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[金融] [转载]由Columbia B-School Summer Research Program说起

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cynthiawyx 发表于 2014-5-1 02:31:26 | 显示全部楼层 |阅读模式

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这是一篇今天在人人和新浪博客上被分享很多次的文章。虽然没有经作者许可就转过来(作者同学如果觉得不合适的话麻烦一定要告诉我啊,我会把帖子删掉),虽然不是所有的观点都赞同,但是觉得还是有很多信息很有收获,在此谢过原作者,也分享给大家,希望大家都有所收获。标题是我肆意加的,没有沿用原来日志的标题纯粹是因为这样,我以为,比较合适的描述了文章的一部分内容,希望大家都不会错过这个好帖子。原文地址是 http://blog.renren.com/GetEntry.do?id=926567572&owner=246956121NY Jotting -- Apr 29, 2014作者: 聂逸华 Mr.囧
(前言:Columbia Business School 2014暑期研究项目的录取工作于上个月已经全部结束。由于自己目前已确定不会继续留任至来年春季,并且来年录取过程的全部题库都将更新,因此才方便将这篇文章写出。
对于一个米国典型的“毕业即失业”的master学生而言,有幸能够在BSchool工作一段时间并且参与到与商科领域相关,academic-oriented项目的整个审核录取过程的确是人生不可多得的一段经历。由于本文更多是以流水账的形式记录并且没有过多的辞藻修饰(估计各位能看到大量typo),而且整个过程还明显带有笔者一定的主观色彩,因此这篇文章仅仅当作一次比较长的日记而已,笔者对里面的内容的参考价值不作任何保证。)
(注:文末已经附上这次面试题库中的一些有趣的样题~)

I. CV Screening (Passing Rate: 150/1000+)
今年CBS Summer Research Program 共计收到超过1000份简历(最终录取19人,录取率不到2%),其中中国pool申请者(不包括ABC)为400个左右 —— 事实上由于这里面夹杂了将近150份印度申请者几乎完全不对口的申请材料(。。。)因此真实的中国申请者比例达到了将近50%,其中超过70%集中在了Finance和Economics的两个主要方向。(BTW记得收到简历刚开始的那段时间同事们每天的一项业余活动就是在吃午饭的时候相互分享一些“优秀”的中国pool的申请PS,比如说从自己小就对这里某个教授仰慕已久啊(然后名字还拼错了),想从欧洲申请这边的暑期实习方便来看女朋友啊,农村呆多了想体验大城市氛围啊之类的。。。)

冷静下来后,接下来就是捋起袖子开始准备刷人。整个过程中我们又将中国申请者分为以下几个sub-group:
(1). 海外留学的中国本科生(当然主要是美本),占中国申请人数的近50%。说实话整个录取过程中最令笔者感到震惊的就是美本整体恐怖的实力:GPA 3.85+ 一捞一大片倒不是什么最为稀奇的事情(米国泛滥的Grading制度简直令人发指),关键是大约近六七成的简历都是“数经双专”(数学OR统计+经济OR商科双专业),一些冒尖的简历更是出现了接近完美的Triple Major背景组合(“数经双专” 再加上计算机OR运筹学作为第三专业),再加上一些适当的实习或者科研经历以及Top School(众所周知的8+3或者米国文理学院的Top5)。。。;

(2). 中国本科背景,海外master项目学生(或者本科联合项目,比如说交大密歇根的2+2之类),同样占中国申请人数的近50%。GPA在这个pool里更是成为了一个joke —— 我们的director开玩笑说对中国master学生只要整数位不是4就可以刷下来(当然事实上没这么做,GPA没有成为刷人的关键因素,后面会提及到);

