Superb WSJ op-ed by (former hedge fund manager turned author) Andy Kessler about the corporate social responsibility “gospel” and the importance of profit; Kessler’s essay is essentially an homage to Milton Friedman’s famous 1970 New York Times Magazine article entitled “The Social Responsibility of Business Is to Increase Its Profits.”
Problem Set 2 consists of two problems. The first problem requires calculating expected value, standard deviation, and correlation, and using this information as inputs into determining expected return and standard deviation for 2-asset portfolios. We covered these concepts during last Thursday’s statistics tutorial; also see pp. 10-20 of the http://fin4366.garven.com/spring2018/lecture3.pdf lecture note. The second problem involves using the standard normal probability distribution to calculate probabilities of earning various levels of return by investing in risky securities and portfolios. We will devote next Tuesday’s class meeting to this and related topics.
This coming Tuesday, we will complete the probability and statistics tutorial by studying the binomial and normal probability distributions. On Thursday, we introduce financial derivatives, relying upon a combination of textbook chapters and teaching notes that I have authored. We will begin by defining financial derivatives and motivating their study with examples of forwards, futures, and options. Derivatives are so named because the prices of these instruments are derived from the prices of one or more underlying assets. The types of underlying assets upon which derivatives are based are often traded financial assets such as stocks, bonds, currencies, or other derivatives, but they can be pretty much anything. For example, the Chicago Mercantile Exchange (CME) offers exchange-traded weather futures contracts and options on such contracts (see “Market Futures: Introduction To Weather Derivatives“). There are also so-called “prediction” markets in which derivatives based upon the outcome of political events are actively traded (see “Prediction Markets“).
Besides introducing derivatives and discussing various institutional aspects of markets in which they are traded, we’ll consider various properties of forward and option contracts, since virtually all financial derivatives feature payoffs that are isomorphic to either or both of these schemes. For example, a futures contract is simply an exchange-traded version of a forward contract. Similarly, since swaps involve exchanges between counter-parties of payment streams over time, these instruments essentially represent a series of forward contracts. In the option space, besides traded stock options there are also embedded options in corporate securities; e.g., a convertible bond represents a combination of a non-convertible bond plus a call option on company stock. Similarly, when a company makes an investment, there may be embedded “real” options to expand or abandon the investment at some future date.
Perhaps the most important (pre-Midterm 1) idea that we’ll introduce is the concept of a so-called “arbitrage-free” price for a financial derivative. While details will follow, the basic idea is that one can replicate the payoffs on a forward or option by forming a portfolio consisting of the underlying asset and a riskless bond. This portfolio is called the “replicating” portfolio, since it is designed to perfectly replicate the payoffs on the forward or option. Since the forward or option and its replicating portfolio produce the same payoffs, then they must also have the same value. However, suppose the replicating portfolio (forward or option) is more expensive than the forward or option (replicating portfolio). It this occurs, then one can earn a riskless arbitrage profit by simply selling the replicating portfolio (forward or option) and buying the forward or option (replicating portfolio). However, competition will ensure that opportunities for riskless arbitrage profits vanish very quickly. Thus the forward or option will be priced such that one cannot earn arbitrage profit from playing this game.
During last Thursday’s Finance 4366 class meeting, I introduced the concept of statistical independence. This coming Tuesday, much of our class discussion will focus on the implications of statistical independence for probability distributions such as the binomial and normal distributions which we will rely upon throughout the semester.
Whenever risks are statistically independent of each other, this implies that they are uncorrelated; i.e., random variations in one variable are not meaningfully related to random variations in another. For example, auto accident risks are largely uncorrelated random variables; just because I happen to get into a car accident, this does not make it any more likely that you will suffer a similar fate (that is, unless we happen to run into each other!). Another example of statistical independence is a sequence of coin tosses. Just because a coin toss comes up “heads,” this does not make it any more likely that subsequent coin tosses will also come up “heads.”
Computationally, the joint probability that we both get into car accidents or heads comes up on two consecutive tosses of a coin is equal to the product of the two event probabilities. Suppose your probability of getting into an auto accident during 2017 is 1%, whereas my probability is 2%. Then the likelihood that we both get into auto accidents during 2017 is .01 x .02 = .0002, or .02% (1/50th of 1 percent). Similarly, when tossing a “fair” coin, the probability of observing two “heads” in a row is .5 x .5 = 25%. The probability rule which emerges from these examples can be generalized as follows:
Suppose Xi and Xj are uncorrelated random variables with probabilities pi and pj respectively. Then the joint probability that both Xi and Xj occur is equal to pipj.
I have decided to offer the following extra credit opportunity for Finance 4366. You can earn extra credit by attending and reporting on Dr. Robert P. George‘s upcoming lecture entitled “Why the Humanities Matter: Intellectual Freedom, Self-Mastery, and the Liberal Arts”:
If you decide to take advantage of this opportunity, I will use the grade you earn to replace your lowest quiz grade in Finance 4366 (assuming that your grade on the extra credit is higher than your lowest quiz grade). The report should be in the form of a 1-2 page executive summary in which you provide a critical analysis of Dr. George’s lecture. In order to receive credit, the report must be submitted via email to email@example.com in either Word or PDF formats by no later than Friday, January 26 at 5 p.m.
… are available at http://fin4366.garven.com/spring2018/ps1solutions.pdf.
For more information concerning Bitcoin (other than the Motley Fool articles that I posted a few minutes ago), I recommend reading the Wikipedia article at https://en.wikipedia.org/wiki/Bitcoin. Technically, Bitcoin is an “application” of so-called “Blockchain” technology. Of course, I wish that I would have had the foresight to have purchased (for that matter, even “mined”) Bitcoin starting back in 2009, but such is the nature of uncertainty – what may seem “obvious” now seemed borderline silly back then.
The level of volatility in Bitcoin spot and futures prices can be quite breathtaking at times. Indeed, daily volatility of Bitcoin is roughly ten times the daily volatility of the SP 500 stock index (see WSJ Daily Shot, 11-January-2018). While there may be some entertainment value in buying and selling cryptocurrencies in the spot and futures markets, these instruments are clearly not suitable for most investors.
For more on Blockchain, I recommend watching either NYU finance professor David Yermack (cf. https://www.youtube.com/watch?v=Irc-VMuUs3c) or Duke finance professor Cam Harvey (cf. https://www.youtube.com/watch?v=G1tVnXTcDBU) – they are the best of the best finance experts on this topic.
In case if you are interested in learning more about cryptocurrencies and blockchain, the following (recently published, non-technical) Motley Fool articles are quite helpful: