Personal Finance- Saving & Investing

You will hopefully achieve the situation where- owing to your earnings exceeding your total expenses over an extended period- you begin to amass some savings. You then will have options as to what to do with your savings. In general, there is a direct correlation between risk and expected returns. You can fairly accurately describe the situation visually by drawing an upward sloping line, represented on a graph such that risk is along the horizontal axis and expected returns on the vertical axis. Low risk/low return investments include savings accounts and investment CDs at the extreme lower left, with a risk of virtually zero (if under $250,000 at an FDIC-insured bank). Moving slightly up on the line, we have money market funds; money that has been deposited into investment banks and not presently invested in stocks, bonds, etc. is often automatically held in money market funds when being held on the sidelines. While superficially almost indistinguishable from savings account and almost equally liquid, they do involve investment in short-term notes and bonds, and thus have a slight risk. Returns are better than most savings accounts, commensurate with CDs of several months (with the benefit that your money is not tied up for several months with these funds). Higher returns come with the price of slight risk; losses are rare, but possible. In 2008, at the height of the recent financial crisis, some money market funds lost as much as 3% in value. Although significant, this is far less than the losses of 50% or more faced by investors and retirees highly invested in the stock market. Moving further up this line, highly rated "safe" bonds, such as municipal and government bonds, offer higher returns, well over 2%. (Being tax-free, this usually converts to over 3% on taxable bonds). The government being unlikely to collapse and default, we consider these bonds safe. Corporate bonds of large companies are a bit further up, as there is the potential of even such large companies failing unexpectedly; thus, we would expect higher interest rates from such corporate bonds. Moving up further still, we reach "junk bonds"- bonds with low ratings, usually owing to uncertainty regarding a company's stability. For accepting such uncertainty, investors expect the highest returns among bonds. Approaching the upper right area of this line, high risk/high returns, we find stocks. Moving up along the line, we first pass conservative stocks (large companies unlikely to fail), and then progressively speculative stocks, with progressively risky stocks valued to provide increasing expected returns. Finally, at the upper right end we find the most speculative investments, such as venture capital, money offered by investors in return for equity in companies with an at-best shaky likelihood of success. Venture capitalist demand extremely high returns, with 40-50% being reasonable, given the strong possibility they will lose their entire investment. The decision of how to invest is ultimately up to you. You must decide how much risk you are willing to accept in order to increase your expected returns. Investment firms managing large portfolios, such as family trusts, tend to diversify and hold a mixture of bond and stock funds, a "moderate" approach allowing for moderate returns with moderate risk; you might find such an approach for savings you want to have appreciate in the long-term without excessive risk. Use of stockbrokers in brokerage firms for purchasing individual stocks or stock indices has fallen drastically over the past decade. In lieu of paying stockbrokers hundreds of dollars per trade, investors can invest with online investment firms, with commissions as low as $10 per trade, and financial information once provided by stockbrokers is now easily accessible online.

