It's that time of the year again - Good Luck on Finals and Congrats to seniors!

Hi Students,

It was a pleasure having you in my class this past semester.  

I wish you all the best on finals and wish to congratulate the seniors for all their hard work over the years.

The finals schedule for my class will be as follows:

Tuesday May 1st:  Business Math (Tuesday) class

Wednesday May 2nd:  Applications in Math 

Thursday May 3rd:  Business Math (Thursday) class

If you wish to see a graded copy of your exam you can pick it up at the WHAE office - I will leave them with Patty.   

Thanks again and keep up the good work going forward.  

I wish you all the best of luck!

For those returning in the fall, I hope to see you again then.  Keep in mind that I will be teaching a new course on Investing for Your Retirement in which I will be reviewing how to harness the power of compound growth using stock and bond funds for individual retirement accounts. 

Hope to see you then,

Richard Wiegand

The Reward to Risk Trade-Off of Investing

Like many things in life, there's a trade-off of some sort. 

When it comes to investing, there's a reward-to-risk trade-off, which essentially means that if you want higher returns you have to assume more risk.  

If you have good data, you can measure and compare levels of risk in terms of the dispersion of the data in relation to its mean (or average).  This is known as standard deviation.  The more disperse the data, the more volatile that item is.  The less disperse (or more concentrated) it is, the more predictable the outcomes are likely to be.  So, risk (variance, uncertainty or volatility), is the opposite of predictability.  

Let's investigate the concept of dispersion around a mean (or average).  Here are 5 sets of test scores from students in a class.  In this exercise, you will learn how to calculate the mean, the median, the mode, and the standard deviation.  To access the exercise please click on this link.




Some risks are worthwhile, while some aren't.  Good investors really get to know the reward and risk characteristics of what they're investing in before they jump in.  When it comes to investing, it's not that we should avoid risky assets altogether, but rather we should be getting paid more for each additional ounce of risk that we take.  If we aren't getting paid for sticking out our neck, that particular investment should be avoided.  

Consequently, we should invest the most to those securities or strategies that are giving us the highest pay-out per ounce of risk - even if those risk levels are much higher than the riskless investment (CDs, Treasury bills, e.g.)

In this exercise, we will learn how to measure reward and risk, and then explore the reward-to-risk characteristics of major asset classes.

To begin the exercise, please click on this link.


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Scatter Plots and Correlations

Scatter plots measure behavioral relationships between two items.  Sometimes, they may not appear to be related conceptually, while in other cases there may indeed be something going on.   

The fun part is to hypothesize whether there indeed is some sort of relationship between two things.  Next, you have to go out, find and collect the data to bolster your case.  The goal is to collect as many data points as possible, to make your findings statistically meaningful (or valid).  

Ideally, you want to have at least 100 data points to find a meaningful behavioral relationship between the two items.  You cannot make any meaningful discoveries if you have only a few data points (or pairs of data points, in this case).  In other words, you can’t generalize based on a small set of cases. 

Above is an example that plots the relationship between GDP per capita and life expectancy, among countries of the world.  Notice that there are two data sets, from 1952 and from 2007.   

1.    Is there a sufficient number of data points to draw any conclusions?  That is, is this study statistically valid? (R-squared: 0 to 1) 

2.   Is there a positive, negative, zero slope to the data points or are the results inconclusive? (Correlation coefficient: -1 to 0 to +1) 

3.   Does correlation imply causation? 

  

Some Interesting Correlation Scatter Plot Questions 

1.   Are higher temperatures positively correlated with higher sales? 

2.   Is the number of hours spent doing homework positively correlated with higher grades? 

3.   Is the number of hours spent on social media per person positively correlated with GDP per capita? 

4.   Is a person’s height positively correlated with age? 

5.   Is the probability that you will need a complete tooth extraction positively correlated with a person’s annual income level? 

6.   Is income equality (or lack thereof) positively correlated with political revolutions? 

7.   Is the # of cigarettes smoked by an individual positively correlated with incidence of cancer? 

8.   Is the quantity of alcohol imbibed by an individual positively correlated with dementia (Alzheimers, Parkinsons, severe amnesia, etc.)? 

9.   For males, is the amount of marijuana or hashish consumed positively correlated with sperm count? 

10.   Is the level of academic certification or degree attained positively correlated with a person’s annual income level? 

11. Is the number of languages spoken by an individual positively correlated with annual income levels? 

When answering these questions, provide a link or mention the source of a study that you used to answer each question.