In a previous post, I mentioned that thinking exhaustively is exhausting! Volatility and uncertainty are ever present and must be factored into our decision making — yet, we often don’t have the time or data to properly account for it.

在上一篇文章中，我提到详尽的思考令人筋疲力尽！ 波动性和不确定性一直存在，必须将其纳入我们的决策制定中，但是，我们通常没有时间或数据来适当地说明这一点。

That’s where thinking relatively (comparing things) may come in handy. Often in life, we need to make judgments or choices such as “should I work for this company?” When viewed as an isolated decision, even seemingly simple decisions like this one can be pretty hard. If you care a lot about making the right choice, then you will probably need to consider all of the following:

这就是相对思考(比较事物)可能会派上用场的地方。 在生活中，我们经常需要做出判断或选择，例如“我应该为这家公司工作吗？” 当被视为一个孤立的决定时，即使像这样的看似简单的决定也可能很难。 如果您非常关心做出正确的选择，那么您可能需要考虑以下所有方面：

• Company culture and team culture公司文化和团队文化
• Personality of your boss你老板的个性
• Company’s competitive edge公司的竞争优势
• Quality of compensation, perks, and other benefits补偿质量，津贴和其他好处
• Work/life balance工作与生活的平衡
• Types of projects you will work on您将从事的项目类型
• Opportunities to grow and develop成长和发展的机会
• Location and commute位置和通勤

A very thorough person would be making spreadsheets, conducting interviews (with both current and ex employees of the company), and taking tons of notes — all in the name of trying to figure out whether this is truly the perfect job. And if it were me, I can imagine myself quickly becoming overwhelmed by the deluge of information (especially if it’s conflicting).

一个非常透彻的人将制作电子表格，进行采访(与公司的现任和前任雇员)，并记下大量笔记，所有这些都是以试图弄清楚这是否真的是完美的工作为名。 如果是我，我可以想象自己很快就被大量的信息淹没(尤其是在发生冲突的情况下)。

The truth is that no matter how much due diligence we do, we can never eliminate the chance of making a wrong mistake. We can make it smaller by gathering lots of data and thinking things through, but there’s always the risk that something we failed to consider or a black swan (unpredictable) type of event mucks things up.

事实是，无论我们进行了多少尽职调查，我们都无法消除犯错的机会。 我们可以通过收集大量数据并仔细考虑来缩小它的大小，但是始终存在我们无法考虑的事情或黑天鹅(不可预测的)事件掩盖了事情的风险。

Moreover, time is a scarce resource and, on average, the incremental amount of signal that each new piece of information brings is diminishing. Besides running the risk of becoming paralyzed by information overload, there is a cost in terms of both time and missed opportunities from taking too long to decide. That’s why we should always try to think relatively.

而且，时间是一种稀缺资源，平均而言，每条新信息带来的信号增量正在减少。 除了承担因信息过载而瘫痪的风险外，还有时间和机会错失的代价，因为决策时间太长。 这就是为什么我们应该始终尝试相对思考。

通过相对思考简化 (Simplify By Thinking Relatively)

A simpler framework for making decisions is to ask the following three questions:

一个更简单的决策框架是提出以下三个问题：

1. Out of the go-forward set of choices currently available to me and taking into account my personal situation, what’s the best option?

   走出去进组选择目前提供给我，并考虑到我的个人情况的，什么是最好的选择吗？

2. How does the expected outcome of my go-forward choice compare to picking “none of the above” (a.k.a. doing nothing)?我的前瞻性选择的预期结果与选择“上述都不是”(也就是什么也不做)相比如何？
3. If I choose to go forward (with the answer of question 1), can I accept the outcome if the worst case scenario occurs?如果我选择前进(回答问题1)，如果发生最坏情况，我可以接受结果吗？

Question 1 sounds obvious but it serves to move the decision making process from an absolute one to a relative one. It’s much easier to figure out whether job A is better than job B versus trying to decide in absolute terms how good job A is. The key is to frame everything within the context of the opportunity set. If we don’t have a reasonably clear idea of the alternative options available to us, then we are not yet ready to properly evaluate the current action. Note that I call these the go-forward choices as they all involve action (as opposed to doing nothing).

