Professors in D&D (Episode 2021.8)

DM: As you will recall from our last adventure, the Crimson Cleric has risen to be the Supreme Leader of Unigard.  He has cast many crafty and sinister spells and has drawn away many of your retainers and followers.  The battle lines have been drawn, and your small force of Professors stands arrayed against the forces of the Crimson Cleric.  Dawn approaches, and the battle will soon be joined.  There have been two weeks of downtime since our last adventure.  Did any of you do anything that might sway the outcome of the battle? 

Psychology Professor (5th Level):  I cast Social Media Appeal and argue passionately for rationality and human decency.   

DM: You make a bold and convincing argument, but the Crimson Cleric’s Misinformation spell is very powerful and few people hear your pleas.

Criminal Justice Professor (19th Level): I don’t think we can win this one.  I cast Early Retirement.  

DM: That’s a pretty good strategy, but the material component for that is 1,250 Gold Pieces.  Do you have that?

CJ Prof:  Ugh. No.  Guess I’ll have to stay and fight.

Political Science Professor (Level 6):  I give a stirring oration at the largest public venue I can find, appealing to civic unity and human decency.

DM: You manage to win over a few of the town’s folk, but in the main, they can’t understand your arguments because of the -10 penalty to their intelligence checks due to the Crimson Cleric’s sinister spells.

Right.  All of you make valiant attempts to sway the people, but you accomplish little.  The power of the Crimson Cleric is seemingly limitless when it comes to charming the masses.  You hear dark incantations drifting across the field between your forces and the armies of the Crimson Cleric.  He has summoned a swarm of plague rats.

Biology Professor (8th level):  I cast mass immunization to counter the plague rats.

DM: The spell description says that those affected must be willing, and only about half of them choose to be involved.

Bio Prof: Fine then.  I cast Summon Scientists and have them explain how terrible the plague is to the people.

DM: A worthy attempt, but your spell fizzled when it encountered the Crimson Cleric’s Anti-science Shell.

CJ Prof: Okay, it looks like battle can’t be avoided.  I’m going to cast Distance Learning on all of my classes. 

DM: That’s a high-level spell.  Do you have the spell slots for that? 

CJ Prof:   Yep, I’m pretty high level.  I’ve got tons of experience in the classroom.

DM: Right.  You cast your spell, but your Grand Potentate has been charmed by the Crimson Cleric, so only half of your online classes get approved.  You still have two face-to-face courses.  Oh, and by the way, defections on your side result in your summer classes and extra fall classes being canceled.  

CJ Prof:  That sucks.  I certainly don’t have the gold to cast Early Retirement in that case.  Okay, I cast Polymorph on those two, making them as small as possible.   Also, I invoke seniority and schedule them at unpopular times.

DM: Good strategy.  You hear further incantations off in the distance.  The Crimson Cleric has cast Befuddle on your people.  Many are wandering around in circles confused, several have wandered off into the woods, and a dozen or so have captured 6d6 plague rates are trying to teach them tricks.  Is there anything else anyone wishes to do?

[All players look dejected, shaking their heads in the negative.]

DM:  The sun has crested the horizon, and a distant bell signals that 8:00 AM has arrived.  Roll initiative.  

Demystifying Beta

It has often been said that “the market loves certainty.”  Most investors (excluding those who seek to capitalize on volatility) would love it if stocks grew in a nice, linear way that was easy to predict and explain.  Alas, stocks don’t do that. They grow in an up and down pattern that is reminiscent of an EKG readout. All that up and down movement overwhelms the brain, and makes it hard to figure out what is going on over the long run.  Since we can’t get stocks to grow in value as a nice, elegant linear function, we tend to look at trends.   

On graphs, we can often use lines to show what the trend of a particular stock’s value is over time.  One particular method of doing this is a statistical technique called linear regression.  It essentially takes the average of all the ups and downs and draws a line based on those averages.   You could do the same thing with a ruler by “eyeballing it,” but the results wouldn’t be as precise as the trend line and associated equation that is mathematically generated by a computer.  

That last line may have made you cringe a little; I used the words “mathematically” and “equation” in the same sentence.  If you had flashbacks to your high school algebra class, I apologize. But you needn’t be afraid; all of the math is done by computers these days.  All you need to remember from algebra class is that equations can be shown as a line on a graph. Regression analysis capitalizes on this idea in predicting the average movement of data points (stock prices) that don’t move in a nice, straight line like those homework problems from algebra class.  Regression analysis has gotten a bad reputation because of its association with math. Try to forget that; regression is a very useful tool for the investor. All the hard work is done behind the scenes. All you have to do is interpret the results. There are very easy rules of thumbs for interpreting that information.  Feel free to write those down; this isn’t algebra class, and you can’t get in trouble for cheating.

