Alpha Found Playlist (32 videos)
https://www.youtube.com/playlist?list=PLVJCHz7wypA8uMFrlGhmbuGl3aBBfAOcC
0. Series Overview
This prequel video motivates a new model of stock market dynamics with this statement: “The new model predicts, as both a mathematical expectation and economic expectation, that low volatility portfolios will outperform high volatility portfolios on a risk adjusted basis.” In this video only a couple of highlights are mentioned.
The series takes about four hours to watch. There are over 200 mathematical expressions that have to be derived and implemented.
1. Introduction
This video begins the series by describing the excitement around the concept of “alpha,” which has been called the Holy Grail of investing. It is the first of 8 videos that serve as needed background before the development of the new model gets started. Someone with a strong background in capital market theory, including MPT, CAPM, multi-moment models, and multi-factor models, could start with the 9th video. After the 8th video, skipping ahead is not recommended. The new model has to be built carefully from scratch.
2. Preliminaries
Mathematical approaches to investing have been around since Louis Bachelier wrote his Ph.D. thesis in 1900 called, “The Theory of Speculation.” Since then many have used a mathematical approach to investing in the stock market, with varying levels of sophistication and varying levels of success. This video reviews the early history of such attempts without showing the higher math.
3. Harry Markowitz and MPT
Harry Markowitz won the Nobel Prize in Economics in 1990 for his 14-page thesis of 1952. It seems amazing, but all he did was show the importance of diversification. His method, like Bachelier’s, is more challenging than most people want to deal with. Nevertheless, he showed rigorously that the most sensible approach to investing is to minimize risk given the amount of return sought, or put differently, to maximize return for the amount of risk taken on. His work is called Modern Portfolio Theory or MPT.
4. CAPM
Twelve years after Markowitz made his big contribution, William F. Sharpe successfully reduced the mathematical level of MPT to high school algebra (the equation of a line). His contribution is called the Capital Asset Pricing Model, or CAPM. Like Markowitz, he was awarded the Nobel Prize in Economics (also in 1990). But can it be improved?
5. Jensen’s Alpha
All the fascination with alpha began with a 1968 paper where Michael Jensen showed that CAPM could be used to measure investment success. With a small change to the way Sharpe constructed his model, Jensen invented what we call “alpha.” Alpha is understood to be excess return after adjusting for risk. Ever since then, investors have been seeking alpha. However, the theory did not work as expected. The difference between expectation and reality is called the volatility effect.
6. Multi Moment Models
MPT and CAPM use mean and variance (called the first two moments) in their calculations. Some people have argued that including higher moments, such as skew and kurtosis, will explain the discrepancies found in lower moment models. This video discusses the higher moment approach.
7. Multi Factor Models
Using expected mean return and variance to explain risk and return does not capture the realized patterns in stock market data. If other factors are included, such as market capitalization, and book to market ratio, perhaps the return patterns would be better explained. The pros and cons of multi-factor models are examined in this video.
8. Explanations nearby to CAPM
Multi-factor and multi-moment models do not really give us the answers we would like. The only place left to look for an explanation of the anomalies in investment returns is in violations of the assumptions of CAPM. Many of the assumptions underlying CAPM are not valid. If these assumptions are relaxed, can we explain the data? Maybe in part, but not as well as we would like.
9. Setting the Table, Part 1
Statistics such and correlation and Shape ratio have been examined extensively in the investment literature. Yet, it seems some important theorems and observations have been missed. This video takes a new look at these two statistics. Also, some new notation will be introduced. One of the issues highlighted with respect to correlation is examined further in videos 30 and 31. The mathematical sophistication starts to climb.
From this video forward, skipping ahead will prevent you from understanding what the new model tells us.
10. Setting the Table, Part 2
The volatility effect is shown in this video to be much more prevalent than previously thought. By constructing 2-stock indices with 1-stock portfolios, we see that the volatility effect exists at every scale, and that the observations concerning correlation in the previous video are correct. Since the effect is obvious, why is the cause not obvious?
11. The New Model
Finally, we see the new model. Most of the video is spent motivating the model rather discussing it. However, what discussion there is, is fundamental. The model does not seem promising at first, but as we push on it, it gets better and better. It will take several videos before the model’s power will be evident. Several important new definitions and some new notation are introduced.
12. Perturbation Risk
Now that we have a new model with a new measure of risk, in this video we develop the notation and derive the mathematics that describes the new model. Also, the differences and similarities between the new model and CAPM are be highlighted, particularly the differences between idiosyncratic risk and perturbation risk. Here we enter the mathematical weeds of the model and will remain there for the rest of the videos. There is no way simply to watch once and understand. Watching more than once may be the best way forward for this and the remaining videos.
13. An Example
The previous two videos introduced over 30 new formulas. In this video those formulas are implemented in a way designed to clarify what the model means. In the videos that follow, the long march toward a complete mathematical description and derivation begins.
