.

信用卡利息就是个很好的例子。

So credit card interest is a great example here.

虽然我说过复利是可见的，但我觉得大多数信用卡持有者可能并不真正了解信用卡利息的实际运作方式。

While I did say that compound interest is visible, I think most credit card owners are probably unaware of just how credit card interest actually works.

这并不是他们的错。

And it's not their fault.

我认为信用卡公司故意对利息计算方式含糊其辞。

I think credit card companies are intentionally vague about how it works.

毕竟，如果你每月还清信用卡账单避免支付利息，信用卡公司就无法从你身上赚到钱。

After all, if you pay off your credit card each month and avoid paying any interest, then the credit companies aren't making any money off of you.

假设某人目前有5000美元的信用卡欠款，年利率为20%。

So let's say someone is currently carrying a credit card balance of $5,000 with an annual interest rate of 20%.

20%听起来像是一年只计息一次，但这里有个大多数人不知道的巨大陷阱。

At 20% may sound like it's applied just once a year, but there's a pretty epic catch here, which most people don't know.

实际上信用卡利息是按日复利计算的。

And that's that credit card interest is actually compounded daily.

具体运作方式是这样的。

So here's how it works.

将20%的年利率除以365天，得出每日利率为0.055%——这个数字表面上看起来完全无害。

You divide the 20% by three hundred sixty five days, which gives us a daily rate of point zero five five percent, a number which seems, you know, completely harmless on the face of things.

但每天这个人欠款时，他们都要为不断增长的余额支付利息。

But each day the person owes, they're getting charged interest on a growing balance.

现在假设这个人一年都没有还款。

Now let's imagine the person doesn't make a payment for a year.

所以他们的余额不会只是6000美元（即5000美元的20%加上5000美元）。

So their balance won't just be $6,000 which would be 20% of 5,000 added to the 5,000.

由于这种每日复利效应，实际金额将达到6100美元。

It would actually be $6,100 because of these daily compounding effects.

你额外支付的100美元纯粹来自复利过程。

You are paying an additional $100 solely from the compounding process.

这就是为什么当你去支付信用卡账单时，他们会有最低还款额选项，而绝不会让你全额还款。

This is why when you go and pay your credit card bill, they have the minimum payment button, which is never the entire balance.

信用卡公司知道，如果让你只还最低还款额，你的利息会不断累积，他们就能从你身上赚更多钱。

Credit card companies know that if they get you to pay the minimum, your interest payments will accrue and they'll make more money off of you.

关于复利的另一个反直觉概念是：复利向上呈凸性增长，向下呈凹性衰减。

Another very non intuitive concept regarding compounding is how compounding is convex to the upside and concave to the downside.

意思是它具有正向不对称性。

Meaning it has positive asymmetry.

我的搭档克莱·芬克在TIP第583期采访了高塔姆·巴伊德，我会在节目笔记中附上链接。

So my cohost Clay Finck interviewed Gautam Bayde on TIP five eighty three, which I'll have linked in the show notes.

他向我介绍这个概念做得非常出色。

And he just did a fantastic job of introducing this concept to me.

大多数投资者都非常熟悉复利的概念，你知道的。

Most investors are very familiar with the concept of compounding, you know, okay.

如果一个企业每年以26%的速度复利增长，大约三年就能翻倍。

If if a business compounds at 26% per year, it doubles in about three years.

如果继续保持这个增长率，大约二十年就能获得百倍回报。

If it continues compounding at this rate, you get a punter bagger in about twenty years.

这很棒。

That's great.

但真正的威力在于上行与下行差异，在更现实的场景中比如你的投资组合里。

But where the real power comes into play is in the differences between the upside and downside in a more realistic scenario such as your portfolio.

假设我们持有两只股票，每只价值100美元。

So let's say we have two stocks for that we own for a $100 each.

一只以26%的增长率复利，另一只则以-26%的增长率复利。

One compound to 26% and the other one compounds at negative 26%.

人们通常会认为只要它们保持这样的增长率，最终会相互抵消。

So the natural belief here is that they end up canceling each other out as long as they continue to compound at those rates.

一年后，赢家的价值约为126美元，输家则降至74美元。

After one year, the winner is worth about a $126 and the loser is down to $74.

加起来仍然是200美元，和我们最初投入的一样。

Add them up and we're still at $200 right where we started.

但十年后会发生什么？

But what happens ten years down the road?

我们仍然保持在200美元这个数字吗？

Are we still at that same $200 number?

答案并非零，甚至相差甚远。

The keger is not zero, not even close.

实际上大约是18%

It's actually around 18%.

是的，其中一只股票基本归零，但赢家的收益如此之高，足以轻松弥补损失，尽管有归零的股票，仍能带来强劲的整体回报

Yes, one stock essentially is a zero, but the gains on the winners are so high that they easily make up for the loss delivering strong overall returns despite that zero.

高塔姆关于复利真正力量的结论是：即使他50%的时候判断错误，依然可以获得可观的回报

Gautam's conclusion on the real power of compounding was that he could be wrong 50% of the time and still make a great return.

我们稍事休息，听听今天的赞助商怎么说

Let's take a quick break and hear from today's sponsors.

你知道是什么让最优秀的企业脱颖而出吗？

You know what sets the best businesses apart?

正是他们如何利用创新将复杂性转化为增长

It's how they leverage innovation to turn complexity into growth.

这正是亚马逊广告正在做的，由AWS人工智能驱动

That's exactly what Amazon ads is doing, powered by AWS AI.

每天，亚马逊广告处理数十亿实时决策，在310亿美元的广告生态系统中优化广告表现

Every day, Amazon ads processes billions of real time decisions, optimizing ad performance across a $31,000,000,000 advertising ecosystem.

最终实现的广告活动运行速度提升30%，并在大规模范围内带来可衡量的商业影响。

The result is campaigns that run 30% faster and deliver measurable business impact at scale.

这正是亚马逊自身推动增长的方式。

And this is how Amazon itself drives growth.

其智能AI将营销从资源密集型流程转变为智能自主系统，最大化投资回报率，并让营销人员能专注于创意与策略。

Their agentic AI transforms marketing from a resource heavy process into an intelligent autonomous system that maximizes ROI and empowers marketers to focus on creativity and strategy.

亚马逊广告证明，AI驱动的广告不仅是未来趋势，更是新的竞争优势。

Amazon Ads is proving that AI driven advertising isn't just the future, it's the new competitive advantage.

更棒的是，每家企业都能运用亚马逊内部完善的相同创新策略。

And better yet, every enterprise can apply the same innovation playbook that Amazon perfected in house.

