鮑宝的餐厅还能开多久

　　一位叫做@10-K Diver 的外国网友，一直在做金融和投资方面的分享。我昨天看他写了一篇很长的文字，介绍如何做企业的预期生存寿命分析，以及背后的原理。觉得还挺有趣，所以把它翻译为中文，分享出来：

　　uppose a restaurant， on average， stays open for 8 years before shutting down. And suppose Bob has a restaurant -- that has been open for 3 years now. How much longer should we expect Bob's restaurant to stay in business？

　　假设一家餐厅平均而言可以生存8年。再假设鮑宝开了家餐厅，目前已经运营3年。那么，我们可以预计他的这家餐厅能再开多久？

　　We may be tempted to answer: 5 years. After all, restaurants last 8 years on average. And Bob is already 3 years in. So, on average, he has 8 - 3 = 5 years left, right？ Not necessarily. This 8 - 3 = 5 logic may lead us very far off the mark.

　　我们可能想回答说是5年。毕竟餐厅的平均生存时间是8年，鮑宝的餐厅已经开了3年，所以平均而言，他还有8-3=5年，对不对？不是这样的，这个8-3=5的逻辑根本就是谬之千里。

　　Why? Because 8 years is the average lifetime across ALL restaurants -- those that survived their first 3 years AND those that didn't. The statistics of these two groups may be VERY different.

　　为什么？因为8年这个餐馆平均生存时间时间是指所有的餐厅，包括了所有那些熬过了最初三年的，同时也包括所有那些没熬过的。它们各自的统计数据可能完全不同。

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　　（蓝字：所有的餐厅，平均生命周期8年；橙字：所有熬过头3年的餐厅，平均生命周期应该要更长一些，鮑宝的餐厅就在这一组里）

　　Lots of new restaurants open their doors each year. But the restaurant business is tough. Failure rates are high. Many new restaurants may not even survive 1 year. Just the fact that Bob has survived 3 years in this environment may mean he's doing something right.

　　每年都有许多新餐厅开张，但是餐饮业这个行当很难，失败率很高。许多新餐厅也许熬不过第一年。而就在这种环境下，鮑宝的餐厅事实上已经开了三年，那说明他也许是做对了什么事情。

　　Maybe people like Bob's food. Or maybe Bob is unusually talented as a restaurant operator. So, the key question to ask is: what's the average lifetime AMONG restaurants that have survived 3 years?

　　也许人们喜欢鮑宝家做的菜，或许作为餐厅老板鮑宝身怀别才。所以需要问的核心问题是：那些熬过头三年的餐厅，它们的平均生命周期是多久？

　　This is a *CONDITIONAL* probability question. We DON'T want the average lifetime across ALL restaurants. That's misleading. We ONLY want the average of restaurants that meet a *specific* condition -- namely, surviving 3 years. That's far more representative of Bob.

　　这是一个条件概率问题。我们根本不需要所有餐厅的平均生命周期，那个数据会误导我们。我们仅仅需要那些满足特定条件的餐厅，即为：存活超过3年遇上的餐厅。它们的平均生命周期更能体现鮑宝餐厅的预期寿命。

　　For this, we need to have a *model* for how restaurants tend to fail over time. How many restaurants don't make it past Year 1, how many fail in Year 2, etc. For example, here's one such model:

　　为此，我们需要一个模型来说明餐厅随着时间流逝会有怎样失败率。有多少餐厅没有熬过第一年，有多少餐厅没有熬过第二年，以此类推。举个例子，下面就是一个这样的模型：

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　　（蓝字从左到右：开始、刚开张、生存一年、生存待遇等于2年；绿字：50%可能、75%可能、95%可能；红色字第一行：50%可能，25%可能、5%可能；红字第二行：关张、吸收状态；红字第三行：100%可能）

　　According to this model: We open a restaurant. It has a 50% chance of dying in Year 1. IF we make it past Year 1, it has a 25% chance of dying in Year 2. And beyond Year 2, there's a 5% chance of dying in any subsequent year.