问题1听起来很明显，但是它有助于将决策过程从绝对决策转变为相对决策。 相对于绝对地确定工作A的好坏，要弄清楚工作A是否比工作B好得多。 关键是在机会集的背景下构筑一切。 如果我们对可用的替代方案没有一个合理清晰的认识，那么我们还没有准备好正确评估当前的措施。 请注意，我将这些称为前进选择，因为它们都涉及动作(而不是什么也不做)。

Question 2 recognizes that sometimes the best choice is “none of the above”. Note that the expected outcome of our chosen go-forward option is not equivalent to the scenario that is the most likely to occur. Rather, it should be a weighted (by probability) sum of the outcomes of all the scenarios with a material chance of occurring. That’s an important distinction — the most likely outcome when Steph Curry shoots a free throw is that it goes in for one point. However, the expected outcome when Curry shoots a free throw is 0.9 points (1 point times his career free throw conversion percentage of 90%).

问题2认识到有时最好的选择是“以上皆非”。 请注意，我们选择的前进选项的预期结果并不等于最有可能发生的情况。 相反，它应该是所有场景具有重大发生机会的结果的加权(按概率)总和。 这是一个重要的区别-斯蒂芬·库里(Steph Curry)罚球时，最有可能的结果是得分提高了1个百分点。 但是，库里罚球时的预期结果是0.9分(1分乘以他职业生涯90％的罚球转化率)。

If it isn’t a bell curve, the shape of the distribution of outcomes becomes important to consider as well. Averages can lead us astray when the outcomes are binary or follow some other distribution where the bulk of the possibilities lie in the extremes (as opposed to near the mean).

如果不是钟形曲线，则结果分布的形状也必须考虑。 当结果是二进制的或遵循其他分布(其中大多数可能性处于极值(而不是接近均值))时，平均值会使我们误入歧途。

I struggled over whether to include question 3. Being overly worried about worst case outcomes can cause suboptimal decision making such as refusing to fly (due to fear of plane crashes) or overpaying for insurance. But if after objective analysis, the worst case (no matter how low the probability) is still found to be completely unpalatable, then it makes sense to hedge it out. For example assuming a healthy lifestyle, the probability of getting a serious illness is low — but health insurance still makes sense because if you develop a serious illness without insurance, then you (and your loves ones) face complete financial ruin.

我为是否要包含问题3而苦苦挣扎。过于担心最坏的情况会导致决策不佳，例如拒绝飞行(由于担心飞机失事)或为保险支付过多的费用。 但是，如果经过客观分析，发现最坏的情况(无论概率有多低)仍然完全不受欢迎，那么就可以将其对冲了。 例如，假设一种健康的生活方式，患上重病的可能性很低，但是健康保险仍然有意义，因为如果您在没有保险的情况下患上重病，那么您(和您的亲人)将面临完全的财务损失。

Honestly answering questions 2 and 3 protect us from uncertainty, analytical error, and risk.

诚实地回答问题2和3可以保护我们免受不确定性，分析错误和风险的影响。

案例研究-我应该购买一些股票吗？ (Case Study — Should I Buy Some Stock?)

Given the craziness (and exuberance) in the financial markets these days, let’s use stock picking as our case study. Say we recently received a lump sum of $10,000. We would like to make our money work for us, so we are looking into whether buying some company stock is a good idea.

考虑到这些天金融市场的疯狂(和繁荣)，让我们以选股作为案例研究。 假设我们最近一次收到了一笔10,000美元的款项。 我们想让钱对我们有用，所以我们正在研究购买一些公司股票是否是一个好主意。

回答问题1 (Answering Question 1)

Let’s first define our opportunity set. What are some reasonable things that we can we do with our money besides buying stock? This list doesn’t need to be exhaustive — we are looking for reasonable alternatives that align with our personality, interests, and risk tolerance. For example, assuming we are kind of lazy and already fully employed, then using the money to start a coffee shop is out of the question. Here’s my list of go-forward options:

首先定义机会集。 除了买股票，我们还能用钱做些合理的事情吗？ 此列表并不需要详尽无遗-我们正在寻找与我们的个性，兴趣和风险承受能力相称的合理替代方案。 例如，假设我们有点懒惰并且已经充分就业，那么花钱开一家咖啡店就不成问题了。 这是我的前进选项列表：

• Buy company stock购买公司股票
• Gamble on stock options赌博股票期权
• Buy a market index购买市场指数
• Invest via a robo-advisor in a diversified portfolio通过机器人顾问投资多元化的投资组合
• Pay a financial advisor to manage the money支付财务顾问来管理资金
• Pay down debt (if applicable)偿还债务(如果适用)
• Buy something really nice买东西真的很好

What we see when we define the opportunity set is that even this reasonably short list is widely variant in terms of riskiness and potential future outcomes. Note that these are all go-forward options where we’ve decided to invest in something that has the potential to deliver us a decent return (or pleasure in the case of buying something really nice). So how do we go about evaluating each option and answering question 1? Well, first we need to understand our own situation. Let’s say we are:

当我们定义机会集时，我们看到的是，即使是这个合理的简短列表，在风险和潜在的未来结果方面也存在很大差异。 请注意，这些都是前进的选择，我们已决定投资于那些有可能为我们带来可观回报的东西(或者在购买真正精美的东西时很高兴)。 那么，我们如何评估每个选项并回答问题1？ 好吧，首先我们需要了解我们自己的情况。 假设我们是：

• Gainfully employed with a long working horizon ahead长期从事有远见的工作
• Have some savings already (enough to pay 6 months of expenses), but desire to save more (and compound our money over time)已经有了一些储蓄(足以支付6个月的费用)，但是希望节省更多(随着时间的推移我们的钱会增加)
• No high interest debt, just a low rate mortgage没有高利息债务，只有低利率抵押贷款
• No prior experience investing in stocks没有投资股票的经验

OK, we have enough to answer question 1. Notice how the specifics of our situation eliminate certain options while emphasizing others. Given that we are relatively young and steadily employed, that pushes us towards an investment we can hold and continue adding to for years. Not having any high interest debt and possessing some cash savings are more reasons to prefer a stock heavy portfolio. The fact that we have little experience with investments means we should probably seek professional assistance — and since our financial situation is simple (young and just starting to save), there’s no point to pay for an expensive financial advisor. Finally, given our desire to save and compound, it doesn’t make sense to buy jewelry or gamble on overly risky investments like options.

好的，我们有足够的答案来回答问题1。请注意，我们的具体情况在强调其他选择的同时如何消除某些选择。 鉴于我们还处于相对年轻和稳定的状态，这促使我们朝着可以持有并持续增加的方向投资。 没有任何高息债务并拥有一些现金储蓄是选择股票密集型投资组合的更多原因。 我们几乎没有投资经验，这意味着我们可能应该寻求专业帮助-并且由于我们的财务状况很简单(年轻并且刚刚开始储蓄)，因此没有必要为昂贵的财务顾问付费。 最后，鉴于我们渴望储蓄和增加的意愿，因此购买珠宝或押注期权等过高风险的投资毫无意义。

By process of elimination, it looks like investing via a robo-advisor makes the most sense (with the market index plus some cash a close second). Through the robo-advisor, we get access to a low-cost and diversified portfolio that we can set and forget for several years.

通过淘汰的过程，似乎似乎最有可能通过机器人顾问进行投资(市场指数加上一些现金紧随其后)。 通过机器人顾问，我们可以访问多年来可以设置和忘记的低成本，多元化的产品组合。

现在到问题2 (Now On To Question 2)

What are our “do nothing” options? If we decide that risky investments are not to our liking, we can:

我们的“什么都不做”选项是什么？ 如果我们确定风险投资不符合我们的喜好，我们可以：

• Keep the cash in a checking or savings account将现金存入支票或储蓄帐户
• Invest in short duration Treasury bonds or FDIC insured CDs (certificate of deposit)投资短期国债或FDIC保险CD(存款证明)
• Invest in short duration TIPS (Treasury Inflation Protected Securities).投资短期TIPS(国库通胀保护证券)。

All these options are relatively low risk, meaning that we can be relatively sure that we won’t lose any of the money. But with very little capital markets experience, how do we decide whether or not it’s suitable to take on some risk at the given time? Without the tools, experience, (and cockiness?) to make a market prediction, it’s more reasonable to frame the problem in terms of average outcomes.

所有这些选择的风险都相对较低，这意味着我们可以相对确定我们不会损失任何钱。 但是，由于资本市场经验很少，我们如何确定在给定的时间是否适合承担某些风险？ 没有市场预测的工具，经验和(或自以为是？) ，按照平均结果来构造问题就更合理了 。

We can use historical data that covers a sufficient number of years to estimate the average outcome. Data that covers multiple business cycles captures both good times and bad (recessions) and provides a reasonable estimate of what we can expect going forward in terms of long term expected returns. Let’s say we peruse the data and estimate that a diversified portfolio should earn on average 7% over a long period of time.