访问aws.comai/rstory了解亚马逊广告故事。

See the Amazon ad story at aws.comai/rstory.

网址是aws.comairstory。

That's aws.comairstory.

我们小时候总梦想成为各种角色——宇航员、总统或是王子。

When we were young, we used to dream of being anything, an astronaut, the president, a prince.

但随着年龄增长，你的梦想会改变，不再执着于改变世界，而是更关注如何将技能与想法转化为现实。

But as you get older, your dreams change focusing less on running the world and more on how you can take your skills and ideas and turn them into something real.

与其梦想遨游太空或拥有城堡，你开始梦想经营自己的事业。

Instead of dreaming of going to space or owning your own castle, maybe you start dreaming of owning your own business.

你需要一个网站、支付系统、品牌标识以及吸引新客户的方式。

You'll need a website, a payment system, a logo, and a way to advertise to new customers.

这一切可能令人无所适从，但幸运的是，今天的赞助商Shopify能为你解决这些问题。

It can all be overwhelming and confusing, but thankfully that is where today's sponsor Shopify comes in.

Shopify是全球数百万家企业的商业平台，支撑着美国10%的电子商务交易。

Shopify is the commerce platform behind millions of businesses all around the world and 10% of all e commerce in The US.

从美泰、Gymshark这样的家喻户晓品牌，到像我这样刚刚起步的品牌。

From household names like Mattel and Gymshark to brands like mine that are still getting started.

与Shopify合作就像有一位商业专家伴您左右，提供世界级的专业支持。

Working with Shopify is like having a commerce expert at your side with world class expertise.

让Shopify助您将宏大的商业构想变为现实。

Turn your big business idea into reality with Shopify on your side.

立即注册享受每月1美元的试用优惠，今天就开始在shopify.com/wsb上销售吧。

Sign up for your $1 per month trial and start selling today at shopify.com/wsb.

网址是shopify.com/wsb。

That's shopify.com/wsb.

说到安全持有比特币，安心始于架构设计。

When it comes to holding Bitcoin securely, peace of mind starts with architecture.

OnRamp的多机构托管模式采用三分之二多重签名机制，将控制权分散给三家独立受监管的密钥持有方。

OnRamp's multi institutional custody model distributes control across three independent regulated key holders in a two of three multisig quorum.

无单点故障，无资金池或综合风险敞口，只有独立客户名义的保险库。

No single point of failure, no pooled or omnibus exposure, just segregated client titled vaults.

您保留完整的法定所有权，而OnRamp在幕后协调安全、合规和运营工作流程。

You retain full legal ownership while OnRamp coordinates security, compliance, and operational workflows behind the scenes.

这是通过单一平台的简洁性实现众多机构的集体优势。

It's the strength of many delivered through the simplicity of one.

多机构托管是OnRamp构建一切服务的基础。

Multi institutional custody is the foundation for everything OnRamp builds.

健全的基础设施，分散对手方风险，提供容错弹性，并配备清晰的审计和机构控制。

Sound infrastructure that distributes counterparty risk and provides fault tolerant resilience with clear audits and institutional controls.

现在OnRamp正在试点固定、可预测的定价方案，使一流的比特币托管和金融服务比以往任何时候都更易获得。

And now OnRamp is piloting flat, predictable pricing, making best in class bit Bitcoin custody and financial services more accessible than ever.

OnRamp，集众家之长，成一家之简。

OnRamp, strength in many, simplicity in one.

访问onrampbitcoin.com了解更多信息。

Visit on rampbitcoin.com to learn more.

好的。

Alright.

回到节目中来。

Back to the show.

为了展示这在拥有多个头寸的更现实投资组合中的表现，你可以使用所谓的贡献度分析。

So to show what this looks like in a more realistic portfolio with more than two positions, you can use something called contribution analysis.

这会显示哪些股票对你的回报贡献最大。

This shows which stocks make up the most of your returns.

高塔姆在与克莱的访谈中做这个分析时指出，在他持有的23个仓位中，约80%的收益仅来自四只股票。

When Gautam did this during his interview with Clay, he noted that out of the 23 positions, about 80% of his returns came from only four stocks.

我刚查看了自己投资组合今年至今的贡献分析。

I have just checked the contribution analysis for my own portfolio year to date.

今年至今，我的前四大仓位贡献了约53%的收益。

So my top four positions year to date make up about 53% of my gains.

其中两只股票的收益占我投资组合总回报的42%。

And two of those positions make up 42% of my portfolio's returns.

这个数据涵盖了我今年持有的19个仓位。

This takes into account the 19 positions that I've owned this year.

当我把时间范围从今年至今扩展到整个投资组合存续期时，约57%的收益仅来自五家企业。

So when I extended that time frame from year to date to the inception of my portfolio, about 57% of my returns have come from only five businesses.

我还进一步查看了表现最差的五个仓位。

I also went ahead and looked at my bottom five positions.

它们造成了17%的负收益。

They contributed negative 17%.

因此，你可以很容易地看出凸性复利与凹性复利之间的区别。

So here you can quite easily see the differences between convex and concave compounding.

我的顶级赢家轻松超越了顶级输家，使我能够持续进行资金复利。

My top winners have easily surpassed my top losers allowing me to continue to compound my money.

所以关于复利中凸性与凹性的讨论，实际上是在探讨所谓的幂律现象。

So what this talk of convexity and concavity in compounding is really discussing something called power laws.

幂律描述的是一种分布模式，其中少数结果占据了整体成果的绝大部分。

So a power law describes a distribution in which a small number of outcomes accounts for a large proportion of the overall result.

企业本身也可能受到幂律的支配。

So a business itself can be governed by power laws.

一个产品或一项新服务就能轻易将企业推向巅峰。

One product or one new service can easily catapult a business into the stratosphere.

当你观察一家企业时，最坏的情况是变得一文不值。

When you look at a business, the worst it can do is become completely worthless.

但最好的情况是其价值可能增长十倍、二十倍、百倍甚至千倍。

But the best it can do is multiply its value by ten, twenty, 100, or even a thousand times.

因此当你评估一家企业时，想象力对于看清其潜在上升空间至关重要。

So when you are viewing a business, imagination is very potent in seeing the upside optionality that a business has.

尽管这些举措成功的可能性可能很低，但想象它们仍然很重要，以防你发现一家真正能快速扩张的企业。

And even though the likelihood of these initiatives might be very low, it can still be integral to imagine them in case you find a business that can truly scale quickly.