(3). 其余一些例外,比如今年遇到三四个左右的其余学校在读PHD学生(Uchicago,Upenn,MIT,Purdue),国内本科直接申请的学生也有个别几个,这些材料就逐个进行case-by-case checking。
. 鐗涗汉浜戦泦,涓浜╀笁鍒嗗湴
第一道关是卡硬性条件,主要是GPA,以及是否具备了一定的课程要求(该环节卡掉50%的申请者)。
对于拥有中国本科背景的申请人,首先先给本科学校标上一个Ranking区间,然后结合本科+海外硕士成绩进行综合考虑(一般来说需要“海外成绩基本全A” + “本科国内Top学校 OR 非Top学校Top班级排名”)才能过第一道关。当然不同学校的GPA标准线也是不同的,比如说对海外给分较严的Uchicago要求就会下降一些;
对于海本,由于美国统一的Letter Grade制度加上课程数量比较多(相比master学生申请截止前海外成绩单上只有只有4~5门课而言),筛选起来就非常的简单:成绩单上圈出对口课程然后扫一下这些课的大致成绩,同样也是基本全A即过关。
第二道关是详细查看剩余申请者CV中的过往经历(该环节卡掉了剩余申请者中的70%~80%)。每份材料将会被三个人快速浏览,一般要两个人给出“Yes”或者至少一个“Yes”加上剩余两个“Maybe”方可通过。在这一环节里,申请人以往经历的“含金量”以及“对口性”是能否过关的重要因素 —— 这个时候许多中国大陆背景申请者的劣势就开始显现出来:一方面,国内的实习经历的描述大多都过于地宽泛,缺少一些能够令人信服的 “硬技能(Hard-skill)” 以及具有一定价值的工作内容;另一方面,若是比较课题背景的话,基本上具有价值的研究课题大部分都是在国外上学期间完成的,因此在这一环节上就被在美国浸染时间更长的美本给硬生生地比了下去(很多美本这次申请都附上了课题教授的推荐信,真切地让笔者意识到了一个教授要想把一个学生往死里夸会是什么样子。。。)。
最后筛选出来进入面试名单的中国pool申请者都具有纸面上非常强的实力,这里给出部分的sample:
(1). 国内 Top 2 本科,Ivy master 项目 GPA 4.2+的Engineering背景申请人;另一个是国内学校一般(Top30,Class Rank 2/200+),但Ivy CS master期间课程全A+(也就是4.33),并有一个国外CS教授指导下的biology network课题;
(2). Yale 大三本科,Triple Major (Economic Major + CS Minor + Math Minor) , GPA 3.97,两个National Research Labortary 经历 + 1个Mortgage market modelling有关Intern;
(3). 国内Top10本科 + Top5 Master + 3年工作经验 + Ivy mfe(GPA4.0);
(4). 复旦经院Rank 1st +转学到法国Econ major Rank 1st,并且明确指定了要跟的暑期研究导师(这是欧洲的pool因此不甚了解);
(5). 美本+Top 20 Bschool Master+5门 Econ &STAT PHD课程背景,GPA3.95;
(6). stanford本科+Uchicago STAT PHD二年级学生,还有一个是Upenn MATH PHD二年级,不过似乎是ABC。
当然不是说光中国人很强,美国人里面也有非常BT的例子。这里列出两个我了解到的:
(1). Stanford 大二本科,预计三年毕业,高中Stuyvesant High School(不知道的可以自己去查一下),数经双专+掌握Python,MATLAB,STATA,Java,GPA 4.00,到大二结束已经学完一些grad level课程(Real Analysis, Time Series, Game Theory, Advanced Micro, Advanced Econometrics),已经和Columbia Business School的教授有working paper并且在Stanford有一个Gender Research的课题,同时在课余活动中担任Stanford Economics Association 的 Vice President以及Stanford Undergraduate Research Journal的主编(这个BT的背景是我们所有人公认的Rock Star级别,因此就提前面试并且入取了。。。)
(2). Columbia 大三本科,Financial Engingeering Major + CS Minor + Economics Minor, GPA 4.04(一门通识课拿了B拉下来了成绩,去掉这门课就是4.14),掌握C++,Java,STATA,Python,R,NET,MATLAB,Perl,研究兴趣是 algorithm trading strategy,有一个Goldman Sachs的实习,加上四个课题分别是:
backtesting trading strategies (store tick data and convert into indicators for trading signal);
Algorithm trading of futures, 通过QuoteTracker数据建立交易信号并且通过 Interactive Brokers Trader Workstation的API上传并进行交易;
对一个匿名交易网络执行优化算法,以用于猜测市场参与者的交易倾向极其投资组合的相关信息;
以及一个Columbia Business School 有关international stock diversification的课题(还拿了这里教授的推荐信进行申请。。。)

