… are located at http://fin4366.garven.com/spring2018/ps6solutions.pdf.

# All posts by jgarven

# Tomorrow’s meeting of Finance 4366

Since we completed our discussion of pricing European options using the binomial model just prior to spring break, tomorrow we will turn our attention to pricing American options. I plan to cover the reading entitled “Early Exercise of American Call and Put Options on Non-Dividend Paying Stocks”, and if time permits we’ll also move on to pricing options on dividend-paying stocks. Since I am late in bringing this change in schedule to your attention, I won’t have a quiz at the beginning of class. However, I highly recommend that y’all read this teaching note prior to coming to class tomorrow so that you can be somewhat familiar with the topic that we will be covering.

# Hands-on Small-Cap Investment Course

**About the Course and How to Apply**

# Overview:

Designed as a two-semester progression, this course will give students valuable hands-on experience researching, analyzing, and managing a portfolio of small capitalization (small-cap) stocks. The fall course will begin with lectures that introduce equity research methods, including valuation, modeling, fundamental analysis, and cultivating resources. Then the student analysts, in teams, will complete an initiation-of-coverage research report on a firm that will require the team to talk to or meet with company management, visit company sites, and utilize various information sources including financial documents, trade associations, and competitors, customers, and suppliers of the firm. Each student will also learn to use Bloomberg, FactSet, Thomson Eikon, and other resources commonly used in the investment management industry. Based on the research reports and recommendations of the student teams, the members of the class, as the small-cap portfolio’s investment committee, will decide which firms to include in the portfolio. In the spring, one team of students will compete in the CFA Investment Research Challenge, while other student teams will complete another initiation-of-coverage research report.

# The Classes:

**Time:** Mondays, 2:30-5:00pm, for a total of 16 weeks spread across the two semesters

**Location:** Hodges Financial Markets Center

**Structure:** The main emphasis is on out-of-class assignments supplemented by in-class discussion

and decision-making. Small-Cap I is a two-hour class held in the fall, which is intended to

be followed by Small-Cap II, a one-hour class, in the spring.

# Professors:

- Brandon Troegle, CFA®, is a Managing Director and Portfolio Manager with Hillcrest Asset Management, focusing on the firm’s securities selections across various strategies. Before joining Hillcrest, Brandon was an equity analyst at Morningstar. Prior to Morningstar, he worked for Luther King Capital Management and Bank of America.
- Wesley Wright, CFA®, is a Portfolio Manager at Hillcrest Asset Management focusing on the firm’s International Value Strategy. Prior to joining Hillcrest, Wesley was a Portfolio Manager at Dreman Value Management in New York where he managed the firm’s International Value product and U.S. All- Cap Value product.

**How to Apply:**Complete the online application at https://www.baylor.edu/business/financialmarkets/apply.

In addition to the usual contact and background information you will need to provide:

- A statement of why you wish to take the course
- Description(s) of any investment and/or finance-related experience
- Descriptions of three academic and/or personal achievements
- Uploaded copies of your current resume and current unofficial transcript

The deadline for submission is 5:00pm, Tuesday, March 20.

Enrollment is limited to 15 graduate and undergraduate business students with a minimum 3.2 GPA, a strong academic record, and an interest in investments. Applicants will be evaluated by a Finance faculty committee chaired by Dr. Bill Reichenstein, Professor of Finance and Chair of the Board of Trustees of the Investment Fund.

**For More Information**:

Contact Dr. Bill Reichenstein or go to: http://www.baylor.edu/business/financial_markets

# Stock Buybacks Are Proof of Tax Reform’s Success

Masterful commentary by Hoover Institution senior fellow John Cochrane in today’s *Wall Street Journal* on how stock buybacks perform an integral role in allocating capital to its most highly valued uses…

Companies help workers not by being philanthropic but by investing capital in profitable ideas.

# Midterm Exam 1 Descriptive Statistics

Here are the descriptive statistics for Midterm Exam 1 in Finance 4366. Twenty-five students are enrolled in Finance 4366 this semester, and all 25 students took this midterm exam. The average exam score came to 87.44 and the standard deviation was 14.68. The minimum exam score was 33 (one student) and the maximum exam score was 100 (five students). Nineteen students scored 85 or better, thirteen students scored 91 or better, and seven students scored 98 or better.

I plan to pass out the graded exam booklets in class on Tuesday . In the meantime, you can find out your exam score by logging into Canvas.

Mean | 87.44 |

Standard Deviation | 14.68 |

Minimum | 33.00 |

25th percentile | 85 |

50th percentile | 91 |

75th percentile | 98 |

Maximum | 100.00 |

# On the origins of the binomial option pricing model

In my previous posting entitled “Historical context for the Black-Scholes-Merton option pricing model,” I provide links to the papers in which Black-Scholes and Merton presented the so-called “continuous time” version of the option pricing formula. Both of these papers were published in 1973 and eventually won their authors (with the exception of Fischer Black) Nobel prizes in 1997 (Black was not cited because he passed away in 1995 and Nobel prizes cannot be awarded posthumously).

Six years after the Black-Scholes and Merton papers were published, Cox, Ross, and Rubinstein (CRR) published a paper entitled “Option Pricing: A Simplified Approach”. This paper is historically significant because it presents (as per its title) a much simpler method for pricing options which contains (as a special limiting case) the Black-Scholes-Merton formula. The reason why we began our analysis of options by first studying CRR’s binomial model is because pedagogically, this makes the economics of option pricing much easier to comprehend. Furthermore, such an approach removes much (if not most of) the mystery and complexity of Black-Scholes-Merton and also makes that model much easier to comprehend.