如果你缺乏理解幂律法则的想象力，无法构想更光明的未来，你很可能会抛售一只可能带来人生转折性财富的股票。

If you don't have imagination to understand power laws and imagine a much brighter future, you're likely to dump a stock that could offer you life changing wealth.

幂律法则同样适用于投资组合的分散化。

Power laws also govern portfolio diversification.

如果投资者定期调整投资组合以限制单一头寸的集中度，这可以被视为非常明智的风险缓释策略。

If an investor rebalances their portfolio regularly to cap the concentration of a position, this can be seen as a highly intelligent risk mitigation.

但这也可以被视为糟糕的资本配置。

But it can also be seen as poor capital allocation.

在我看来，遵循幂律法则的企业在我的投资组合中应该占据最大比重。

In my opinion, businesses that follow power laws inside of my portfolio should be the biggest positions.

减持这些头寸是个错误，因为我实际上是在消除未来收益最大化的可能性。

And removing parts of them is a mistake because I'm really just eliminating the possibility of maximizing future returns.

这是贪婪吗？

Is this greed?

也许是吧。

Maybe.

但我认为这是可控的贪婪，我认为这是创造财富所必需的。

But I believe it to be control greed, which I think is necessary to generate wealth.

幂律可以解释为什么使用竞争对手的平均值会产生误导。

Power laws can explain why using averages from competitors can be misleading.

当你观察一个行业的普通企业时，不存在整个行业竞争者都具有不对称上升空间的情况。

When you're looking at the average business in an industry, there's no such thing as an industry that's full of competitors with asymmetric upside.

所以总会有输家，因为在大多数情况下，资本主义本质上是个零和游戏。

So there's always gonna be losers because most of the time, capitalism is really a zero sum game.

我见过一些高速增长的企业，投资者却采用与竞争对手更接近的未来增长率来估值。

I've seen this with some businesses that are growing at very high rates and investors use growth rates in the future that are more in line with those of their competitors.

现在让我们设想是2015年，你正在考虑将Shopify作为潜在投资对象。

So let's imagine now that it's 2015 and you're considering Shopify as a potential investment.

你看看Shopify的收入增长，会发现它遥遥领先于竞争对手。

You look at Shopify's revenue growth and you see that it's miles ahead of its competition.

这些行业的业务正以每年20%的平均速度增长。

Business in these industries are growing at an average rate of 20% per annum.

于是你假设Shopify的收入增长会像行业其他公司一样降至这个水平。

So you assume that Shopify is just going to decrease its revenue growth to that number along with the rest of the industry.

你买入后大约两个季度就清仓了，因为你认为Shopify将经历收入增长的大幅下滑，并获得了两位数的利润。

You buy it and end up selling out in about two quarters because you believe Shopify will experience a massive reduction in revenue growth and you take a double digit profit.

这种思维方式存在一个问题。

Here's the problem with this way of thinking.

Shopify并非普通的竞争者。

Shopify just wasn't another competitor.

它是一个正在崛起的幂律赢家。

It was an emerging power law winner.

它当时正处于增强网络效应、构建生态系统、吸引顶尖商户群体以及完善合作伙伴飞轮的进程中。

It was in the midst of improving network effects, building an ecosystem, capturing the top decile of merchants, and improving its partner flywheel.

竞争对手们根本没有享受到这些同样的优势。

Competitors just did not experience these same advantages.

普通竞争对手大多由失败者主导，他们平台停滞不前、产品同质化、客户基础萎缩、市场份额不断流失。

The average competitor was dominated by losers with stagnant platforms, commoditized products, a declining customer base, and eroding market shares.

因此Shopify不仅没有回归平庸（这是我们稍后会讨论的另一个概念），反而以50%的复合年增长率实现了收入增长。

So instead of Shopify regressing to the meme, another concept that we'll cover shortly, compounded revenue at a 50% CAGR.

其商品交易总额以63%的复合年增长率增长，成为了一个定义品类的平台，拥有极其深厚的网络效应。

It grew its gross merchandise volume by a CAGR of 63% and became a category defining platform with incredibly deep network effects.

因此，通过研究竞争对手的平均水平，根本无法推断出这一结果。

So nothing about this outcome can be inferred from examining its competitors averages.

这一点在您的投资组合中最为关键。

Where this is most important is inside of your own portfolio.

这些异类可能已经存在于您的组合中，所以不要通过卖出最佳头寸并用平庸标的替代来限制自己的收益。

These outliers might already be there, so don't handicap yourself by selling your best positions and replacing with something that is merely average.

但关于复利增长，有这样一个关键点。

But here's the thing about compounding.

这在理论上听起来很顺滑。

It sounds smooth on paper.

这是一条美妙的指数曲线，在不知不觉中积累财富。

It's this, you know, beautiful exponential curve that just quietly build wealth in the background.

但在现实世界中，复利不会发生在如此干净可预测的环境中。

But in the real world, compounding doesn't happen in this kind of clean and predictable environment.

它发生在一个充满意外、冲击和不确定性的世界里。

It occurs in a world that's just full of surprises, shocks, and uncertainty.

关键点在于：复利是对抗随机性生存下来的奖励。

And really, the key point here is that compounding is a reward for surviving randomness.

我之前提到的那些显著异常值——那些贡献大部分回报的少数持仓，就是绝佳例证。

Those significant outliers that I mentioned earlier, you know, the few positions that drive most of the returns are great examples.

没有人能真正提前预测什么会成为幂律赢家。

No one can really predict ahead of time what will become the power law winner.

这个结果只有在随机性真正展开后才会显现。

That outcome only becomes apparent after randomness really kinda unfolds.

那么随着我们继续深入，值得一问的是：复利效应究竟存在于怎样的世界中？

So as we move forward, it's worth asking what kind of world does compounding actually live in?

这不是一个线性世界。

It's not a linear world.

这是一个由概率主导的世界，受机会、变异性和意外结果等因素支配。

It's a probabilistic one, governed by factors such as chance, variance, and unexpected outcomes.

这引出了我们的下一个思维模型——随机性。

And this brings us to our next mental model, which is randomness.

除非你理解支撑复利效应的随机性，否则无法真正领会复利是如何运作的。

Unless you understand randomness that underlies compounding, you can't fully appreciate how compounding truly works.

需要注意的是，随机性不应与混乱混为一谈。

Now, randomness should not be confused with chaos.

它实际上是指单个事件中缺乏可预测的模式。

Instead, it's a lack of predictable patterns in individual events.

你或许能把握结果的整体分布，但永远无法高度确定地预测任何单一结果。

You may be able to get a grasp on the distribution of outcomes, but you can never predict any single outcome with a high degree of certainty.

