python金融風(fēng)控評(píng)分卡模型和數(shù)據(jù)分析微專(zhuān)業(yè)課：http://dwz.date/b9vv

由于模型是以特定時(shí)期的樣本所開(kāi)發(fā)的，此模型是否適用于開(kāi)發(fā)樣本之外的族群，必須經(jīng)過(guò)穩(wěn)定性測(cè)試才能得知。穩(wěn)定度指標(biāo)(population stability index ,PSI)可衡量測(cè)試樣本及模型開(kāi)發(fā)樣本評(píng)分的的分布差異，為最常見(jiàn)的模型穩(wěn)定度評(píng)估指針。其實(shí)PSI表示的就是按分?jǐn)?shù)分檔后，針對(duì)不同樣本，或者不同時(shí)間的樣本，population分布是否有變化，就是看各個(gè)分?jǐn)?shù)區(qū)間內(nèi)人數(shù)占總?cè)藬?shù)的占比是否有顯著變化。公式如下：

?補(bǔ)充解釋ln()為自然對(duì)數(shù)函數(shù)

PSI實(shí)際應(yīng)用范例：

1）樣本外測(cè)試

　　針對(duì)不同的樣本測(cè)試一下模型穩(wěn)定度，比如訓(xùn)練集與測(cè)試集，也能看出模型的訓(xùn)練情況，我理解是看出模型的方差情況。

2）時(shí)間外測(cè)試

　　測(cè)試基準(zhǔn)日與建?；鶞?zhǔn)日相隔越遠(yuǎn)，測(cè)試樣本的風(fēng)險(xiǎn)特征和建模樣本的差異可能就越大，因此PSI值通常較高。至此也可以看出模型建的時(shí)間太長(zhǎng)了，是不是需要重新用新樣本建模了。

?

http://ucanalytics.com/blogs/population-stability-index-psi-banking-case-study/參考

This is a continuation of the banking case study for the creation of application risk scorecards we have discussed in some previous articles. You could find the previous parts of the series at the following links?(Part 1),?(Part 2),?(Part 3)?and (Part 4).

In this article, we will discuss the Population Stability Index (PSI), an important metric to identify a shift in population for retail credit scorecards. Before we delve deeper into the calculation of the population stability index (PSI) and its utility, let’s try to understand the overall purpose of the PSI and similar indexes by connecting a few dots between.

這是我們?cè)谥暗囊恍┪恼轮杏懻撨^(guò)的創(chuàng)建應(yīng)用程序風(fēng)險(xiǎn)記分卡的銀行案例研究的延續(xù)。 您可以在以下鏈接（第1部分），（第2部分），（第3部分）和（第4部分）中找到該系列的前幾部分。

在本文中，我們將討論人口穩(wěn)定性指數(shù)（PSI），這是確定零售信用記分卡人口變化的重要指標(biāo)。 在我們深入研究人口穩(wěn)定性指數(shù)（PSI）及其效用的計(jì)算之前，讓我們嘗試通過(guò)在兩者之間連接幾個(gè)點(diǎn)來(lái)理解PSI和類(lèi)似指數(shù)的總體目的。

Dictators and Credit Crisis ?

What is similar between Napoleon’s and then Hitler’s attempts to invade Russia and financial crisis of 2007-08?

Napoleon tried to invade Russia in 1812 and Hitler repeated Napoleon’s misdeeds in 1941 – both invasions ended with severe defeats for the armies of the dictators. The armies of both Napoleon and Hitler were far superior to the Russians. It was the conditions in which the battles were fought that resulted in these defeats. Russian winters are often held responsible for the fate of these armies. In reality, it was the ill-preparedness and bad judgment of both Napoleon’s and Hitler’s men that caused them the humiliating defeats. They were very well trained men but they were trained in benevolent conditions of France and Germany. This time, the battle was in completely different and extreme conditions, and they could not cope with it.

The failure of credit risk models during the financial crisis 0f 2007-08 could be related to the fate of both the French and German armies. The models were built and trained in a benevolent economic environment and were ill-prepared to deal with extreme economic conditions at the time. Additionally, there were series of bad judgments by the executives at the financial firms that resulted in total economic collapse.

The moral of the above stories is that one has to keep a close tab on a change in conditions in the currently prevalent environment and training environment. The Basel III accord has paid a significant attention towards monitoring portfolio on a regular basis for a good reason. The ?population stability index (PSI) is one such index that helps risk managers in performing this task for retail credit scorecards.