II. Interview (Passing Rate:40/150)
简历关pass过的剩余申请者进入面试环节,由包括笔者在内的六个同事根据各自不同擅长的领域分配被面试的申请者以及编写共享的面试题库(笔者和另一个同事负责申请人较多的finance concentration,其中笔者主要集中负责部分的中国申请者)。
在准备面试材料的时候,我们关注的一个共同问题是:对于一个 academic oriented 研究项目而言,申请者的什么因素是我们最为看重的?不同的面试官给出的面试风格因此有着很大的区别(比如说我们有一个同事专门挑了一些CV中擅长R语言的申请者然后整个面试的一个小时全都是在问R语言编程以及计量经济学的内容。。。),笔者负责的这片申请者的面试内容大致是如下的风格:
(1). 覆盖面较大,问的内容比较tricky但是知识背景要求不深,面试过程节奏偏快。整个大致一小时的时间将会问15~20道左右大题(根据申请者的表现调整面试难度,基本控制在回答正确率在30%~40%左右,包含部分得分),覆盖数学/统计+经济+金融(若申请者是finance concentration的话),编程(基本是每一种常用的programming tool都准备了对应的1~2道题目)+Research-based questions,以及其余一些personal questions,例如对申请者的CV提出一些质疑性问题,未来规划,等等;
(2). 面试过程中允许(甚至是鼓励)被面试者遇到卡住的题目时提出一些疑问,从而得到一些Hints。 Communication skills是研究过程中极其重要的软实力部分 —— 个人的观念是,没有人能够什么题目都能答得上来,但是TA的思考过程是否在正确的轨迹上,以及是否能够将自己的疑问转化为有价值的问题并且用流畅的英文语言进行交谈,将会很大程度上决定一个人在现实环境中能够高效完成研究任务;此外编程题目难度要求很低(在细节上卡住的话甚至可以当场在网上查),但若对问题完全没有思路的话则将会对该申请人CV上的相关经验产生严重质疑(诸如MATLAB系统的Debug Mode的了解,Python基本工具包的了解,等等)
(3). Personality —— 整个面试过程全部要求skype视频(或者直接on-site),以便于观察被面试者面试时(尤其是面对难题时)的整体反应。有部分CV纸面很强申请者在遇到难题时容易气馁甚至对后面的题目失去信心,但是大部分面试过关的申请者在整个过程中都是保持非常冷静并且积极思考的态度;
(4). Research-Based Question是整个面试最有趣的地方——有几道大题是我们直接从自己平时做project的经历中转化过来的题目,这种问题通常需要申请者去自己理解问题所处的环境究竟需要什么样的答案,以及如何通过开放的思维一步步在提示下给出正确的解决方法(部分的题目我附在了文末,有兴趣的话可以看一下)。

整个面试过程中笔者发现了一些非常有意思的现象:
Case No.1:许多美本有着看似非常fancy的CV背景,但在面试过程中有不少暴露出严重的基本功不扎实,以及CV水分太多。面试中有一个Columbia GPA ~3.9 Engineering + Econ Double Major的美本,在CV中列出自己分别和商学院两名教授做过课题(一个用到natrual language processing,另一个用到了web-scraping和SAS软件),后来去办公室问这两个教授得到的答案是根本不知道这个学生是谁(后来了解到该申请人是和这两名教授手下的PHD干活,且反馈都很一般)。针对该申请人背景,面试中笔者便准备了一些有关自然语言处理以及统计软件的基本问题,对方基本就是totally lost —— 面试完后我就问TA为什么这些CV上列出来的东西TA竟然完全都不了解,得到的答案是该申请人直接把申请RA时教授在网上写的“课题介绍”直接复制粘贴到了CV里面。。。
Case No.2:对于中国本科背景,海外硕士背景的申请人,在海外GPA严重泛滥的大环境下,本科期间在国内的表现的确能够反映出该申请人的真实水平 —— 而且通常情况下国内学校Ranking30~50的top 2%的学生在硬实力上的确要优于国内清华北大average水平的学生,甚至可能还不止如此。这次笔者面试的pool中有~4个国内排名30开外的本科,在美国硕士期间GPA都>= 4.0的申请者,但在面试时的表现完全大相径庭(有一名学生甚至面到最后直接跳起来质疑这些题目换做身边其余的同学没人能够回答的上来……),后来看了一下表现较好的两个,在国内的本科专业排名一个是2/~200,一个是1/~140,当时我就在想“如果这样的学生当时就是在美国读本科,将会毫无疑问的击败大部分其余的美本”,其中有一个同学在面试完以后我问他为什么master面对课程压力的同时还找教授做两个这么深的课题,他给出的回答是自己想申PHD,但是知道自己本科院校背景不是很硬,因此需要在美国表现的格外出色才有扳回来的可能 —— 这个申请者就是我前文提到的 GPA 4.33全A+的学生,和那些美本一对比下来简直是。。。
Case No.3:在申请finance或者economics方向的研究的这一块名单里,明显出现了以(1). Mathematical OR Computational Finance背景 以及 (2) Financial Economics背景的两派(我这里避免了用Quant Finance这种定义比较模糊的词),而且一般来说前者数学/统计题+script language回答的较好,后者经济学题目&统计软件回答的较好(当然也有人两方面都不好的。。。)。但是当问到最关键的Research-Based Question时,令笔者比较惊讶的是Financial Economics的背景的学生明显更容易能够找到问题的思路(虽然数学上不一定解的出来),但是Mathematical OR Computational Finance的学生很容易totally at lost,直到笔者给出一个明显的提示时才会恍然大悟“原来是这个样子”。。。个人的看法是对于比较传统的finance方向(也就是对立于一些现在新兴的financial engineering或者mathematical finance),研究的真正难点不在于给你一个已经定义好问题让你去搭一个model去解决,而是如何如找到一个研究课题背后真正的关键问题在哪里,在此基础上如何将自己的建模思想始终紧跟着你想要去证明的思路,使得你的模型最后从经济学角度上有意义(economically make sense)。
笔者自己原先本科也是science背景(本科physics),在来米国前一直觉得数学是做finance的王道,但是经历了三年的种种思考,个人后来逐渐觉得Mathematical OR Computational Finance可能在industry就业上比较有一定优势(毕竟实用至上),但是对于对modelling idea背后的深入理解,最最重要的反而是很多人认为比较容易的经济学知识一块儿 —— 而且这一块儿挖深了的话难度绝对远远超过于“解一个数学题”那么简单(经济学是所有专业里本科到研究生难度跨度最大的专业之一)。当然这些完全是个人的见解,有不同意见的话可以把我的观点当笑话看。
Case No.4:最后顺便提一下,整个面试过程中真正stand out出来的是Uchicago Ugrad + Master的一个韩国学生(并且有在Microsoft全职工作和Canyon Partners暑期实习的经验),面试时基本找不出某一块有明显的弱点,尤其是Econ的问题不经过提醒能够给出基本完全正确的答案(我在想那么多在美国数经双专的筒子们为什么就做不到。。。),整体正确率也超过了70%(远远超过其余人的30%~40%)。面试最后闲聊时我问为什么他不想在微软继续待下去(以及未来打算),他给我的回答是那种life style不是他想要的,而且自己想做一些关于financial research的东西(虽然对于是走PHD还是走industry没有明确的答案)。整个面试过程没有太多fancy的回答,但是背景无论是sense还是hard-skill上都相当的出色,理所应当的进入了最后的final pool。