我们总爱在不存在规律的地方寻找规律。

We love to see patterns even when they don't exist.

而随机性常常会愚弄我们，让我们误以为在这个本质上不确定的世界里存在确定性。

And randomness can often fool us into believing that certainty is available in a truly uncertain world.

关键是要认识到，设计精良的流程仍可能产生糟糕的结果，而执行不力的流程却可能带来出色的成果。

Now it's essential to recognize that a well designed process can still yield a poor outcome, and a poorly executed process can still produce a great outcome.

这解释了为何短期表现几乎不能说明任何问题。

This helps explain why short term performance tells you almost nothing.

细想之下，每日股价、季度收益、分析师预期和市场情绪都只是噪音的不同形式。

When you think about it, daily stock prices, quarterly earnings, analyst expectations, and market sentiment are all just forms of noise.

短期内，随机性确实会完全掩盖基本面因素。

In the short term, sure, randomness completely drowns out fundamentals.

但从长期来看，基本面终将战胜随机性。

But in the long term, fundamentals drown out randomness.

刚才我们讨论了幂律法则，而随机性与幂律的运作机制其实高度契合。

So I just spent some time discussing power laws, and randomness plays well with how power laws function.

既然我们永远无法百分百确定我们所持有的企业中哪家具有最佳上涨潜力，提前识别我们的重大赢家某种程度上是不可知的。

Since we can never be 100% certain about which business that we own is going to have the best upside potential, identifying our big winners is kind of unknowable upfront.

但我们确实知道回报的分布是可预知的。

But we do know the distribution of returns is knowable.

我分享了自己的投资分布，并让贝茨评估——我猜测其他投资者可能也有非常相似的分布模式。

I shared my own and got them Bates my guess is that other investors probably have pretty similar distributions.

如果我们理解随机性在投资组合中的运作方式，就应该为各种情景做好准备，从而利用随机性获利。

If we understand how randomness will work within our portfolio, we should be prepared for a variety of scenarios allowing us to take advantage of randomness.

这意味着当我们积极投资时，需要在接触随机性的同时保护自己免受其负面影响。

This means that when we are actively investing, we need to expose ourselves to randomness while simultaneously protecting ourselves from its downside.

对我而言，这归结为投资信念与仓位控制。

For me, this comes down to conviction and position sizing.

今天我多次谈到确定性，我认为如果你对某个仓位越确定，可能结果的分布范围就越窄。

I've discussed certainty a lot today, and I think that if you are more certain on a specific position, the distribution of outcomes becomes narrower.

所有你预想可能破坏企业发展的负面情况，其发生概率会越来越低，从而保留更多上涨空间并减少下行风险。

All that bad stuff that maybe you envision could happen to derail the business becomes less and less likely to occur, leaving more upside and less downside.

在我看来，从你认为风险已经降低的头寸中撤资，然后重新分配到风险更高的企业，这种做法毫无道理，但许多投资者仍然这么做。

To me, taking money out of a position that you think is derisked and and allocating it back into a business that carries more risk is just nonsensical, but that's what many investors do anyway.

因此，如果你接受投资组合构建中的随机性，就需要确保运气有展现的空间。

So if you accept randomness into your portfolio construction, you need to ensure that luck has a place to show up.

这意味着几件事。

This means a few things.

不对赢家设限，通过头寸规模控制来限制下行风险，在评估企业时使用安全边际，并确保你的赢家能真正产生重大影响。

No capping of winners, limiting downside through position sizing and using margins of safety when evaluating businesses, and then just ensuring that your winners can actually make a meaningful impact.

这意味着如果你过度分散投资，很可能一个赢家对你的整体表现影响不大。

That means if you're over diversified, chances are that one winner isn't going to make much of a difference to your overall performance.

由于人类热爱模式识别，这也会让我们相信能在不存在模式的地方找到模式。

Since humans love pattern recognition, it also leads us to believe that we can find patterns where none exist.

市场择时就是个很好的例子。

Market timing is a great example.

如果你看看Twitter或财经新闻，从不缺少预测宏观事件的人。

If you look at something like Twitter or financial news, there's never a shortage of people forecasting macro events.

他们往往显得知识渊博，因为他们洞悉了与现实事件相关联的历史规律，并将这些模式推演至当下。

And they often appear to be knowledgeable because they understand patterns in the world that correlate to past events, and then they extrapolate those patterns to the present.

然而随机性导致这些宏观经济预测者的判断几乎总是错误的——即便偶尔正确也不过是运气使然。

However, randomness causes nearly all of these macroeconomic forecasters to be wrong with their forecasts or just to be lucky when they're actually right.

当我们审视世界中的随机性时，无论是过去、现在还是未来，往往只看到幸存者。

When we examine randomness in the world, whether that's in the past, the present, or the future, we tend to only see survivors.

我们看不见那些未被选择的道路，以及那些惨败的结局。

We fail to see the paths that weren't taken or the ones that failed miserably.

随机性也意味着小概率事件会相对频繁地发生。

Randomness also means that rare events occur relatively frequently.

如果我们无法预测小概率事件，那么任何预测都将毫无意义。

And if we cannot predict rare events, then making forecasts becomes completely pointless.

回想新冠疫情初期，根本没人料到它会对市场造成如此重大的冲击。

You know, when you go back and look at COVID-nineteen initially, nobody really thought that COVID-nineteen was going to have too much of an impact on the markets.

而当大规模封锁开始时，所有人又都认为市场必将崩溃。

Then when we got the big giant shutdowns, everybody thought that the markets would absolutely crumble.

然而在2022年，市场却上涨了超过18%。

Yet in 2022, the market was up over 18%.

所以我之前提到过程和结果。

So I mentioned earlier about process and outcomes.

关于过程最具挑战性的部分是，当我们反思并观察到所有糟糕的结果时，可能会误认为我们的流程存在缺陷。

And the challenging part about the process is that when we reflect on it and observe all the poor outcomes that we've had, we might actually reason that our process is flawed.

但一个好的流程总会为出错的可能性留有余地。

But a good process will always make room for the possibility of being wrong.

假设你进行一项投资，有90%概率让资金翻倍，10%概率亏损一半。

Let's say you make an investment that has a 90% chance of doubling your money and a 10% chance of losing half.

你应该每次都接受这个赌注。

You should make that bet every time.

这就是一个非常合理的流程。

And that's a perfectly fine process.

但由于随机性，即使概率很低，我们仍有可能在这笔赌注中亏损一半。

But due to randomness, there's always a chance that we lose half on the bet even though it's not a very likely outcome.