If you were to ask an economist, she would probably say something like “a particular stock’s beta is calculated by dividing the covariance the stock’s returns and the returns of a specified benchmark by the variance of the benchmark’s returns over a specified period.”  My guess is that you didn’t find that very helpful. Let me break it down for you; it’s an easy concept to grasp once we translate the statistical jargon into trader jargon. When we measure anything (such as a stock price) over time and we get different results, we call that thing a variable as opposed to a constant.  Stocks are certainly variable!  

That movement of the measurement from value to value is called variation.  Statisticians measure this variability with a number called variance (closely related to standard deviation).  Simply put, variance is a particular statistic that measures the variation in something that varies, such as a stock price.  In the case of stock prices, low variability (as measured by variance) means that the stock’s price doesn’t move much. A high variance means that the stock’s price is bouncing around all over the place.  Traders don’t often use the word variability; they talk about the amount of movement in a stock’s price in terms of volatility.  It may not be precise, but you will probably be okay thinking of variance as a measure of volatility.

Enter the idea of covariance.  As you’d expect, “co” is a prefix meaning “together.”  So the idea of covariation is the idea that two measurements will vary together and, if we generate a scatterplot, the dots will form a line.  For example, we’d expect a high degree of covariance between a stock’s market price and its price to earnings ratio. If the PE ratio was the only factor in determining stock prices, then all of the dots would fall on the line perfectly.  Statisticians would refer to this is a bivariate (meaning two variables) problem, because there are only two variables being considered.

Stock prices are a multivariate (meaning many variables) problem. There are dozens of potential factors that influence stock prices, and only some of them are quantifiable (If this weren’t the case, I could come up with an equation to model future growth and have retired already).  Note that the idea of covariance is conceptually identical to the idea of correlation.  

So, the big idea of regression analysis is to demonstrate as precisely as possible how two things systematically vary together.  We can apply this idea to see how much the variability (volatility) of a particular stock matches the variability (volatility) of a benchmark.  That is what Beta is. While any benchmark can be plugged into the equation, most often the variance of the S&P 500 is used with stock prices. Beta, then, is just a ratio of the volatility of a particular stock and the volatility of the S&P 500.  The math tweaks (standardizes) the results for easy interpretation. A Beta of 1.0 indicates that the particular stock you are evaluating moves precisely with the benchmark—it goes up and down exactly as does the S&P 500. A Beta less than 1.0 suggests that (at least in the past) the stock was less volatile than the S&P.  A Beta above 1.0 suggest that the stock is more volatile than the S&P.

Consider the idea that volatility is only a bad thing when it goes against the way you bet. If you are long in a stock, and it shoots past the S&P 500 average, then you picked an awesome stock! If it, however, plummets below the level of the S&P 500, then you are a much bigger loser than the overall market.  Beta assesses volatility objectively. What you ultimately decide to do with that information depends on how risk averse you are. Super conservative investors that are willing to tolerate very little risk will look for stocks with a Beta less than one, such as many utility stocks (often referred to as bond market equivalent stocks).

For example, as of this writing, the Beta for Procter & Gamble Co. (PG) is 0.6. Risk takers seeking big rewards will often look for stocks with a high Beta and the accompanying possibility of big returns—and huge losses.  Note that Beta is neutral as to evaluating great returns or terrible returns. As of this writing, the Beta for Goldman Sachs Group Inc. (GS) is 1.6. Owners of GS are springing for the good stuff this Christmas! Apple Inc. (AAPL), on the other hand, has a Beta of 1.3 and that volatility is unwelcome by investors.

To really get any useful information from Beta, there must be a correlation between the stock you are evaluating and the benchmark used in the computations.  To evaluate this, we can turn to another byproduct of regression analysis known lovingly by economists as R-squared. Think of R-squared as a percentage of covariation.  The closer to 100 you get, the more the stock traces the benchmark’s performance. The closer to zero you get, the less correlation there is between your stock and the benchmark.

More advanced measures have been developed since the advent of computer technology, such as the Sharpe Ratio. The bottom line is that Beta and other measures of volatility are useful tools (among many) that you can use to help you pick a stock that meets your investment needs and form realistic appraisals of how high it can go, and how low it can sink.

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