III. Final pool decision (Passing Rate: 19/40)
最后进入final pool的有近40个学生,但是今年最终下来的课题只有19个,谁能够拿到offer由笔者上级的Research Director以及教授决定。
两周以后入取名单基本确定下来,结果令我们所有人大吃一惊 —— 基本上我们所有同事都发现自己推荐的申请人里最终找到名字的比例根本不到30%(笔者和另一名同时共同负责的finance一块最终加起来只有两名学生入围。。。),后来自己看了一下所有课题的内容时才明白:除了今年发了两个去年参与暑期研究项目学生return offer以外,今年剩余的17个课题里behavioral experiment的课题竟然多达7个(去年好像只有1个) —— 我们有一个负责behavioral方向的同事推荐的5~6名申请人最后基本全部录取,甚至由于数量不够最终由director额外亲自面试了一些学生。。。然后其余的economics,operation management, marketing, accounting大致都有1~3个,而正常情况下占主体的finance方向(一般课题数占到40%左右)今年的课题数只有。。。2个。。。
在最终确认名单的时候,我们有一个同事问了director这样一个问题:“为什么不采取merit-based的方法,挑选一些其余方向的top students并给他们behavioral的课题?要知道他们不一定做的会比那些所谓的"behavioral"申请人来的厉害。”(笔者个人也觉得Undergrad projects大多其实是somehow Bullshit。。。)
director得到的答案是:这其实不是他决定的,主要是教授们就是想要背景对口的学生,而且我们实在无法确认那些看似优秀的其余方向的学生在换到了behavioral也能做得很好,so that's it。。。
到头来,今年一共有1000名申请人(共录取19名,录取率不到2%),在申请时选择finance concentration方向的申请人粗略估计是40%左右,最终该方向只录取了2名学生 —— 也就是finance方向的录取率即使乐观了算也只有0.5%。。。
经历了这一段录取过程,笔者终于明白了申请学校时收到的拒信里的有一些诸如此类的话并不是空穴来风:
“We've received qualified applicants far more than we can accommodate, so our final decision combines both applicant's merit as well as our faculty's research interest.”