因此在这个情境中，你可能已经完美无缺地执行了你的流程。

So in this scenario, you might have executed your process completely flawlessly.

你做出了卓越的决策并拥有合理的推理。

You had excellent decision making and sound reasoning.

你具备完美的评估逻辑，控制了风险，并且在做出决策时处于极佳的心理状态。

You had perfect evaluation logic and you controlled risk, and you were in a great mental space when you made the bet.

但你仍然输了。

But you still lost.

所以这个案例的教训并不一定是你的流程有问题。

So the lesson in this case isn't necessarily that your process is broken.

只是随机性显现出来，让你做了一个结果不如预期的决策。

It's simply that randomness reared its head and made you make a bet that didn't turn out as well as you would have liked.

可以说随机性培养了谦逊。

You can say that randomness fosters humility.

你必须愿意接受犯错，因为你终将会犯错。

You must be willing to be wrong, because you will be.

这就是投资游戏的一部分。

It's part of the investing game.

巴菲特一生中做过大约300到400个投资决策，他将伯克希尔的大部分成功归功于其中约12个关键决策。

Buffett has made approximately 300 to 400 investing decisions in his lifetime, and he attributes the lion's share of Berkshire's success to about a dozen of those decisions.

这并不意味着他在其他所有决策上都完全错误，而是说明他拥有出色的投资流程，即使在市场随机性显示他短期内可能犯错时也坚持执行。

This doesn't necessarily mean he was completely wrong on all the others, but it does mean that he had a great process and stuck to it even during times that randomness of markets show that he might have been wrong in the short term.

既然我们必须接受自己会经常犯错的事实，那么我们也需要优先考虑生存问题。

So speaking of being wrong, since we must accept that we're going to be wrong pretty often, we also need to prioritize survival.

这正是我近年来在自己投资中越来越重视的一个方面。

And this is an area of my own investing that I've begun placing more and more emphasis on.

我也经历过几次重大亏损，有些是源于糟糕的决策流程，有些则不是。

I've had my share of a few big losers, but some were the result of a bad process and others weren't.

但无论如何，当我审视这些亏损案例并观察它们对投资组合表现的影响时，我深刻认识到不亏钱有多么重要。

But either way, when I look at these losers and then observe the impact they had on my portfolio performance, I can see just how important it is to not lose money.

投资的奇妙之处在于，即使以个位数的温和收益率持续复利几十年，最终你也能积累相当可观的财富。

The thing with investing is that if you compound at even modest single digit rates over multiple decades, you'll end up with a pretty nice pile of money.

与其纯粹专注于优化几十年后这笔现金的规模，一些投资者可能会认为，你应该优先确保自己能够到达终点线。

And instead of focusing purely on optimizing how large that pile of cash will be decades down the road, some investors might argue that you should probably optimize just to make sure you end up at the finish line.

太多投资者因为投资组合爆仓而退出市场，然后发誓永远不再投资，从而彻底丧失了复利增长的机会。

Too many investors disappear from the market because they blow up their portfolio, and then they swear off investing forever, putting a prompt end to their chances of compounding.

避免投资组合爆仓最简单的方法就是运用逆向思维，避开可能导致投资组合毁灭的常见错误。

Now the easiest way to avoid blowing up your portfolio is to use inversion and avoid common mistakes that can lead to portfolio destruction.

最容易避免的就是使用保证金交易。

The easiest thing to avoid is using margin.

借钱是输光一切的最快途径。

Borrowing money is an easy way to lose everything.

如果你的押注方向错误，短期内需要偿还 text rim▁，你的投资组合可能归零。

If your bet goes against you and you have to pay back the lender, your portfolio can drop to zero.

现在另一个避免毁灭投资组合的方法就是不做空。

Now another way to avoid destroying your portfolio is to just avoid shorting.

做空无法提供与做多相同的非对称性优势。

So shorting does not offer the same asymmetry that going long offers.

当你做空时，最多只能赚一倍，但可能赔光所有。

When you short, the most you make is a double and the most you lose is everything.

当你做多时，虽然也可能亏光本金，但盈利空间是无限的。

When you go long, yes, you can lose everything, but your upside is limitless.

其次是过度集中投资。

Next is over concentration.

听着，我虽然喜欢集中投资，但从没让单只股票的成本占比超过总资本的15%。

Look, I love being a concentrated investor yet I've never put in more than 15% of my capital by cost basis into one position.

随着经验积累，我现在基本不会让任何头寸超过10%的比例。

And as I gain more and more experience, it becomes increasing unlikely that I will ever go much over 10%.

假设你把全部资金押注一只股票，一旦它归零，你的复利游戏就结束了。

If you had, let's say 100% of your capital in one position and it goes to zero, your compounding is over.

但如果这只股票只占你10%仓位，即使归零也还能承受。

But if you'd had only 10% in that position and it still goes to zero, that sucks.

是啊。

Yeah.

但至少你还剩下90%的资金，这些资金要么正在为你工作，要么随时可以投入使用。

But at least you have 90% of your capital left that's either working for you now or ready to be deployed.

最后是去年的市场择时问题。

And last year's market timing.

正如我已经讨论过的，随机性使得市场预测完全无效。

So as I've already discussed, randomness renders market forecasting completely ineffective.

许多投资者试图参与其中，比如在市场看起来估值过高时卖出，结果错失了许多收益，最终又以更高的价格重新买入。

Many investors attempt to participate in it for instance by you know selling when the market seems expensive thereby missing out on many of the gains and ultimately buying back into the market at elevated prices.

当你以亏损卖出某个头寸，然后又以更高价格买回时，这简直就是失败的配方。

So when you sell a position at a loss then repurchase it for more, that's just a recipe for failure.

随机性的有趣之处在于，它会在短期内愚弄我们，让我们基于周围的大量噪音做出次优决策。

The interesting thing about randomness is that it fools us in the short term into making subpar decisions based on a multitude of noise that surrounds us.

大多数表现优异的企业都只能维持很短的时间，一旦竞争对手了解了它们的做法，就会试图复制。

Most businesses that outperform do so for a pretty short time, then once their competitors learn more about what they're doing, they attempt to replicate it.

如果竞争对手成功复制，短期表现优异的企业就会迅速跌落神坛。

And if they do this successfully, a short term outperformer will just simply fall from grace.

这是均值回归的一个绝佳例证。

This is an excellent example of regression to the mean.

帕里什在《伟大元模型》第三卷中这样写道：

Here's what Parrish writes in volume three of the Great Meta Models.