獨(dú)裁者與信用危機(jī)
拿破侖和希特勒試圖入侵俄羅斯和2007 - 08年的金融危機(jī)有何相似之處？

拿破侖試圖在1812年入侵俄羅斯，希特勒于1941年重復(fù)了拿破侖的不端行為 - 兩次入侵都以獨(dú)裁者軍隊(duì)的嚴(yán)重失敗而告終。拿破侖和希特勒的軍隊(duì)遠(yuǎn)遠(yuǎn)優(yōu)于俄羅斯人。正是這場(chǎng)戰(zhàn)斗的條件導(dǎo)致了這些失敗。俄羅斯的冬天經(jīng)常對(duì)這些軍隊(duì)的命運(yùn)負(fù)責(zé)。實(shí)際上，正是拿破侖和希特勒的男人們的準(zhǔn)備不足和不良判斷導(dǎo)致了他們羞辱性的失敗。他們是訓(xùn)練有素的人，但他們受過(guò)法國(guó)和德國(guó)的良好條件訓(xùn)練。這一次，戰(zhàn)斗處于完全不同的極端條件下，他們無(wú)法應(yīng)對(duì)。

2007-08財(cái)政危機(jī)期間信用風(fēng)險(xiǎn)模型的失敗可能與法國(guó)和德國(guó)軍隊(duì)的命運(yùn)有關(guān)。這些模型是在一個(gè)仁慈的經(jīng)濟(jì)環(huán)境中建立和培訓(xùn)的，并且沒(méi)有準(zhǔn)備好應(yīng)對(duì)當(dāng)時(shí)的極端經(jīng)濟(jì)條件。此外，金融公司的高管們做出了一系列糟糕的判斷，導(dǎo)致經(jīng)濟(jì)全面崩潰。

上述故事的寓意是，必須密切關(guān)注當(dāng)前流行的環(huán)境和培訓(xùn)環(huán)境中的條件變化。 “巴塞爾協(xié)議III”已經(jīng)非常重視監(jiān)督投資組合，這是有充分理由的。人口穩(wěn)定指數(shù)（PSI）就是這樣一個(gè)指數(shù)，它可以幫助風(fēng)險(xiǎn)管理人員完成零售信用記分卡的這項(xiàng)任務(wù)。

Population Stability Index (PSI) – Our Banking Case Continues

You are the chief-risk-officer at CyndiCat bank. It’s been a couple of years since your team, in your supervision, has built the auto-loans credit scorecard. Since then the overall risk assessment process for the bank has improved significantly. Though being a prudent risk manager you have asked your team to regularly compare the population for which the scorecard was built and the existing through-the-door population (applicants for auto loans). A good place to start this comparison is by checking how two populations are distributed across the risk bands created through the scorecard. The following is a representation for the latest quarterly comparison your team has performed against the benchmark sample. Here Actual %’ is the population distribution for the latest quarter and ‘Expected %’ is the population distribution for the validation sample (a.k.a. benchmark sample).

人口穩(wěn)定指數(shù)（PSI） - 我們的銀行業(yè)案例繼續(xù)
您是CyndiCat銀行的首席風(fēng)險(xiǎn)官。 自從您的團(tuán)隊(duì)在您的監(jiān)督下建立了汽車(chē)貸款信用記分卡以來(lái)已經(jīng)過(guò)去了幾年。 從那時(shí)起，銀行的整體風(fēng)險(xiǎn)評(píng)估流程得到了顯著改善。 雖然您是一名謹(jǐn)慎的風(fēng)險(xiǎn)經(jīng)理，但您已經(jīng)要求您的團(tuán)隊(duì)定期比較建立記分卡的人口和現(xiàn)有的門(mén)戶(hù)（汽車(chē)貸款申請(qǐng)人）。 開(kāi)始這種比較的一個(gè)好地方是檢查兩個(gè)種群如何在通過(guò)記分卡創(chuàng)建的風(fēng)險(xiǎn)區(qū)分布。 以下是您的團(tuán)隊(duì)針對(duì)基準(zhǔn)樣本進(jìn)行的最新季度比較的表示。 這里實(shí)際％'是最新季度的人口分布，'預(yù)期％'是驗(yàn)證樣本的人口分布（a.k.a.基準(zhǔn)樣本）。

Comparing two populations visually is a good place to start. The current population seems to have shifted towards the right side of the graph. To a small extent, this is expected since scorecards often influence the through-the-door population as the market starts reacting to the approval strategies of the bank. However, the question we need to ask is whether this a major shift in the population? Essentially, you are comparing two different distributions and could use any goodness-of-fit measure such as Chi-square test. However, the population stability index is an industry-accepted metric that presents some convenient rules of thumb for the same. The population stability index (PSI) formula is displayed below (refer to ‘Credit Risk Scorecards’ by Naeem Siddiqui)