IV. Summary:
1. 米国Bschool 的Academic-oriented Program(主要指PHD,学术类Master,以及Summer Research —— MBA和其余Industrial-oriented本科/硕士项目不算)近几年来申请难度呈现出Highly-rocketing的趋势。从表象上来看,一般来说Ranking比较靠前(比如说Top30)的Bschool这些项目的录取率一般是2%上下,其中有将近一半申请人是属于Chinese Pool(包括海本),但是一般来说录取的学生中美国,欧洲,亚洲学生的人数比例约为2:2:1(不同学校会有一定的差别),其中亚洲名额中中国人比例撑死算上75%,将这一切折合下来后中国学生的申请成功率大约是在千分之六左右,在传统比较热门的Finance, Quantitative Marketing方向的比例可能会更低。
此外,还得考虑到Bschool申请中特殊的三类人群:近年来数量迅速增加的 Double/Triple Major 的美本(Business Major 相比 Science & Engineering Major 而言需求上更倾向于多重专业背景),有industrial 1~N年工作经验的学生,以及极个别的PHD学生(尤其是申请Finance方向的时候,其余专业的PHD转专业跳槽的现象时有发生),这就是为什么在国内我们经常能够看到理工科出国的案例远大于Business方向的客观原因。
. 鐗涗汉浜戦泦,涓浜╀笁鍒嗗湴
2. High randomness。对于finance(甚至包括economics)的研究领域,一个比较公认的现象是:只要成绩达到了一定的level,课堂成绩的高低和学生未来的研究实力之间其实是没有直接的关联性的。基于这个思路,在这类方向的学术类项目申请中,“较高的成绩+具备对口的课程”只是为了过第一道筛选关(当然你如果硬实力极度BT的话——比如国际奥赛数学金牌之类——则另当别论),剩余的筛选过程将会注重于观察申请者的以往经历(实习,课题,研究)以及这些经历中体现出来的实际研究能力(这时候推荐信就成为了重要因素)。但即使如此,一方面笔者可以说各方面符合条件的申请人与入取slot之间的比例依旧能够达到10:1甚至有时更多;另一方面这种在CV上自己写的经历以及所谓的推荐信都是很可能会有很强的bias的(更何况还有很多实力非常强的人因为不会申请时sell自己导致背景“看上去”不够亮眼)。因此在这种情况下,很多时候实在是无法确定到底谁有着更强的学术潜力,这种时候一些“额外因素”,例如personal connection,so-called research matchness等等就会起到决定的作用,但这能够反映出申请人之间的能力差异么?In my option the answer is simply: NO.

3. 转行的困难:前面提到了Computational Finance 和 Mathematical Finance的学生在回答一些问题时很容易出现 Original idea 以及 Economic sense 略显不足的问题,但背后可能更要命的是:这些现象很容易会反过来在申请时给背景比较偏理工科的申请者扣上“偏见”的帽子——如果两个人看似能力差不多,一个比较纯的FINA或者ECON背景,另一个理工科倾向比较明显,最后能有可能的结果就是选择了那么背景更加“正统”的学生——因为后者的不确定性实在太大了。这次申请中笔者也看到了为数不多的物理专业的学生申请Finance Concentration(而且都还有一些经济/金融课程),这样的背景申请Computational Finance/Mathematical Finance方向应该OK,但是若申请Financial Economics方向的话,很有可能连简历关都过不了,因为各方面的积淀(尤其对ECON和FINA领域的了解程度)实在是太少了 —— 更别忘了现在有大批涌现的“数经双专+CS”的申请人,传统理科在数学或者编程上的优势将会进一步被削弱。。。

4. 美本的优势:Double Major(甚至Triple Major)+ GPA >=3.9 + 1~2个summer intern/research + 1~2个对口project + 美国教授较强的推荐信 -- 这是这次笔者见到的纸面上非常亮眼的申请人的标准背景,而且这样的背景在美国实在不是什么稀罕的事儿 —— 相比而言,中国本科背景的学生的申请可以说是全方位处于劣势:
(1). 缺少多重专业的复合背景;
(2). 本科院校以及课程在先天上不大容易被美国完全认可(有些时候课程的英文翻译都让老美看不懂);
(3). 研究和实习的含金量又在客观上不及美国的水平;
(4). 英语综合能力也是一个问号(这对Bschool申请尤其重要)
(5). 再加上种种的客观不利因素(比如说这次CBS暑期研究项目6月初就开始——这时候国内学生都在准备期末考,根本无法去把握这次机会),包括极其重要的推荐信(参见前面的第2点总结)。
那么经过4年在国外的学习,美本的实力真的比中国本科要强么?个人的一个不靠谱的估计是:如果是拿出在中国成绩前20%和在美国前20%的中国美本,在国内专业排名和美国专业排名齐平(比如国内第30和美国第30)的条件下,国内的本科学生在宏观上绝对有超越美本的实力,但是申请过程从来就是一个通过观察“谁看上去更好”去推测“谁真正实力更强”的过程,而且在Finance和Economics这类不纯看硬指标评价学生的领域,表象的bias会给美本带来更大的优势,更何况美本中的确有一些极其拔尖的学生(尤其是在Top School里),在美国环境下又可谓是如虎添翼,然后到了申请时就。。。