运气是随机的，因此带有运气成分的异常结果之后往往会跟随更温和的结果。

Luck is random, so outlier results with luck components are probably followed by more moderate ones.

这就是均值回归现象。

This is regression to the mean.

这个概念最早由弗朗西斯·高尔顿在19世纪末提出。

So, the concept originated with Francis Galton in the late nineteenth century.

高尔顿在研究父母与子女身高关系时发现，异常高或异常矮的父母往往会有身高更接近平均值的子女。

Galton had been researching the heights of parents and their offspring, and he found that unusually tall or short parents tended to have children of a more average height.

身材高大的父母所生子女往往比父母矮些，而身材矮小的父母所生子女往往比父母高些。

A set of tall parents would have kids that tended to be shorter than them, and a set of short parents would have children that tended to be taller than them.

高尔顿指出，如果缺乏均值回归概念，人类和其他生物体将主要由巨人和侏儒构成，这显然与数据不符。

Goldm argued that if regression to the mean concept were absent, humans and other organisms would be predominantly comprised of giants and dwarves, which obviously the data does not support.

现在换个角度，用体育类比来看这个问题。

Now another way of looking at this is through a sports analogy.

我是个狂热的NBA和篮球迷。

I'm a big time NBA and basketball fan.

1985年，包括著名学者阿莫斯·特沃斯基在内的三位研究者对NBA进行了一项引人入胜的研究。

And in 1985, a fascinating study was conducted on the NBA by three researchers, including the renowned Amos Tversky.

在篮球运动中，球员常被认为会进入所谓'手感火热'的状态，看起来怎么投都能进。

In basketball, players are often thought to get something called the hot hand where it doesn't seem like they can miss a shot.

这是真实存在的，还是仅仅是运气使然？

Is this true or is it simply a product of luck?

研究结论表明其实是后者。

The research concluded that it was actually the latter.

优秀球员最终总会连续投进多个球。

A good player will eventually have multiple shots drop consecutively.

鉴于NBA球员是地球上最擅长投篮的人类群体之一，他们在职业生涯或某一年中很可能会经历手感火热的阶段。

And since NBA players are among the most incredible humans on earth that shooting a basketball, chances are very high that they're going to experience a hot streak at some point in their career or even in a given year.

所以像斯蒂芬·库里这样投篮出色的球员，很可能会经历多次手感火热期。

So someone exceptional shooting such as Steph Curry is probably gonna have many hot streaks.

但最终，他们的投篮表现还是会回归平均水平。

But in the end, their shooting is just gonna regress to the mean.

以斯蒂芬·库里为例，他职业生涯的三分命中率平均为42%，这意味着平均每10次三分出手他能命中4个。

For someone like Steph Curry who has shot a career average of 42% from the three point line, it means that on average, he's gonna hit about four out of every 10 of his three pointers.

但由于技术和运气的综合作用，他可能在比赛中连续命中4球，然后接下来6投全失。

But due to a mixture of skill and luck, he may hit four straight shots during a game then miss the following six.

当连续命中4球时，会给人一种他手感火热的错觉。

While hitting those four shots, it gives the mirage that he's on a hot streak.

但从长期来看，他的表现终将回归到个人职业生涯的平均水平。

But over the long term, he's just gonna regress to the mean of his own career average.

关于均值回归，我最喜欢的故事之一来自我的嘉宾斯科特·巴比尔，我在TIP651期节目中采访过他，我会在节目说明中附上链接。

One of my favorite stories of regression to the mean is from one of my guests Scott Barbie who I interviewed on TIP six fifty one which I'll link to in the show notes.

斯科特在金融危机期间经历了一段非常艰难的时期。

Scott went through some very challenging times during the great financial crisis.

他的Aegis基金在2007至2009年间遭遇了72%的回撤。

His Aegis fund had a 72% drawdown between 2007 and 2009.

如果斯科特当时向这个极端事件屈服，他可能就直接清盘退还投资者本金，或是彻底改变投资策略。

If Scott had succumbed to this extreme event, he might have just called it quits and returned his investors capital or maybe just drastically changed his strategy.

毕竟他正承受着来自华尔街和投资者的巨大压力——面对如此大幅度的回撤，投资人显然不会高兴。

After all, he was feeling the heat of Wall Street and from his investors who probably weren't very happy with that big of a drawdown.

但巴比坚信自己这套行之有效的交易体系。

But Barbie had a system that he knew worked.

尽管市场当时并不认可他的决策，但他认为投资组合已完成风险释放，潜在收益空间反而比以往任何时候都大。

And even though the market didn't like his decisions at the time, he simply felt that his portfolio was now derisked and the upside was even greater than it had ever been before.

因此他既没有放弃也没有仓促改变策略，而是坚持了自己的投资理念。

So instead of giving up or rapidly changing his strategy, he just stuck to his guns.

他本人从未使用过这个表述，但在我采访他时，我认为他本质上是在利用正向均值回归。

He never used these words, but when I interviewed him, I think he was essentially taking advantage of positive regression.

到目前为止，在讨论均值回归时，我主要讲的是积极事件多属运气使然，一旦运气耗尽，结果往往会趋于平庸化。

So far, when discussing regression to the mean, I've talked about how positive events are mostly a product of luck, and once that luck runs out, the results will generally move towards becoming more average.

对于像斯科特这样持续跑赢市场的投资者来说，他认为逆境终将过去。

Well, for an investor like Scott who has consistently beaten the market, he thought that an adverse event would eventually pass.

一旦度过难关，他很可能会获得丰厚回报。

And once it did, he was likely to be highly rewarded.

而事实正是如此。

And that's precisely what happened.

该基金在2009年触底后，随后便参与了价值股令人瞠目的反弹行情。

The fund bottomed in 2009, then took part in just a face ripping rally on its value place.

Aegis基金在2009年结束时上涨了91%，让斯科特登上了《华尔街日报》头版——这一切都源于他有足够耐心等待均值回归。

Aegis ended 2009 up 91% getting Scott onto the front page of the Wall Street Journal all because Scott was just patient enough to take advantage of regression to the mean.

那么我们可以从均值回归现象中学到什么关键经验，来帮助当下成为更好的投资者呢？

So what are the key lessons that we can learn from regression to the mean to help us become better investors today?

这里有四点我想详细探讨。

There's four that I'd like to discuss in some detail here.

第一点是极端优异表现不可复制。

The first is that extreme outperformers aren't repeatable.

我经常审阅多份基金报告。

I review several fund letters pretty regularly.

当你仔细研究这些表现优异基金的年度业绩时，你会发现一个现象。

And when you go through the annual results of these outperforming funds, you're gonna notice something.

