“How can we lift up the world together, starting with those at the margins of society?” This question inspired former American Enterprise Institute President Arthur Brooks to travel around the world seeking answers. Released in Spring 2018, Dr. Brooks’ documentary reveals insights into not only alleviating poverty, but also achieving lasting happiness for all.
Now streaming on Netflix @ https://www.netflix.com/title/81088318.
Problem Set 2 is available from the course website at http://fin4335.garven.com/spring2020/ps2.pdf; its due date is Tuesday, January 28.
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 returns and standard deviations for 2-asset portfolios. The second problem involves using the standard normal probability distribution to calculate the probabilities of earning various levels of return by investing in risky securities and portfolios; see pp. 17-23 of the http://fin4335.garven.com/spring2020/lecture4.pdf lecture note for coverage of that topic.
I just posted a new (1 page) reading entitled "Mean and Variance of a Two-Asset Portfolio" which (not surprisingly) explains the origins of the formulas for mean and variance of a two-asset portfolio. I expect you’ll find such knowledge very helpful in understanding and completing the 4th and 5th sections of the Statistics Class Problem as well as parts D, E, and F of Problem 1 and part B of Problem 2 in Problem Set 2.
As of 2:15 p.m. central standard time today, the PredictIt.org prediction market put the odds of President Trump being removed from office at 8%. Specifically, Predictit.org currently offers for sale a “share” which pays $1 if the answer to the question, “Will the Senate convict Donald Trump in his first term?, turns out to be “yes”.
Allow me to provide further context for this “prediction”. PredictIt.org is a New Zealand-based prediction market that offers “shares” on political and financial events. The idea behind PredictIt.org shares (technically, these are binary options, but I digress) is quite simple – you can buy and sell “yes” and “no” shares which pay off $1 if the answer to the contract question ends up being “yes” or “no”. If you buy yes (no) but no (yes) is the answer, then your share expires worthless and you have lost the full value of your original “investment”. However, if you sell yes (no) and no (yes) is the answer, then you don’t owe your counterparty any money and you get to pocket the price received (net of transactions costs) as profit.
Since the payoffs on PredictIt.org shares feature binary payoffs (i.e., $1 if yes and $0 if no), these shares are canonical examples of Arrow-Debreu, or “pure” securities. Arrow-Debreu securities pay $1 if a particular state (in this case, either “yes” or “no”) occurs at a particular time in the future. Thus, the current price for a given PredictIt.org share is the “state price”, which corresponds to the value today of $1 received when a particular future state of the world is realized. Breaking the state price down further, its components include 1) the probability of a particular future state of the world, 2) the rate of interest (to compensate for the time value of money), and 3) a further discount (to compensate for risk averse behavior by the bettor) or premium (to compensate for risk loving behavior by the bettor).
Prediction market prices are frequently referred to in the news media as probabilities for future state-contingent events; if prediction market participants are risk neutral and interest rates are negligible, then this is technically appropriate and roughly correct. What’s fascinating about prediction markets is that they showcase, in very pure form, how market prices reflect the statistical odds of some future event happening. Similarly, prices of speculative assets generally (e.g., corporate securities such as stocks and bonds and derivative securities such as options and futures) also reflect probabilistic beliefs about future states of the world, albeit in more of an opaque fashion.
From November 2016 through October 2017, Financial Times writer Tim Harford presented an economic history documentary radio and podcast series called 50 Things That Made the Modern Economy. This same information is available in book form under the title “Fifty Inventions That Shaped the Modern Economy“. While I recommend listening to the entire series of podcasts (as well as reading the book), I would like to call your attention to Mr. Harford’s episode on the topic of insurance, which I link below. This 9-minute long podcast lays out the history of the development of the various institutions which exist today for the sharing and trading of risk, including markets for financial derivatives as well as for insurance.
“Legally and culturally, there’s a clear distinction between gambling and insurance. Economically, the difference is not so easy to see. Both the gambler and the insurer agree that money will change hands depending on what transpires in some unknowable future. Today the biggest insurance market of all – financial derivatives – blurs the line between insuring and gambling more than ever. Tim Harford tells the story of insurance; an idea as old as gambling but one which is fundamental to the way the modern economy works.”
In his video lesson entitled “Visualizing Taylor polynomial approximations“, Sal Kahn essentially replicates the tail end of last Thursday’s Finance 4335 class meeting in which we approximated y = eˣ with a Taylor polynomial centered at x=0. Sal approximates y = eˣ with a Taylor polynomial centered at x=3 instead of x=0, but the same insight obtains in both cases, which is that one can approximate functions using Taylor polynomials, and the accuracy of the approximation increases as the order of the polynomial increases (see pp. 18-23 in my Mathematics Tutorial lecture note if you wish to review what we did during the tail end of last Thursday’s class meeting).
Problem Set 1 is due at the beginning of tomorrow’s Finance 4335 meeting. We will start class with a brief quiz based upon the assigned readings, which include “The New Religion of Risk Management”, by Peter Bernstein and “Normal and standard normal distribution”, by yours truly.
Going forward, I will typically not post reminders like this concerning Finance 4335 assignment deadlines; however, you’ll be “good to go” in Finance 4335 if you faithfully follow the guidelines listed in my “How to know whether you are on track with Finance 4335 assignments” posting.