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，我提到詳盡的思考令人筋疲力盡！ 波動性和不確定性一直存在，必須將其納入我們的決策制定中，但是，我們通常沒有時間或數據來適當地說明這一點。

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:

這就是相對思考(比較事物)可能會派上用場的地方。 在生活中，我們經常需要做出判斷或選擇，例如“我應該為這家公司工作嗎？” 當被視為一個孤立的決定時，即使像這樣的看似簡單的決定也可能很難。 如果您非常關心做出正確的選擇，那么您可能需要考慮以下所有方面：

• Company culture and team culture
  公司文化和團隊文化
• Personality of your boss
  你老板的個性
• Company’s competitive edge
  公司的競爭優勢
• Quality of compensation, perks, and other benefits
  補償質量，津貼和其他好處
• Work/life balance
  工作與生活的平衡
• Types of projects you will work on
  您將從事的項目類型
• Opportunities to grow and develop
  成長和發展的機會
• 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).

一個非常透徹的人將制作電子表格，進行采訪(與公司的現任和前任雇員)，并記下大量筆記，所有這些都是以試圖弄清楚這是否真的是完美的工作為名。 如果是我，我可以想象自己很快就被大量的信息淹沒(尤其是在發生沖突的情況下)。

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.

事實是，無論我們進行了多少盡職調查，我們都無法消除犯錯的機會。 我們可以通過收集大量數據并仔細考慮來縮小它的大小，但是始終存在我們無法考慮的事情或黑天鵝(不可預測的)事件掩蓋了事情的風險。

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，時間是一種稀缺資源，平均而言，每條新信息帶來的信號增量正在減少。 除了承擔因信息過載而癱瘓的風險外，還有時間和機會錯失的代價，因為決策時間太長。 這就是為什么我們應該始終嘗試相對思考。

通過相對思考簡化 (Simplify By Thinking Relatively)

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

一個更簡單的決策框架是提出以下三個問題：

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?

   走出去進組選擇目前提供給我，并考慮到我的個人情況的，什么是最好的選擇嗎？

2. How does the expected outcome of my go-forward choice compare to picking “none of the above” (a.k.a. doing nothing)?
   我的前瞻性選擇的預期結果與選擇“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?
   如果我選擇前進(回答問題1)，如果發生最壞情況，我可以接受結果嗎？

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).

問題1聽起來很明顯，但是它有助于將決策過程從絕對決策轉變為相對決策。 相對于絕對地確定工作A的好壞，要弄清楚工作A是否比工作B好得多。 關鍵是在機會集的背景下構筑一切。 如果我們對可用的替代方案沒有一個合理清晰的認識，那么我們還沒有準備好正確評估當前的措施。 請注意，我將這些稱為前進選擇，因為它們都涉及動作(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%).

問題2認識到有時最好的選擇是“以上皆非”。 請注意，我們選擇的前進選項的預期結果并不等于最有可能發生的情況。 相反，它應該是所有場景具有重大發生機會的結果的加權(按概率)總和。 這是一個重要的區別-斯蒂芬·庫里(Steph Curry)罰球時，最有可能的結果是得分提高了1個百分點。 但是，庫里罰球時的預期結果是0.9分(1分乘以他職業生涯90％的罰球轉化率)。

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).

如果不是鐘形曲線，則結果分布的形狀也必須考慮。 當結果是二進制的或遵循其他分布(其中大多數可能性處于極值(而不是接近均值))時，平均值會使我們誤入歧途。

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.

我為是否要包含問題3而苦苦掙扎。過于擔心最壞的情況會導致決策不佳，例如拒絕飛行(由于擔心飛機失事)或為保險支付過多的費用。 但是，如果經過客觀分析，發現最壞的情況(無論概率有多低)仍然完全不受歡迎，那么就可以將其對沖了。 例如，假設一種健康的生活方式，患上重病的可能性很低，但是健康保險仍然有意義，因為如果您在沒有保險的情況下患上重病，那么您(和您的親人)將面臨完全的財務損失。

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

誠實地回答問題2和3可以保護我們免受不確定性，分析錯誤和風險的影響。

案例研究-我應該購買一些股票嗎？ (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.

考慮到這些天金融市場的瘋狂(和繁榮)，讓我們以選股作為案例研究。 假設我們最近一次收到了一筆10,000美元的款項。 我們想讓錢對我們有用，所以我們正在研究購買一些公司股票是否是一個好主意。

回答問題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:

首先定義機會集。 除了買股票，我們還能用錢做些合理的事情嗎？ 此列表并不需要詳盡無遺-我們正在尋找與我們的個性，興趣和風險承受能力相稱的合理替代方案。 例如，假設我們有點懶惰并且已經充分就業，那么花錢開一家咖啡店就不成問題了。 這是我的前進選項列表：

• Buy company stock
  購買公司股票
• Gamble on stock options
  賭博股票期權
• Buy a market index
  購買市場指數
• Invest via a robo-advisor in a diversified portfolio
  通過機器人顧問投資多元化的投資組合
• Pay a financial advisor to manage the money
  支付財務顧問來管理資金
• Pay down debt (if applicable)
  償還債務(如果適用)
• Buy something really nice
  買東西真的很好