它们的业绩波动相当大。

The performance is pretty volatile.

它们可能连续一两年表现优异，大幅跑赢指数，但随后又会出现一两年可能无法战胜指数的情况。

They may have strung together one or two good years, crushing the index, but then they'll have a year or two where maybe they fail to beat the index.

然而，如果它们拥有良好的投资流程，那么业绩往往会向均值回归。

However, if they have a good process, then the results will tend to regress to the mean.

对于卓越的投资者而言，这意味着其回报会高于普通投资者，但这个观点依然成立。

For an exceptional investor, it means it will be higher than the average investor, but the point here still stands.

如果你根据某基金经理某年的业绩表现，就期待他们能持续复制这样的回报，那你将会大失所望。

If you looked at a fund manager's performance in a given year and expect them to duplicate those returns regularly, you're going to be sorely disappointed.

现在要说的第二点是：如果你误解了均值回归，就会错误判断技能与运气。

Now the second point here is that if you misunderstand regression, you'll misdiagnose skill and luck.

在2007、2008和2009年斯科特·巴比的案例中，观察他基金的人可能认为斯科特已经失去了优势，他选股的技能开始衰退。

In Scott Barbie's story during 2007, 2008, and 2009, observers of his fund probably thought that Scott had lost his edge and his skills as a stock picker were starting to fade.

这是因为这些观察者低估了那些年困扰Age基金的坏运气的影响。

This was because these observers were underestimating the effects of bad luck that had plagued Age's fund during those years.

对于那些相信斯科特能力的投资者来说，他们在2009年及之后获得了丰厚回报，仅仅是通过按兵不动，让均值回归的力量提升基金表现。

For investors who had faith in Scott's skills, they were very well rewarded in 2009 and onwards by simply doing nothing and allowing the forces of regression to boost the fund's performance.

第三点就是要永远记住基准率。

The third here is just to never forget base rates.

你可以把基准率理解为某种全球平均值。

So you can think of base rates as kind of like a global average.

例如，大多数人都认为自己是好司机。

For instance, most people think they are good drivers.

实际上，大约50%的人应该是高于平均水平的司机。

In reality, approximately 50% of people should be above average drivers.

但奥莱斯·文森的研究表明，约80%的司机认为自己高于平均水平。

But research done by Oles Vinson concluded that about 80% of drivers believe themselves to be above average.

因此，当我们评估自己在几乎所有事情上的技能水平时，必须假设自己处于平均水平附近。

So when you consider our skill levels in nearly anything that we do, we must assume that we're somewhere around average.

如果你是一名选股者，你实际上是在默认自己可能比平均水平更优秀。

And if you're a stock picker, you are implicitly admitting that you're probably better than average.

而验证这一点的唯一方法，就是长期跟踪你的投资表现，并观察你相对于基准的表现优劣。

And the only way to find out if that's true or not is to track the results that you've had over a long period of time and observe how well or poorly you do compared to a benchmark.

就我而言，我选择以标普500指数作为我的基准。

In my case, I've settled on using the S and P 500 as my benchmark.

第四，波动性越大的系统，其均值回归效应就越显著。

And fourth, systems with high variability will show the strongest regression.

就像斯科特·巴比的埃吉斯基金经历了大幅回撤后，随后也迎来了惊人的上涨。

Just like Scott Barbie's Aegis Fund experienced those massive drawdowns, he also experienced a pretty wild ride up.

如果在那段时期，他的基金奇迹般地只下跌了比如5%，那么2009年出现强势均值回归的可能性就会低得多。

If by some miracle during that same time period, his fund had only declined by let's say, you know, 5%, it's highly unlikely that he would have experienced a strong regression back to the upside in 2009.

可能涨幅就只有10%或20%左右。

Maybe it would have been, you know, 10 or 20%.

我认为这是对正在经历回撤的投资者极好的建议。

This is an excellent piece of advice, I think, for investors that are experiencing drawdowns.

如果你对自己企业长期基本面有信心，而投资组合大幅下跌，那么只要你能在市场波动中坚持持有，未来极有可能迎来正向回归。

If you're confident in the long term fundamentals of your businesses and your portfolio is down substantially, then there's an excellent chance that you're in store for some positive regression in the future as long as you can hold your businesses through the volatility that the market offers.

在结束今天这期节目时，我想把我们讨论的所有内容整合起来。

So as we wrap up today's episode, I wanna bring everything we've discussed together into one place.

这些思维模型每一个单独来看都很有力量。

So each of these mental models on its own is powerful.

但正如查理·芒格教导我们的，跨学科思维的真正力量在于将这些思维模型层层叠加。

But as Charlie Munger has taught us, the real strength of multidisciplinary thinking lies in layering the mental models on top of each other.

当你能够深入探究这些模型如何相互关联、协同作用时，就能收获最显著的效益。

When you can closely examine just how these models are interrelated to one another and work together is where you're gonna reap the most significant benefits.

这将为你建立长期思维、智慧投资的基础，以及更平静、更清晰地理解世界和周边市场的认知方式。

That's where you will build the foundation of long term thinking, intelligent investing, and a calmer, clearer way of understanding the world and markets around you.

今天我们首先讨论了反馈循环。

So we started today by discussing feedback loops.

这些无形的机器驱动着我们使用的每个系统，无论是有意识还是无意识的。

These are the invisible machines that power every system we use whether consciously or unconsciously.

增强回路创造指数级增长，平衡回路创造稳定性。

Reinforcing loops create exponential growth and balancing loops create stability.

作为投资者，你必须明白自己参与的是哪种循环，以及尽力避免哪些循环。

As investors, you must understand which loop you're participating in and which ones you're trying best to avoid.

接着我们剖析了我最爱的思维模型之一：终止标准。

From there, we broke down one of my favorite mental models, kill criteria.

这些预先承诺机制能迫使你采取明智行动，克服噪音、情绪和叙事等容易劫持我们判断力的因素。

These are the pre commitment devices used to force your hand into intelligent action and overcome things such as noise, emotions, and narratives that can easily hijack our judgment.

然后我们讨论了不确定性锥形，这个来自斯利普和扎卡里亚的宝贵概念提醒我们：未来其实是有形状的。

Then we discussed the cone of uncertainty, the invaluable idea from sleep and zakaria that reminds us that the future actually has a shape.

虽然我们无法预测未来，但可以观察这个未来是随时间变得更确定还是更不确定。

And while we can't predict the future, we can observe whether that future is becoming less or more certain over time.

最后我们探讨了规模效应。

Then we explored scale.