14. More Detail, Part 1
With this video, nine scenarios of potential expected outcomes for a two portfolio index are defined in terms of their relative alphas and Sharpe ratios. After defining the nine scenarios, the conditions needed to make the first scenario an expectation are derived. The techniques used in the derivation are important as they are used for the remaining 8 scenarios in the videos that follow.
15. More Detail, Part 2
The nine scenarios of potential expected returns are briefly reviewed. Following this, the conditions needed to make scenarios 2 - 5 a mathematical expectation are derived. Scenario 4 is the CAPM scenario, so the conditions for CAPM to be an expectation should be closely examined.
16. More Detail, Part 3
The nine scenarios of potential expected returns are briefly reviewed again. Following this, the conditions needed to make scenarios 6 - 9 a mathematical expectation are derived. Scenario 9 is the volatility effect as we know it. Eventually scenario 9 will have our complete attention.
17. Simulation Setup
The nine scenarios are true on paper, but what about in a simulation? In this video a simulation of the 9 conditions is set up in order to demonstrate that indeed the conditions lead to the 9 scenarios. The outcome of the simulation is discussed in the next video.
18. Simulation Results
The numerical results of the simulation are almost uninteresting because they are exactly as predicted. The interesting part comes from the graphs. The graphs of the simulation results show that alpha is not a point but a curve of potential expected values. Potential expected CAPM betas also fall on a curve. Finally, potential expected Sharpe ratios are not at all what might be expected. Yet, the mathematics is clear. Note that the potential expected outcomes are not the same as potential realized outcomes. Expectation is used in the purely mathematical sense.
19. Backward Perturbation Risk Model
What we have seen so far shows what might be expected ex-ante given model parameters. Now we look at what the parameter values might be given market data. There are a number of unexpected difficulties. Also, the numerical relationship between perturbation risk and idiosyncratic risk is derived carefully.
20. Backward Perturbation Risk Model: Three Examples
Any given data set can lead to a variety of market parameter estimates. Determining which estimate is the correct interpretation of the data is not obvious. Nevertheless, each possible set of parameter estimates leads directly to the same expected value of the statistics CAPM alpha, CAPM beta, and idiosyncratic risk. How is this possible?
21. Another Look at the Backward Perturbation Risk Model
With all the derivations of the past videos, it turns out that the simplifying assumption of zero covariance between perturbations leads to parameter estimates that do not include results from market data. If we include a non-zero covariance term, it works. However, including a non-zero covariance means all the formulas must be updated. With this accomplished, the implications of the model can be explored with confidence. Real market data is analyzed for the first time.
22. Details and Generalizations, Part 1
In this video we set aside data analysis and return to model building. Here we define perturbation alpha, show how it is calculated, and how it is quite different from a CAPM alpha. There are some clarifying comments about how the perturbations are different from perturbation alphas. The mathematics is a step up.
23. Details and Generalizations, Part 2
The purpose of this video is to derive in a careful way the relationship between market perturbation risk and portfolio perturbation risk. When the derivation is complete, it is shown that, surprisingly, market perturbation risk drops out of the 9 conditions, leaving perturbation proportionality and the correlation between perturbations.
24. Details and Generalizations, Part 3
Now that perturbation alpha has been defined, and portfolio perturbation risk has been carefully derived, in this video we exam how perturbation risk affects Sharpe ratios. It appears that condition 6 is the theoretical expectation, but only a small deviation from condition six will give us condition 9 with scenario 9 as a practical expectation. Scenario 9 is the full volatility effect. The mathematics in this video requires careful attention.
25. Details and Generalizations, Part 4
Finally, a review of the conclusions of the previous 3 videos is brought together to show that the goal of the entire series has been reached. The perturbation risk model has the volatility effect as a mathematical and economic expectation.
26. Forward Model for an Individual Stock
The reasoning up until now has concerned two portfolios, one high CAPM beta, the other low CAPM beta. In this video we take a look at how the same reasoning applies to individual stocks or other kinds of portfolio constructions. Some of the analysis is the same, and some different.
27. Loose Ends from Video 10
Video 10 had 3 data anomalies that were ignored. In this video an attempt is made to reconcile those data anomalies to the perturbation risk model.
28. Summary and Additional Insights
A summary table of the possible combinations of perturbation attributes is given and suggestions for further research are listed.
29. Missing Algebra
Several videos had skipped steps in the mathematics. This video fills in the gaps of those derivations.
30. Closing the Open Problem from Video 9, Part 1
The structure of correlation between portfolios ranked by beta decile is looked at more closely, particularly the correlation pattern of symmetric deciles. The mathematics is a step up.
31. Closing the Open Problem from Video 9, Part 2
The analysis of symmetric deciles in the previous video continues. Then we apply similar methods to the analysis of consecutive deciles.