Personal Finance- Banking

Upon reaching your 18th birthday, one of your first actions should be to open bank account(s) (unless you already have minor or custodian accounts which will fall under your control the day you turn 18). You will find a bank account essential for several purposes- writing checks or transferring funds to pay bills, depositing paychecks, safely storing your savings and withdrawing cash when needed, and establishing a financial history in your own name prior to applying for credit. The so-called "Big 4" banks (the huge, 4 largest banks)- namely Bank of America, Citibank, Wells Fargo, and Chase- are usually the most convenient ones to establish accounts, given the easy access to these banks, ATM machines, online banking, etc. throughout the country. However, since these banks have minimum balance requirements often as high as $300 for even basic accounts, with monthly service fees assessed if ever your balance falls under this amount, if your savings are less than this you may be better off starting off at a credit union or other smaller bank with lower minimum balance requirements. You may have noticed that I omitted what was traditionally a strong motivation for opening bank accounts- namely, interest payments. In response to the recent "Great Recession", the Fed opted to lower the interest rates to barely above zero, and hold them there for an extended period. Thus, banks nowadays pay us a ridiculously low interest rate of 0.01% to 0.1% (not a typo), even though they still make at least 4% interest on home loans and over 15% on credit card interest charges. The interest we are paid is surely more than eaten up by the cost of gas to drive to the nearest bank or even corner ATM machine. Thus, for the past 6 years interest has practically vanished as a benefit to holding bank accounts. The other benefits to opening personal accounts still apply, however. Traditionally, however, it has been advisable to maintain a checking account with funds to which you may need immediate access, and perhaps a combination of savings account and/or investment CD's to provide significant income from interest. CD's offer the highest return, as compensation for agreeing to not touch the CD account prior to the maturity date, or face stiff penalties (typically the entire amount of the interest paid) for withdrawing early; use of CD's and high-interest savings accounts should be adequate to provide returns slightly higher than the inflation rate, thus preventing inflation from eating away at your savings.. All of the above-described accounts are considered low-risk, low-return investments. The Big 4 banks (or any other bank you use) should protect your accounts up to $250,000 per person per account type through the FDIC, meaning that if the bank fails the government will reimburse your money, up to $250,000. You should see a sign in the bank itself advertising this fact; if not, the bank should be avoided. If your assets exceed $250,000, you should spread out your funds amongst multiple banks and/or account types, or perhaps in a money market fund or other investment in an investment account (to be discussed later). Many banks do offer a high-risk, high-return investment option. They will offer to invest your savings (if sufficiently high in amount, usually several thousand dollars or more) in mutual fund accounts- basically, in the stock market(s). These accounts are not FDIC insured, and may lose value; they will tend to fluctuate with the stock market. There is, for example, a 529 fund which will invest money to be used for your kids' education, with the idea that the stock markets should appreciate substantially by the time any current kids reach college age. While on average the return will be higher from such an investment, there is a strong element of gambling involved; you need to decide whether you are willing to risk losing money to potentially reap the benefits from such speculative investments. The bank, by the way, takes a percentage of this investment, even if they lose money for you.

Personal Finance- Economic Basics

The modern economic system, using money as the means of exchanging goods, is seen to provide the greatest total amount of utility to humanity as a whole, by creating the most efficient distribution of resources and level of activity in every area. While a pure market economy allows the "invisible hand" to guide this allocation of resources, and allows the severely impoverished to literally perish if their insufficient means prevent their affording the basic necessities of life, a socialist/welfare state imposes government control of economic activity to both provide sufficient means for all citizens to maintain a reasonable standard of life while preventing extravagance among the wealthiest members of society. The United States is essentially a "mixed economy" which is a balance or compromise between these two extremes; socioeconomic classes continue to exist, but the government manages and subsidizes programs to provide even the poorest Americans with access to food, clothing, education, etc. Gross Domestic Product (GDP), total value of all resources in the country, is seen to increase at a healthy rate (perhaps 3-5%) when the economy is strong, at an anemic pace (0-2%) in a sluggish economy, and to decrease during recessions. The distinction between "recession" and "depression" is unclear. The economy is cyclical, with periodic recessions being normal and necessary to direct readjustments needed for the economy's long-term growth.

Personal Finance

Personal Finance- a subject which seems to be of increasing interest among high school students within the California Virtual Academies- is a case of an academic subject with the strong potential to integrate numerous key mathematical concepts to young people's everyday lives. Students who opt to take this class do so with a number of possible motives. Some students are college-bound, already firmly grounded in upper level math, and are taking this as an elective class to acquire exposure in economics, accounting, banking, investing, and the business world. Other students are not necessarily college-bound, seeking to complete their 3rd year of required math with classes such as this which do not involve upper level math that they are unlikely to ever use (from their perspective), and find that Personal Finance covers information that they will find useful immediately upon reaching their 18th birthday. The challenge "When am I going to ever use this?"- a rather cynical question expressed by students in many math classes- is one which is very rarely uttered by students in this particular class. Indeed, the material covered in personal finance is essential for high school students to acquire both to manage their own finances as they enter adulthood, and to avoid being scammed by people who actively endeavor to profit from people's lack of knowledge and awareness in this area. In the posts that follow, I provide a summary of what I hope students will derive from this course. This certainly does not effectively summarize or replace the course text, or provide any readers with an advantage in taking quizzes or completing the written assignments; rather, it might more accurately reflect what is in the back of my mind, as the key concepts I hope students will acquire and retain as a result of completing this course.