正如你们所了解的，规模可以让企业变得更强大，也可能使其更加脆弱。

Scale, as you learned, can make a business much stronger or more fragile.

这两种对立面决定了一家公司是成为一台复合增长机器，还是被自身的重量压垮。

And these two opposites are what determine whether a company becomes a compounding machine or if it just collapses under its own weight.

接着我们转向了算法，这些美妙的配方能将混乱的原料组合转化为可预测且一致的输出。

Then we moved on to algorithms, those beautiful recipes that can turn a messy hodgepodge of ingredients into a predictable and consistent output.

算法与反馈循环配合得天衣无缝，因为如果你向系统输入正确的要素，就能获得你想要的指数级增长或稳定性。

Algorithms interact very well with feedback loops because if you put the right inputs into a system, you'll get exponential growth or stability that you're looking for.

然后我们真正拉远了视角。

Then we really zoomed out.

我们讨论了数学中的一些关键思维模型。

We discussed some key mental models from mathematics.

我们探讨了复合增长的无形力量——只要不被打断，它能在长期中悄然创造出难以置信的成果。

We discussed the invisible forces of compounding, which can quietly build unbelievable outcomes over long periods of time, provided that we don't interrupt it.

在复合增长中，我们讨论了凸性效应：少数几个大赢家就能轻松弥补我们不可避免会犯的错误。

Within compounding, we discuss convexity, where a few big winners can easily compensate for the mistakes that we will inevitably make.

接着我们讨论了幂律法则，它表明我们的大部分成果将源于极少数关键决策。

Then we discussed power laws, which indicate that the majority of our results will stem from a very small number of key decisions.

之后，我们探讨了随机性以及不确定性如何成为生活中不可避免的存在。

After that, we discussed randomness and how uncertainty is just a given in life.

既然随机性是生活的常态，我们必须承认运气在成功与失败中扮演的角色。

Since randomness is a feature of life, we must accept the role that luck plays both in our successes and in our failures.

我们必须明白，成功的关键在于坚持跑完全程，而非试图采取危险的捷径——那些可能让我们永远无法抵达终点的做法。

And we must understand that the key to succeeding is to simply finish the race, and not attempt to take dangerous shortcuts that could easily prevent us from ever getting to the finish line.

最后，我们以均值回归作结，这个规律提醒我们：无论是好是坏，极端状态都不会永久持续。

Lastly, we concluded with regression to the mean, a reminder that extremes, whether they be positive or negative, don't last forever.

生活终将回归常态，基础概率就像引力般将异常事件拉回正常范围。

Life will go on as usual, and base rates act as a gravitational pull that reels in those outlier events.

如果你具备忍耐力与应对极端情况的风险策略，你极有可能取得非常非常出色的成就。

If you have the patience and risk strategy to survive extremes, chances are you're gonna do very, very well.

不过，在这些来自系统学和数学的不同思维模型之下，我认为存在一个统一的主题。

However, beneath all of these different mental models from systems and mathematics, I think lies kind of a unifying theme.

如果你能在思考过程中经常运用这些模型，就为自己提供了一种方式，不仅能在纷扰的世界中生存，还能在其中蓬勃发展。

And if you can use them regularly in your thinking process, you offer yourself a way not only to survive in a noisy world, but to thrive despite it.

如果你能建立系统来减少情绪的不利影响，能识别自己所在的反馈循环，能拥抱随机性而非被其支配，并能致力于长期复利积累，那么你就跻身于少数精英之列。

If you can build systems that help reduce the adverse effects of emotion, if you can recognize the feedback loops you're operating in, if you can embrace randomness rather being dominated by it, and can commit to long term compounding, then you put yourself into rare company.

是那种能够长期保持成功的精英群体。

The kind of company that succeeds over a long period of time.

但要明白，长期成功必然伴随着各种障碍。

Just realize that long term success comes with its share of roadblocks.

正如我们从随机性和均值回归中看到的，现实中充斥着极端事件，这些事件短期内往往对我们造成伤害，但从长期来看不过是微不足道的小波动。

As we saw from randomness and regression to the mean, reality is just littered with extreme events that often hurt us in the short term, but act as nothing more than a tiny blip in the long term.

如果你做好准备承受这些波动，并能看得更长远一些，就能避免那些导致大多数投资者获得远低于平均收益的错误决策。

If you set yourself up to withstand these blips and can think a little further into the future, you'll be able to avoid some of the flawed decision making that causes most investors to get results that are far below average.

本期内容真正强化了一个核心理念：你无需预知未来也能获得成功。

Making this episode really reinforce the concept that you don't need to see the future to succeed.

你的重点应该放在避免那些会阻碍你拥有未来的错误上。

Your focus should be on avoiding the mistakes that will stop you from having one.

在避免失败的同时，让自己有机会迎接那些最意想不到的积极惊喜。

And while you avoid failure, expose yourself to the possibility of positive surprises that may come from the most unlikely places.

感谢你今天花时间与我交流。

Thanks for spending time with me today.

哪怕这些模型中有一个能帮你做出清晰决策、避免代价高昂的错误，或是让你以更智慧的视角看待投资组合，那么今天就非常值得。

If even one of these models helps you make a clear decision, avoid a costly error, or see your portfolio through a smarter lens, then today was well worth it.

如果你想继续交流，请在Twitter上关注@irrationalmrkts，或在LinkedIn上与我联系。

And if you'd like to continue the conversation, please follow me on Twitter irrationalmrkts or connect with me on LinkedIn.

直接搜索Kyle Grief即可。

Just search for Kyle Grief.

我非常欢迎反馈意见，请随时分享如何能让这个播客对你更有价值。

I'm always open to feedback, so please feel free to share how I can make this podcast even better for you.

感谢收听，我们下次再见。

Thanks for listening, and see you next time.

感谢您收听TIP节目。

Thank you for listening to TIP.

请确保在您喜爱的播客应用中关注《亿万富豪研究》，不错过任何节目内容。

Make sure to follow We Study Billionaires on your favorite podcast app and never miss out on episodes.

要获取我们的节目笔记、文字稿或课程，请访问investors podcast dot com。

To access our show notes, transcripts, or courses, go to the investors podcast dot com.

本节目仅供娱乐目的。

This show is for entertainment purposes only.

在做出任何决策前，请咨询专业人士。

Before making any decision, consult a professional.

本节目版权归The Investor's Podcast Network所有。

This show is copyrighted by The Investor's Podcast Network.

未经书面许可，不得进行节目转播或重播。

Written permission must be granted before syndication or rebroadcasting.