5. Everything is only a starting point。今年的录取19个申请人客观上来说背景都很强,但是当笔者看到project list的时候,就已经意识到无论是课题的含金量和深度还是导师的权威性上都有着非常大的差别。回想自己去年参与上一届CBS暑期项目时,当看到一些来自Stanford或者harvard的同学暑期的整体表现因为种种原因甚至可能还不及average level的时候,自己便意识到所谓的“名校情结”或者进入Target Program很大程度上只是给外面人看的东西,而真正能够决定自己长远未来的到头来还是取决于自己综合实力的不断积累。—— 籍此条以自勉,望自己能够避免浮躁,不断进步。

最后,附上这次面试在面试题库里笔者出的部分题目,供各位茶余饭后一乐 (注:min是每道题大致允许回答的时间):

General Questions:
1. (3 min, 1.5 min for interviewees + 1.5 min for raising questions)
Could you tell me one of the research / internship / project experiences that you're most proud of yourself? Please explain the detail of this experience, especially your original contribution in it.

2. (1 min)
Could you briefly say something about your career plan in the next 5 to 10 years?

MATH / STAT Questions:
3. (1 min + 2 min. 4 min at most)
(1). Assume there are two indepentdent, normal random variables A and B. A is with mean 2 and standard deviation 3, B is with mean 3 and standard deviation 4. What is the distribution of C=A-B?
(2). (After 1) Now A & B are still normal random variables once observed separately, BUT now they are correlated with unknown correlation level. Once again consider C=A-B. Is C now still follows normal distribution? What is the range of possible mean value? What is the range of possible variance?

4. (5~6 min)
Assume there is a stock price following STANDARD, no-drift Brownian Motion (NOTE: NOT Geometical Brownian Motion -- the model has been simplified). Assume at time 0, the initial stock price is 0.
(1). What is the probability that stock price will hit +1 first, before it hits -1? (Answer and brief explanations only)
(2). What is the probability that stock price will hit +4 first, before it hits -2? (Need explicit derivation steps)
(3). If the expected time for stock price to hit either +1 OR -2 is "k", what is the expected time for stock price to hit either +2 OR -4? (Answer and brief explanations only)
(4). (Hard) If the expected time for stock price to hit either +1 OR -2 is "k", what is the expected time for stock price to hit either +1 OR -8? (Answer and brief explanations only)

5. (3~4 min)
If I have 9 balls in a bag (3 red balls, 3 blue balls, 3 white balls). We wanna calculate the probability for getting 3 balls with red, blue,  white color each.
(1). What is the probability if each time we take one ball, record the color, and put it back (so there are still 9 balls when we make 2nd pick)?
(2). What is the probability if each time we take one ball, record the color, but NOT put it back (so there are only 8 balls remaining when we take the 2nd one)?
(3). What is the probability if each time we take one ball, record the color, but put back TWO ball with same color as you pick (so now there are 10 balls when we take the 2nd one)?

ECON/FINA Questions:
6. (Finance Concentration) (2.5min)
(1). Please briefly describe the key conceptial difference between "absolute risk aversion" and "relative risk aversion";
(2). Suppose there are two people A and B exactly same absolute risk aversion level. A has $1000 and he spent $200 on S&P 500 and $800 on T-Bill (risk-free); Now if we know B has $300 only, what is the allocation of B between S&P 500 and T-Bill (risk-free)?

7. (3min)
Now consider Manhattan as a isolated economic system. If a helicopter flies to Columbia Business School and drops a huge bag of money (which are picked away by students in Columbia Business School, as we assume naturally), is that event equivalent to simply adding taxes on all other Manhattan citizens? Please briefly explain why.

8. (2min)
(1). (Non-Finance Concentration) Please give 1 positive and 1 negative effect of economic globalization. For each effect, please give one specific example happened in our history (Those two examples must be on different events).
(2). (Finance Concentration) Considering the financial crisis event happened around 2008 as an example, could you give 1 positive and 1 negative effect of economic globalization (and each one with a specific example related with financial crisis)?