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:

當我們定義機會集時，我們看到的是，即使是這個合理的簡短列表，在風險和潛在的未來結果方面也存在很大差異。 請注意，這些都是前進的選擇，我們已決定投資于那些有可能為我們帶來可觀回報的東西(或者在購買真正精美的東西時很高興)。 那么，我們如何評估每個選項并回答問題1？ 好吧，首先我們需要了解我們自己的情況。 假設我們是：

• Gainfully employed with a long working horizon ahead
  長期從事有遠見的工作
• Have some savings already (enough to pay 6 months of expenses), but desire to save more (and compound our money over time)
  已經有了一些儲蓄(足以支付6個月的費用)，但是希望節省更多(隨著時間的推移我們的錢會增加)
• No high interest debt, just a low rate mortgage
  沒有高利息債務，只有低利率抵押貸款
• No prior experience investing in stocks
  沒有投資股票的經驗

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，我們有足夠的答案來回答問題1。請注意，我們的具體情況在強調其他選擇的同時如何消除某些選擇。 鑒于我們還處于相對年輕和穩定的狀態，這促使我們朝著可以持有并持續增加的方向投資。 沒有任何高息債務并擁有一些現金儲蓄是選擇股票密集型投資組合的更多原因。 我們幾乎沒有投資經驗，這意味著我們可能應該尋求專業幫助-并且由于我們的財務狀況很簡單(年輕并且剛剛開始儲蓄)，因此沒有必要為昂貴的財務顧問付費。 最后，鑒于我們渴望儲蓄和增加的意愿，因此購買珠寶或押注期權等過高風險的投資毫無意義。

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.

通過淘汰的過程，似乎似乎最有可能通過機器人顧問進行投資(市場指數加上一些現金緊隨其后)。 通過機器人顧問，我們可以訪問多年來可以設置和忘記的低成本，多元化的產品組合。

現在到問題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:

我們的“什么都不做”選項是什么？ 如果我們確定風險投資不符合我們的喜好，我們可以：

• Keep the cash in a checking or savings account
  將現金存入支票或儲蓄帳戶
• Invest in short duration Treasury bonds or FDIC insured CDs (certificate of deposit)
  投資短期國債或FDIC保險CD(存款證明)
• Invest in short duration TIPS (Treasury Inflation Protected Securities).
  投資短期TIPS(國庫通脹保護證券)。

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.

所有這些選擇的風險都相對較低，這意味著我們可以相對確定我們不會損失任何錢。 但是，由于資本市場經驗很少，我們如何確定在給定的時間是否適合承擔某些風險？ 沒有市場預測的工具，經驗和(或自以為是？) ，按照平均結果來構造問題就更合理了 。

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.

我們可以使用涵蓋足夠多年的歷史數據來估計平均結果。 涵蓋多個業務周期的數據既可以捕捉好時光，也可以捕捉壞處(衰退)，并就長期預期收益而言，可以合理地估算我們的預期。 假設我們仔細研究了數據，并估計多元化的投資組合在長期內應能平均獲得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.

使用相同的數據，我們發現現金和其他低風險投資僅產生了1％，通貨膨脹通常滯后。 鑒于我們計劃投資幾十年，甚至不計入風險，投資組合的平均結果似乎要相對于現金而言足夠高(不做任何事情)，這證明了我們決定投資多元化投資組合的理由。

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.

實際上，我個人想考慮的不僅僅是我剛才介紹的簡單分析。 投資組合的預期收益和風險都隨時間而變化，并且在任何給定時刻，您都想確保自己正承受承擔的風險(根據預期收益)得到適當的補償。 但是，這需要經驗來估計，并且可能會帶來重大的分析錯誤風險。

問題3：可能發生的更壞的情況是什么 (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?

現在讓我們考慮最壞的情況。 如果在進行投資后經濟崩潰，我們的投資組合將如何表現？ 回顧過去的衰退，我們發現我們正在考慮的多元化投資組合將損失約25％。 在接下來的幾周或接下來的幾個月中，我們在10,000美元的初始投資中損失了2500美元至3,000美元，我們還可以嗎？

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.

如果我們認為結果可以接受，那就去吧。 就我個人而言，我發現決策的這一部分最為棘手，因為我非常喜歡冒險。 負面結果一點都不有趣。 盡管我們盡了最大的努力，但總有一個可怕的機會，那就是我們低估了真正的風險。 在考慮負面結果和損失時，重要的是要牢記我們自己的心理構成-我是否會厭惡或尋求風險？ 記住，人們通常會感到損失多于享受收益( 前景理論 )。 牢記我們的偏見可以防止我們被恐懼所支配和過度影響。

結論 (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).

決策對我來說是一個非常有趣的話題。 數據科學本身就是要利用數據的力量做出更好的決策(并能夠編纂，自動化和迭代/改善該決策過程)。

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.

但是擁有一個自己的堅實的決策框架比教導機器做出良好的決策更為重要。 在我看來，這一切都始于我們識別機會集，確定每種選擇的規模并量化所涉及風險的能力。