　　根据这个模型：我们开了一家餐厅，它在第一年有50%的可能会关张；如果我们熬过了第一年，那么在第二年里它有25%的可能会关张；超过2年以后，在接下来的任何一年里，它都有5%的可能会关张。

　　This is a simple model. But it has several useful features. First, it's a "Markov Chain". We start at a particular "state". And each year, we move to a possibly different state -- based on the outcome of a random, coin-flip type event. For more:

　　这是个简单的模型，但是它有几样有用的功能。首先，它是“一个马尔科夫链”。我们从一个特定的“状态”开始，然后在每一年里，基于一个随机抛硬币类型事件的结果，落入不同的状态中去。还有，

　　econd, this Markov Chain has exactly one "absorbing state" -- namely, death. That is, once our restaurant dies, we stay in this dead state forever. There's no coming back from death. Because death is "absorbing".

　　第二点，这个马尔科夫链只有一个“吸收状态”，那就是关张。这就是说，一旦我们的餐厅倒闭了，我们就会永远保持关张这个状态，不会从这个状态里重新活回来，因为关张是“吸收的”。

　　Third, our restaurant gets *harder* to kill with each surviving year: 50% chance of death in Year 1 --> 25% in Year 2 --> 5% in Years 3 and beyond. This is called "aging in reverse". It's the *opposite* of how humans and other living beings work for the most part.

　　第三点，我们的餐厅每多生存一年，就变得更加“难以”倒闭：第一年50%的关张可能---第二年25%---第三年以上5%。这叫做“逆龄”。在大多数情况下，这和人类以及其他生物生存的方式完全相反。

　　As living things get older, they usually become *more* (not *less*) prone to death. 80 year old humans are generally *more* likely to die before they turn 81, than 40 year old humans are before they turn 41. But *restaurants* may work differently.

　　随着生物逐渐变老，它们会有更多而非更少的可能死去。相对于40岁的人在41岁前死去，80岁的人更有可能活不到81岁。但是，餐厅的情况则完全不同。

　　In fact, even with humans, many societies/countries have high *infant mortality*. That is, infants tend to be more prone to death. But past a certain age (5 years or so), this "prone-ness to death" starts decreasing. And then it picks up again in old age. Like so:

　　事实上即便是人类自身，在许多社会/国家都有很高的婴儿死亡率。这就是说，婴儿往往更容易死亡，但是过了一定年岁之后（5岁左右），这种死亡的趋势就开始迅速下降，直到老年才会重上又升，如图：

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　　（将就着看吧，懒得翻了）

　　This "prone-ness to death" has another name: the Force of Mortality. It's the probability of encountering death within a short time interval, at any given age. The "Force of Mortality" vs "Age" graph tells us what kind of *aging* a particular system exhibits:

　　这种死亡的趋势有一个专门的名字：死亡力。它表示了在任何给定的年龄，在短时间内遇见死亡的概率。死亡力-年龄图告诉我们，在特定的系统中会有怎样的“老化过程”：

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　　（红线表示我们通常认为的老化，死亡力随年龄增长而增长；绿色线为逆龄，死亡力随年龄增加反而下降；紫色线为恒纪，死亡力不随年龄变化而变化）

　　If we apply the basics of probability to our restaurant aging model, we can calculate both the expected life of a restaurant (8 years) and the *conditional* expected life left for Bob's restaurant. Note: The latter is NOT 8 - 3 = 5 years. It's actually 19 years！

　　如果我们将概率的基础知识应用于我们的餐厅老化模型，我们可以计算出餐厅的预期寿命（8年）和鲍宝餐厅的“”条件“”预期寿命还有多长。注意：后者不是8-3=5年。它实际上是19年！

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　　（一些花了吧唧的图示和计算公式）

　　Thus, aging in reverse is wonderful. With each surviving year, the expected remaining life of a business that exhibits this type of aging gets longer and longer. Such businesses tend to have "moats". Over time, competitors tend to find them harder and harder to destroy.

　　因此，逆龄是美妙的。随着每多生存一年，这种逆龄企业的预期生存寿命就会变得越来越长。这样的企业往往有 "护城河"。随着时间的推移，竞争对手往往会发现它们越来越难被摧毁。

　　For investors, businesses that "age in reverse" are likely to generate future cash flows that, a) last longer, and b) are more certain. This in turn means investors can pay a bit more for such businesses, and still do reasonably well in the long run.

　　对于投资者而言，逆龄企业在未来产生的现金流可能会1、更持久；2、更确定。这反过来意味着投资者可以为这样的企业多投入一些钱，从长远来看仍然会表现良好。