9. (1.5min)
Could you give one specific example about adverse selection (HINT: This concept is from Game Theory)

Programming Questions:
10. R (2 mins):
(1). I want to delete all the rows that have missing values (NA) in "age". How would you do this?
(2). These are questions about accessing the R documention from within R. How do you look up the "hist" function within R?. How do you do a fuzzy search for "median" (which means you are looking for a function with its name somehow like "median" but not exactly the same) from within R?

11. Python:
(1) (2min). Please mention 3 uncommon python modules/packages that you have used before, and explain under what circumstances did you use them (NOTE: "uncommon" means these packages are not originally included in python but need to be downloaded online)
(2) (2min). Now I have a string = "Welcome\to\Columbia" and I wanna write one-line code to change the string into the following: "*Welcome*\*to*\*Columbia*", how should I do that?
(3) (2min). Suppose there is an array containing 3 elements, each of them itself is an array containing 3 numbers. Suppose I want to sort these elements by their 2nd number in decending order (i.e., if originally A=[[4,5,6],[1,2,3],[7,8,9]], The result after processing should be B=[[7,8,9],[4,5,6],[1,2,3]]). How should we do that by using a one-line command?

12. MATLAB:
(1) (1.5min). Given an array "A" which contains 100 numbers, how to quickly find out the difference between the 3rd biggest element with the 3rd smallest element?
(2) (2min~3min) Debug is always important in any programming language. Suppose you have a 1000 line code to run and there comes an error as follows: "Index exceeds matrix dimensions." How can you check your code to figure out the error step by step? (HINT: Do you know anything about Debug Mode in MATLAB?)
(3) (2min~3min) We want to solve the x from following formula: Ax=b, where A is a n by k matrix and b is n by 1 array, the unknown x is k by 1 array. Mathematically, we know that we should multiply the inverse of A with b. However, in MATLAB, how do you input the formula that brings the best precision of the result of x? Explicit formula is needed for this question.
Hint: (If answer is wrong) Choose the answer among the following three: inv(A)*b, A/b, or A\b?.
(If answer is correct) What is the possible problems behind if one person use inv(A)*b and another guy use A\b?

13. STATA:
How do you only select observations where an "age" variable no less than 20? Please realize there might have missing numbers (denoted as ".") in STATA table.
How would you rename a set of variables named var1-var200 to VAR1-VAR200?
There are two columns (with many observations in it) in STATA table: First column is labeled as "GroupID" (1,2,...,10), Second column is labelled as "score". Please write a short code to tabulate the average score performance: Fist column is GroupId again, but second column is the average score of items with same GroupID.

14. Excel:
You wanna create a 9*9 multiplication table. To do this, you type in the first number series 1~9 on first row (from B1 to J1) and the second number series 1~9 on first column (from A2 to A10). How do you quickly fill in this 9*9 table, with each block shows the multiplication of number on the row and number on the column?

Research-Based Questions:
15.  (4~5 min)
Now we have millions of news articles extracted from the section "Abreast of Market" of Wall Street Journal. We want to find how these news information reflects the general market MACROECONOMIC situation. We designed a Python program to read two lists -- One called "Article exclusion list" and the other called "Article Acception List" -- And do following steps:
Step 1: For each news article, If it contains ANY unigram/bigrams in "Article exclusion list", it will be regarded only focused on specific company event but NOT on general market event, so it will be deleted from our database;
Step 2: For all articles passing step 1, we ONLY save those articles contains ANY unigram/bigrams in "Article Acception List", since we regard them indeed relecting the general market event.
Based on the research procedure above, please list 5 unigram (words) OR bigrams (two-word phrases) that should be possibly included in "Article exclusion list" or "Article Acception List" (5 words for each list). Please realize that:
(1). NO words can be used repeatedly (e.g., if you use "apple tree", you can not further use "apple pie", "apple tart" or "banana tree", "orange tree"...)
(2). NO words within similar category can be used more than once as well (e.g., If you use "apple", you cannot further use "banana", "orange", etc.)
(3). The quality of word (depending on whether it fits the purpose of our task) determines the final credit for this question.
.鏈枃鍘熷垱鑷1point3acres璁哄潧
16. (Non-ECON major only)  (4~5min)
Suppose you wanna open a bakery beside Columbia University and you are working on estimating the consumption level of bread in this area. You have collected adequate amount of data from the neighborhood and now designing to do linear regression on personal bread consumption (Y) with other three variables(X_1, X_2, X_3):
Y:     Each individual's yearly spending on bread ($)
X_1: Each individual's annual income level ($)
X_2: Each individual's distance to our bakery shop (miles)
X_3: Each individual's annual spending on shopping on amazon ($)
The linear regression model is supposed to be Y=a*X_1+b*X_2+c*X_3+d, with a,b,c,d as coefficients.
Assume the data is with high quality and we only focus on these four variables (i.e., do not consider other possible external variables). Please point out THREE crucial mistakes of this modelling process, and explain why.