目視比較兩個(gè)人群是一個(gè)很好的起點(diǎn)。 目前的人口似乎已轉(zhuǎn)向圖表的右側(cè)。 在很小程度上，這是預(yù)期的，因?yàn)槭袌?chǎng)開(kāi)始對(duì)銀行的審批策略作出反應(yīng)，因?yàn)橛浄挚ń?jīng)常影響到門(mén)戶(hù)。 但是，我們需要問(wèn)的問(wèn)題是，這是否是人口的重大轉(zhuǎn)變？ 基本上，您正在比較兩種不同的分布，并且可以使用任何擬合度度量，例如卡方檢驗(yàn)。 然而，人口穩(wěn)定性指數(shù)是一個(gè)行業(yè)認(rèn)可的指標(biāo)，為此提供了一些方便的經(jīng)驗(yàn)法則。 人口穩(wěn)定性指數(shù)（PSI）公式如下所示（參見(jiàn)Naeem Siddiqui的“信用風(fēng)險(xiǎn)記分卡”）

Again like the weight of evidence and the information value, PSI seems to have it’s root in information theory. Let’s calculate the population stability index (PSI) for our population (we have already seen a histogram for this above).

再次像證據(jù)的重量和信息價(jià)值，PSI似乎已經(jīng)成為信息理論的根源。 讓我們計(jì)算人口的人口穩(wěn)定性指數(shù)（PSI）（我們已經(jīng)看到了上面的直方圖）。

The last column in the above table is what we care for. Let us consider the score band 251-290 and calculate the index value for this row.

上表中的最后一列是我們關(guān)心的。 讓我們考慮分?jǐn)?shù)帶251-290并計(jì)算該行的索引值。

The final value for the PSI i.e. 0.13 is the sum of all the values of the last column. Now the question is how to interpret this value? The rule of thumb for the PSI is displayed below

PSI的最終值，即0.13，是最后一列的所有值的總和。 現(xiàn)在的問(wèn)題是如何解釋這個(gè)值？ PSI的經(jīng)驗(yàn)法則如下所示

The value of 0.13 falls in the second bucket which indicates a minor shift in population from the validation or benchmark sample. These are handy rules to have. However, one must ask, how is this population shift going to make any difference in the scorecard? Actually, it may or may not make any difference. Each score band of a scorecard has an associated bad rate or probability of customers not paying off their loans.? For instance, score band 251-290 in our scorecard has a bad rate of 10% or one customer out of the population of 10 in this score band won’t service his/her loan. The population stability index simply indicates changes in the population of loan applicants. However, this may or may not result in deterioration in performance of the scorecard to predict risk. Nevertheless, the PSI indicates changes in the environment which need to be further investigated through analyzing the change in macroeconomic conditions and overall lending policies of the bank.

值為0.13屬于第二個(gè)桶，表示人口與驗(yàn)證或基準(zhǔn)樣本的微小變化。這些都是方便的規(guī)則。但是，必須要問(wèn)的是，這個(gè)人口如何轉(zhuǎn)變會(huì)對(duì)記分卡產(chǎn)生任何影響？實(shí)際上，它可能有也可能沒(méi)有任何區(qū)別。記分卡的每個(gè)分?jǐn)?shù)帶都有相關(guān)的不良率或客戶(hù)未償還貸款的概率。例如，我們的記分卡中的分?jǐn)?shù)帶251-290具有10％的不良率，或者該分?jǐn)?shù)帶中的10個(gè)人口中的一個(gè)客戶(hù)將不會(huì)為他/她的貸款提供服務(wù)。人口穩(wěn)定指數(shù)僅表明貸款申請(qǐng)人口的變化。然而，這可能會(huì)或可能不會(huì)導(dǎo)致記分卡的性能惡化以預(yù)測(cè)風(fēng)險(xiǎn)。然而，PSI表明環(huán)境的變化需要通過(guò)分析銀行宏觀(guān)經(jīng)濟(jì)狀況和整體貸款政策的變化進(jìn)一步調(diào)查。

Sign-off Note

The population stability index is one of the metrics to keep a check on changing conditions – however, the idea is clear that one has to capture robust metrics to keep a close look on the ever changing economic winds to prevent a crash landing. On the other side, Russian winters did change the history of the planet for better – I guess change is not always for bad.

This was a bit of a detour from our previous article on books to learn probability and Bayesian statistics. Hopefully, you have got a chance to check out some of the books mentioned in the earlier article, see you soon with the second part of that article.

簽收說(shuō)明
人口穩(wěn)定性指數(shù)是檢查不斷變化的條件的指標(biāo)之一 - 但是，很明顯，人們必須捕捉到強(qiáng)大的指標(biāo)，以便密切關(guān)注不斷變化的經(jīng)濟(jì)風(fēng)，以防止崩潰著陸。另一方面，俄羅斯的冬天確實(shí)改變了地球的歷史 - 我想改變并不總是壞事。

這與我們之前關(guān)于學(xué)習(xí)概率和貝葉斯統(tǒng)計(jì)的書(shū)籍的文章有點(diǎn)迂回。希望您有機(jī)會(huì)查看前一篇文章中提到的一些書(shū)籍，很快就會(huì)看到該文章的第二部分。

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