Psychohistory

This blog would be incomplete without some discussion of psychohistory. I should begin with a disclaimer; if you, dear reader, are unfamiliar with the science of "psychohistory", this is no surprise- unless you have read Isaac Asimov's Foundation series, and understand the reference. Psychohistory is a fictional science formulated about 22,000 years in our future, according to Isaac Asimov's fictional robot/empire/foundation historical universe, and incorporates the notion that human behavior can be reduced to mathematical equations. One of the primary principles involved is that while the behavior of an individual human being is extremely difficult to predict- with increasingly large numbers of humans being incorporated into the system, we have increasing ability to predict accurately. Those with basic knowledge of statistics should recall the law of large numbers; a similar principle applies here, with the average behavior of a large number of repetitions more accurately predictable than a single event. "Wait a minute," you might exclaim. "There is nothing new here!" In this you would be correct. Indeed, the basic principle of psychohistory is derived directly from economic theory, which in turn is largely the product of the Enlightenment (18th century). Economics does involve the representation of human behavior in the (now global) marketplace in mathematical form. A primary principle of economics is the notion that while an individual human being is essentially unpredictable, within a large system we have the "extremes" represented by different humans' personalities and the like cancelling each other, so that we can with increasing accuracy model the system based on the behavior of the "average" human being. Economics- and the areas of finance and accounting- are thus of particular interest to mathematicians, not merely because of the amount of math involved in these areas, but because of the ability to express the behavior of human beings in mathematical form, and potentially their future behavior.

Definitions and Mathematicians

Any mathematician will freely admit to our obsession with definitions. As an example of this, observe the result of asking any mathematician "Are you okay?" A normal individual would reply "Yes" or "No". Not so with a mathematician; you can fully expect a mathematician to reply, "How do you define 'okay'?" This is the main point I wanted to make; a mathematician will resist attempting any problem until he understands every word contained in the problem itself.
I should forewarn anyone reading this who might be either taking or planning to take any math courses at the university level and has the need to visit a professor during office hours: Please DO NOT ask for assistance with solving a problem without first understanding all relevant definitions. If you do this, you will at the very least annoy your professor, who will usually be unrestrained in expressing his annoyance at you. I should clarify: There is nothing wrong with being confused at definitions in material recently learned, and a math professor will have no problems if you say, "I am confused on problem 9. FIRST OFF, I AM CONFUSED BY THE DEFINITION OF...". In expressing your confusion while simultaneously admitting that you are unclear regarding one or more definitions, you are at least acknowledging that your confusion regarding definition(s) is obstructing your progress. If, however, you simply ask for help on a problem and- when the professor queries you regarding one of the definitions in the problem itself you reply that you do not know - then your professor will almost certainly become annoyed.
How does this notion apply in real world situations? We have seen several examples of this in terms of current events. For instance, what is the definition of an economic "depression" as compared to a "recession"? The lack of a clear quantitative definition raises the following question: Was the recent (and possibly still ongoing) economic crisis a recession or a depression? The term "Great
Recession" seems like an absurd attempt at sidestepping this issue.

MBA program overview

Having completed all but one course of the MBA program, I am now in a position to offer a better perspective concerning this program. Certainly the MBA can be considered a very useful professional degree, providing students with a wealth of knowledge applicable to the corporate world, particularly to intelligent and self-driven individuals aspiring to eventually rise to management and/or positions affecting the strategic direction of organization(s). Required courses include a combination of subjects involving a large amount of reading and synthesis- particularly in strategic planning, human behavior in organizations, operations management, leadership, information technology- as well as quantitatively based subjects including finance and accounting. The finance classes involve the most intense and advanced mathematical content. Mathematicians opting to complete the MBA program will likely derive the most enjoyment from these classes. Unsurprisingly, I opted for the finance emphasis in this program; as such, I completed classes in corporate valuation, investment and portfolio analysis, in addition to the required basic finance class. The strategic management class was also quite interesting, as it involved a business simulation game in which the class was broken down into 10 competing companies in the same industry. Over a 10-week period, we competed to optimize our own company's value and market share; each week, we made decisions regarding pricing, marketing, production, etc., with performance in the subsequent "year" dependent on the decisions made and entered into the simulation by each team. It was a fascinating illustration of game theory in practice.