17. (Finance concentration only) (8~10min):
Suppose I wanna use simulation method to evaluate the price of a derivative, which is the combination of one European call option (with strike price K_1 = $10) and one European put option (with strike price K_2 = $8).
For all following question, assume there is no discount rate, and investor is risk neutral.
(1). (Easy) Conceptually, What is the difference between European option and American option?
(2). (Easy) Given the final stock value at time of maturity as S, write the payoff function in terms of K_1, K_2 and S.
Now we wanna use simulation method to evaluate the price of this derivative. Assume the remaining time to maturity is 5 years, initial stock price is 6, following a simple Brownian motion (Notice: NOT geometric Brownian motion) with drift $1 per year and volatility 0.4 per year.
(3). (Medium) Please design this simulation method to evaluate the price of this derivative. (Hint: How to establish the relationsihp between simulation result and the derivative's final price?)
(4). (Hard) Now Assume everything as same of question (3), except now at the end of year of 3, the investor has an additional chance to choose whether he sell his derivative with fixed price 8.5 (thus he/she quits the market) or keep holding his derivative and wait till the maturity date. Under this new addition condition, please use simulation method to evaluate the price of derivative. (Hint: What is the main diffucult point of this price evaluation? How we try to nail it?)
.鏈枃鍘熷垱鑷1point3acres璁哄潧
18. (Non-finance concentration only) (8~10min):
(For this question, assume you always have a laptop in your hand, with any statistical software as you want.)
Suppose now I give you a weird coin: At the first flip, it will heads up/tails up with 50%-50% chance. But from now on, once it heads up on the previous flip, it will keep heads up with probability 3/5 on the next flip; Once it tails up on the previous flip, it will keep tails up with probability 4/5 on the next flip.
Now you want to figure out the 95% confidence level of the number of times the coin heads up if we flip it for 1000 times -- Here we just simply assume the # of times the coin heads up is symmetically distributed (but actually it's not, of course)
(1). (Easy) Basically, what is the definition of 95% confidence level?
(2). (Medium) Based on the assumption above, How to use simulation method to find the 95% confidence level of this problem? If you wanna use "if" function, please define the corresponding variable.
Now I take this coin back and give you another coin -- You know nothing about how weird this coin's flipping pattern is. But I want you try to use statistical method to guess the flipping pattern of this coin.
(3). (Medium) Before doing that, could you tell me what would you do to confirm this is NOT a simple fair coin ("fair coins" means every time it heads up/tails up with 50%-50% chance independently)?
(4). (Hard) Now embrace yourself with this question! Please tell me what's your methodology to figure out the filpping pattern of this coin step by step.
(HINT: Many students will first spend 1~2 minutes and figure out making statistics to get mean and standard deviation of flips, which is a good start; After that I will ask them:"Now you suspect that your interviewer just made a trick on you -- Actually this is exactly the SAME coin I gave to you for question (1) and (2)! Now going back to look that that weird coin -- Do you get any idea about what aspect you think necessary to figure out, in order to get the full picture of this coin's flipping pattern? After that, could you now disregard this specific coin and extend your methodology to a more general aspect?)





来源:聂逸华 Mr.囧. visit 1point3acres.com for more.
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.鏈枃鍘熷垱鑷1point3acres璁哄潧
源地址: http://blog.renren.com/GetEntry.do?id=926567572&owner=246956121




shangyt 发表于 2014-5-1 23:11:22 来自手机 | 显示全部楼层
写得很好。非常受用!
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quantjason 发表于 2014-5-3 13:12:16 | 显示全部楼层
此贴在人人初读就觉得很赞
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Clairelin 发表于 2014-5-3 13:23:37 | 显示全部楼层
没懂这里要录的是Bschool的PHD还是什么啊?
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kathrine2008 发表于 2014-5-3 16:11:34 | 显示全部楼层
大赞好文章!!!!!!!
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janezkk 发表于 2014-6-27 15:43:08 | 显示全部楼层
挺好,thx for sharing
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超人往往外 发表于 2016-1-13 15:04:29 | 显示全部楼层
曾经面过。。。这个summer program...特别高冷。。。
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