Principal Component Analysis (PCA) is a powerful data analytics tool used in many areas of machine learning. However, despite its versatility and effectiveness, its application in finance is not as widely discussed.
Today, I will talk about how PCA can be used in the stock market, how it relates to the Capital Asset Pricing Model (CAPM), and how we can use PCA to analyse the impact of COVID19.
(You can find the full code and additional resources here)
The first principal component explains most of the variance in the data.
In a nutshell, Principal Component Analysis (PCA) decomposes the data into many vectors called principal components that essentially “summarise” the given data. More specifically, these summaries are linear combinations of the input features that try to explain as much variance in the data as possible. By convention, these principal components are ordered by the amount of variance they can explain, with the first principal component explaining most of the data.
The returns of a stock can be decomposed into: (1) the returns of the risk-free asset, (2) the returns of the market factor, and (3) the idiosyncratic returns of the stock. Overall, the market factor is the primary driver of all stock returns.
The Capital Asset Pricing Model (CAPM) is a famous framework for pricing the returns of an asset such as a stock, with many interesting connections to the modern portfolio theory, which I will discuss in a future post.
Before diving into the details of the CAPM, it is important to understand the notion of risk-free assets and the market factor. A risk-free asset is essentially an asset than can give you returns at virtually no risk (e.g. a government bond). The market factor instead monitors the state of the overall stock market as a whole and is often measured through an index such as the S&P500. Generally speaking, the overall market is more volatile/risky than government bonds, but it also provides more returns to the investors.
With those definitions in mind, let’s look at the concept of the Security Market Line (SML) from CAPM. In practice, SML decomposes the returns of a stock **_r_i _**into three main factors:
Security Market Line Equation — Image by author
The intuition behind this equation is that:
(1) the return of a stock should be at least equal to the return of the risk-free asset (otherwise why take the extra risk in the first place?)
(2) the return of the asset is also explained by the market factor, which is captured by the term **(r_m-r_f) **(measures the excess return of the market with respect to the risk-free asset) and _beta_i _(measures the degree to which the asset is affected by the market factor).
(3) the return of a stock is also affected by idiosyncratic factors, which are stock specific factors (e.g. the earnings release of a stock affects that individual stock only, but not the overall market).
Empirically speaking, the market factor is the primary driver of the stock market returns, as it tends to explain most of the returns of any given stock in any given day.
When applying PCA to daily stock returns, the first principal component approximates the market factor.
Let’s consider the 500 stocks in the S&P500 index, and compute their daily returns, as shown in the figures below.
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Is the stock market crashing in 2021? In this video, we are going over why and when the stock market will crash, what you can do to prepare for it and profit, and what stocks I’m buying right now that are great long term holds.
Make sure to watch until the end, as I will go over what’s happening with the markets right now, what’s causing it, and my sentiment about why a crash will occur.
📺 The video in this post was made by Charlie Chang
The origin of the article: https://www.youtube.com/watch?v=vOIxDL5XCjY
🔺 DISCLAIMER: The article is for information sharing. The content of this video is solely the opinions of the speaker who is not a licensed financial advisor or registered investment advisor. Not investment advice or legal advice.
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“What is the day-to-day really, truly like in marketing analytics?”. I’m over halfway through my summer internship as a marketing automation and analytics intern at a company in the Dallas-Fort Worth area. I’ve had a lot of my fellow peers ask me what it’s really like because many of them had their internships cancelled or moved to an online format.
The skills I’ve acquired during this internship have been amazing! I did a lot of research beforehand however, and honestly didn’t find that much information on what it’s like to really be in marketing analytics during the day-to-day operations. I’ve enjoyed talking about my experience with my peers, however, I wanted to put my experience on a platform where more people who are curious about what it is like can see for themselves, and show what it is like from the very beginning to the very end of my day. So, let’s get ready to wake up!
Disclaimer: I am not a full time marketing analytics professional, I am simply relaying my observations of what I did and saw. This is not meant to teach you all the skills and tools used in marketing analytics, as I am still learning. For this information, please check out Towards Data Science. If you are interested in what it’s like to be in a marketing analytics intern or entry-level role, keep reading!