# Historical context for the Black-Scholes-Merton option pricing model

Although we won’t get into the “gory” details on the famous Black-Scholes-Merton option pricing model until sometime later this semester when we cover Hull’s chapter entitled “The Black-Scholes-Merton Model” and my teaching note entitled “Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Equations“, I’d like to call your attention to the fact that the original papers by Black-Scholes and Merton are available on the web:

- The Black-Scholes paper entitled “The Pricing of Options and Corporate Liabilities” is available at http://www.jstor.org/stable/1831029.
- The Merton paper entitled “Theory of Rational Option Pricing” is available at http://www.jstor.org/stable/3003143.

The Black-Scholes paper originally appeared in the *Journal of Political Economy *(Vol. 81, No. 3 (May – Jun., 1973), pp. 637-654). The Merton paper appeared at around the same time in *The Bell Journal of Economics and Management Science *(now called *The Rand Journal*). Coincidentally, the publication dates for these articles on pricing options roughly coincide with the founding of the Chicago Board Options Exchange, which was the first marketplace established for the purpose of trading listed options.

Apparently neither Black and Scholes nor Merton ever gave serious consideration to publishing their famous option pricing articles in a finance journal, instead choosing two top economics journals; specifically, the *Journal of Political Economy* and *The Bell Journal of Economics and Management Science*. Mehrling (2005) notes that Black and Scholes:

“… could have tried finance journals, but the kind of finance they were doing was outside the rubric of finance as it was then organized. There was a reason for the economist’s low opinion of finance, and that reason was the low analytical level of most of the work being done in the field. Finance was at that time substantially a descriptive field, involved mainly with recording the range of real-world practice and summarizing it in rules of thumb rather than analytical principles and models.”

Another interesting anecdote about Black-Scholes is the difficulty that they experienced in getting their paper published in the first place. Devlin (1997) notes: “So revolutionary was the very idea that you could use mathematics to price derivatives that initially Black and Scholes had difficulty publishing their work. When they first tried in 1970, Chicago University’s *Journal of Political Economy* and Harvard’s *Review of Economics and Statistics* both rejected the paper without even bothering to have it refereed. It was only in 1973, after some influential members of the Chicago faculty put pressure on the journal editors, that the *Journal of Political Economy* published the paper.”

**References**

Devlin, K., 1997, “A Nobel Formula”.

Mehrling, P., 2005, *Fischer Black and the Revolutionary Idea of Finance* (Hoboken, NJ: John Wiley & Sons, Inc.).

# Delta hedging, replicating portfolio, and risk neutral valuation approaches to pricing options

The delta hedging, replicating portfolio and risk neutral valuation perspectives for pricing options are important in that they enable us to think carefully as well as deeply concerning the economics of option pricing. For example, the delta hedging approach illustrates that an appropriately hedged portfolio consisting of either long-short call-share positions or long-long put-share positions is riskless and consequently must produce a riskless rate of return. Similarly, the replicating portfolio approach reminds us that a call option represents a “synthetic” margined stock investment, whereas a put option represents a “synthetic” short sale of the share combined with lending money. As we saw in our study earlier this semester of forward contracts, if there is any difference between the value of a derivative and its replicating portfolio, then one can earn profits with zero net investment and no exposure to risk. Thus, the “arbitrage-free” price for the derivative (option or forward) corresponds to the value of its replicating portfolio. The arbitrage-free pricing principle further implies that a risk-neutral valuation relationship exists between the derivative and its underlying asset, which in turn enables us to calculate risk neutral probabilities. Once we know what the risk-neutral probabilities are for up and down price movements, we can price options by discounting the risk-neutral expected value of the option payoff (i.e., its certainty-equivalent) at the riskless rate of interest.

During our next class meeting tomorrow, we will spend a bit more time on the risk neutral valuation approach, as well as extend our analysis from a single timestep to a multiple timestep setting. To do this, we need to introduce an important concept called *backward induction. *Backward induction involves beginning at the very end of the binomial tree and working our way back to the beginning. We’ll continue with the numerical example introduced during class today and illustrate the backward induction method for the delta hedging, replicating portfolio and risk neutral valuation approaches. We’ll discover that multiple timesteps imply that the delta hedging and replicating portfolio methods imply “dynamic” trading strategies which require portfolio rebalancing as the price of the underlying asset changes over time.

# Midterm 1 exam booklet and solutions…

Midterm exam 1 booklets: http://fin4366.garven.com/spring2018/midterm1_spring2018.pdf

Midterm exam 1 solutions: http://fin4366.garven.com/spring2018/midterm1_spring2018_solutions.pdf

# Next Tuesday’s reading assignment for Finance 4366

Here’s the list of assigned readings for next Tuesday’s class meeting:

- Hull Chapter 13 (“Binomial Trees”)
- Binomial Option Pricing Model (single-period)
- Multiple Period Binomial Option Framework
- Dynamic Delta Hedging Numerical Example (calls and puts)
- Dynamic Replicating Portfolio Numerical Example (calls and puts)
- Convergence of the Cox-Ross-Rubinstein (CRR) Binomial Option and Black-Scholes-Merton (BSM) Option Pricing Formulas

The two most important readings for next Tuesday’s Finance 4366 quiz and class meeting are Hull’s “Binomial Trees” chapter and my teaching note entitled “Binomial Option Pricing Model (single-period)”. Tuesday’s class meeting will be primarily devoted to covering the latter reading in particular, although the other readings are also quite important for the next few Finance 4366 class meetings.