我们可以使用涵盖足够多年的历史数据来估计平均结果。 涵盖多个业务周期的数据既可以捕捉好时光，也可以捕捉坏处(衰退)，并就长期预期收益而言，可以合理地估算我们的预期。 假设我们仔细研究了数据，并估计多元化的投资组合在长期内应能平均获得7％的收益。

Using the same data, we find that cash and other low risk investments produced a mere 1% and often lagged inflation. Given that we plan to be invested for several decades and even without accounting for risk, the average outcome of the portfolio seems sufficiently high relative to that of cash (doing nothing) — justifying our decision to invest in the diversified portfolio.

使用相同的数据，我们发现现金和其他低风险投资仅产生了1％，通货膨胀通常滞后。 鉴于我们计划投资几十年，甚至不计入风险，投资组合的平均结果似乎要相对于现金而言足够高(不做任何事情)，这证明了我们决定投资多元化投资组合的理由。

In reality, I personally would want to consider more than just the simplistic analysis I presented just now. Both the expected return and risk of a portfolio vary over time and at any given moment, you want to make sure that you are being properly compensated (in terms of expected return) for the risk that you are taking on. But this takes experience to estimate and can involve significant risk of analytical error.

实际上，我个人想考虑的不仅仅是我刚才介绍的简单分析。 投资组合的预期收益和风险都随时间而变化，并且在任何给定时刻，您都想确保自己正承受承担的风险(根据预期收益)得到适当的补偿。 但是，这需要经验来估计，并且可能会带来重大的分析错误风险。

问题3：可能发生的更坏的情况是什么 (Question 3: What’s The Worse That Could Happen)

Now let’s think about the worst case. If the economy crashed right after we made our investment, how would our portfolio perform? Looking at past recessions, we find that the diversified portfolio we’re considering would have lost around 25%. Would we be OK with losing $2,500 to $3,000 of our $10,000 initial investment over the next few weeks or the next few months?

现在让我们考虑最坏的情况。 如果在进行投资后经济崩溃，我们的投资组合将如何表现？ 回顾过去的衰退，我们发现我们正在考虑的多元化投资组合将损失约25％。 在接下来的几周或接下来的几个月中，我们在10,000美元的初始投资中损失了2500美元至3,000美元，我们还可以吗？

If we find the outcome bearable, then it’s a go. Personally, I find this part of the decision trickiest as I’m pretty risk averse. Negative outcomes are not fun at all. And there’s always the scary chance that despite our best attempt, we’ve underestimated the true risk. While thinking about negative outcomes and loss, it’s important to keep in mind our own psychological makeup — am I risk averse or risk seeking? It’s also helpful to keep in mind that people on average tend to feel losses more than they enjoy gains (prospect theory). Keeping our biases in mind prevents us from being dominated and overly influenced by our fears.

如果我们认为结果可以接受，那就去吧。 就我个人而言，我发现决策的这一部分最为棘手，因为我非常喜欢冒险。 负面结果一点都不有趣。 尽管我们尽了最大的努力，但总有一个可怕的机会，那就是我们低估了真正的风险。 在考虑负面结果和损失时，重要的是要牢记我们自己的心理构成-我是否会厌恶或寻求风险？ 记住，人们通常会感到损失多于享受收益( 前景理论 )。 牢记我们的偏见可以防止我们被恐惧所支配和过度影响。

结论 (Conclusion)

Decision making is a really interesting topic to me. Data science, itself, is about harnessing the power of data to make better decisions (and being able to codify, automate, and iterate/improve this decision making process).

决策对我来说是一个非常有趣的话题。 数据科学本身就是要利用数据的力量做出更好的决策(并能够编纂，自动化和迭代/改善该决策过程)。

But even more important than teaching a machine to make good decisions, is possessing our own solid framework for decision making. And in my opinion, it all starts with our ability to identify the opportunity set, size up each option, and quantify the risks involved.

但是拥有一个自己的坚实的决策框架比教导机器做出良好的决策更为重要。 在我看来，这一切都始于我们识别机会集，确定每种选择的规模并量化所涉及风险的能力。