I typically will wake up around 6:15 AM every morning before the workday. This gives me about an hour to read Medium articles from other amazing writers, and gives me some things to learn in small, manageable chunks! Other than the basic morning routine that we all do, I also make a cup of coffee, because this is a role that requires you to think critically most of the day, and I promise you will get tired at some point! After some coffee, I get changed, pack my bag, and head to work!
I walk through the doors, find my way to my desk, and get ready for the work day! Here are a couple things that I do at the very beginning of the day:
In the midst of COVID-19, email and video calls are now the primary method of communication, even while in the office. We are required to wear masks and social distance, but we also try our best to stick to email and video calls if at all possible. During the summer, interns are given two major projects for the whole summer, one in teams where you present a solution to a problem that the executive team gives you, and one where you do a project on your own and present it to your department, which in my case is marketing. I also always try to spend some time with the marketing analyst, and watch him work through a problem and how he approaches it.
After I’m finished getting ready for the day, I will typically spend some time practicing my Python and analytical skills by applying them to a dataset that the marketing analyst gives me. This is not meant for a client or stakeholder, but is rather a way to solidify what I’ve learned from the marketing analyst that morning. I might whip up a linear regression model using sklearn, try to make my data cleaning more efficient with Pandas, or create quick visualizations with matplotlib. What I’ve noticed is that it doesn’t really matter how you get the job done. It is perfectly acceptable to have Stack Overflow opened on my left screen and a Jupyter Notebook on my right. I have found that analysts are always working on so many different projects, that knowing how to be efficient in your code is the skill to refine as you move through your internship or entry-level position.
Normally around the middle of the morning, all of the interns will meet via a Zoom call, or a very large conference room that allows for social distancing, and will listen to different speakers from within the company. These speakers are typically Vice Presidents or Senior Vice Presidents, and will talk about their experiences, offer their advice, and allow time for questions. For an entry-level position, the next part of the day would normally start around this time!
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We take goals very seriously at Instagram. Goals are important anchors and focus points. They ensure everyone is aligned and set expectations on what a particular marketing program is trying to achieve.
As a Marketing Analytics leader, it is my responsibility to set goals for marketing programs.
However, setting a goal isn’t always easy. Time constraints, complex organizational structures, differing opinions and unclear strategies are some of the many factors that can obscure the goal setting process.
To counter-act these and limit bias, I lean on a set of principles to set goals for each marketing program.
Here are the seven principles I use to allocate goals for Instagram Marketing:
There should be a natural thread from business problem, to action, to strategy and then to the goal. Let’s take a hypothetical example.
The business problem is this — we launched Story Stickers to increase overall content production but users are avoiding the Stickers because they think they are too hard to use.
Action — we want users to try using the stickers and lift overall content production.
Strategy — Use a tutorial based ad to show “non sticker users” an easy way to use a sticker in their Instagram story.
So we’d set our goal around lifting new content production among this selected audience of “non sticker users”.
The idea here is simple. We want a marketing program to drive both action (as measured by our product goal) and positive sentiment (as measured by our sentiment metric).
If a marketing program delivers on immediate action but not sentiment, then it is not helping us in the long term. If a marketing program lifts sentiment but not action, then it’s not helping us drive immediate business value.
A good measurement program measures many metrics. But there should only be two goals. All other metrics should form part of a learning agenda.
Linked with Principle 2 — Among the two goals, there should be a primary and secondary goal.
Success should be judged against the primary goal first and whether that was achieved. If yes, we move to the second goal. The role of this primary and secondary goal hierarchy is to help prioritize the many go-to-market components.
We set top-line goals. What we mean here is that, ultimately, everything we do should move the overall business forward. That might mean adding more users, increasing overall engagement or something.
We need to avoid goals that are too granular. Granular goals don’t tell us if we are moving the business forward, overall.
Returning to our Sticker example from Principle 1. We could set the goal on lifting sticker usage, but that wouldn’t tell us if we’re contributing to the overall business. That’s because the sticker product is ultimately about lifting overall content production, not just sticker usage. A lift in sticker usage may just mean our marketing is cannibalizing another part of the business and not actually raising overall content production and not helping the overall business.
So we set the goal around the overall content production increase.
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