Category Archives: Management Science

Solution to Management Science Series #189: Using Binomial Option Pricing Model to Value a Put 🧮

As an options trader at the CBOE, you are tasked with pricing a European put option on Quake Games, Inc.

The strike price is $75 and there are 6 months until expiration. Quake Games’ common stock does not pay dividends and is currently trading at $57.

Based on your models, the future stock price is predicted to be either $92 or $40 at the end of the next 6-month period. The effective annual risk-free rate is 4%. Estimate the price of the put?

How much of a share of the stock do you need to buy or short and how much do you need borrow or lend at the risk-free rate to replicate the put through a synthetic portfolio?

Check whether your synthetic portfolio replicating the put will have the same payoffs as those of the put at expiration!

Financial Accounting is a forensic tool! This time, the focus is accounting for receivables! Detecting frauds ranging from channel stuffing and bill and hold to roundtripping

Ability to use financial accounting at expert level gives the user a forensic tool.
Accounting frauds and schemes will become easier to detect, solve, and track when one masters it.
Innumerable scandals in the business world have been related to accounting frauds and they are still happening (why it is so is a long debate)
For example, think of a retailer having a hard time to hit its fourth quarter sales target. The trend shows that it will not hit the target by quarter end. However, by a sleight of hand, it magically hit the revenue target.
Where would you look at first? Which accounts and ratios would lead you to the detection of these inflated revenue numbers?
While answering all of these questions, I will also provide you with some recent examples of accounting scandals and how you could have detected them in the first place. I will also present you with some additional resources concerning the topic.

Solution to Management Science Series #188: Using Binomial Option Pricing Model to Value a Call 🧮

Using Binomial Option Pricing Model to Value a Call 🧮

As an options trader at the CBOE, you are tasked with pricing a European call option on Quake Games, Inc. The strike price is $75 and there are 6 months until expiration.

Quake Games’ common stock does not pay dividends and is currently trading at $57.

Based on your models, the future stock price is predicted to be either $92 or $40 at the end of the next 6-month period.

The effective annual risk-free rate is 4%. Estimate the price of the call?

How much of a share of the stock do you need to buy and how much do you need borrow at the risk-free rate to replicate the call through a synthetic portfolio?

Check whether your synthetic portfolio replicating the call will have the same payoffs as those of the call at expiration!

Businesses built around Network Effects Part 2: Diving a little deeper into E-commerce businesses

This time, the focus is e-commerce.
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Marketplace is a very important vertical for many e-commerce companies.

Some are solely based on it while others rely on it for effortless revenue (but most importantly profit) generation as direct retail operations in e-commerce are financially less viable.

Marketplace vertical, as is the case with social platforms, is reliant on network effects, and the accompanying proprietary tech is well-connected to network effects.

The connection is strong for both social media platforms and pure e-commerce businesses as almost any front-end feature of any platform can be replicated very easily and quickly by all players.

The similarity between two business models, however, is that proprietary technology and network effects facilitate mainly usage in one and mainly purchasing process in the other so that users build “necessary” habits and never quit the platforms.
In this article, I will dive deeper into e-commerce businesses including pure e-commerce business and e-commerce giants that have many adjacent and disparate business activities. I will try to analyze and assess the viability of different business models while also elaborating a little bit more on how network effects increase the sustainability and longevity of these different companies.

Solution to Management Science Series #187: Prologue to Black-Scholes Option Pricing Model: Binomial Option Pricing Model in a Single Period Example 🧮

Prologue to Black-Scholes Option Pricing Model: Binomial Option Pricing Model in a Single Period Example 🧮

As an equity analyst working at Silverman Fox, you are tasked with pricing a European call option maturing in one year from now.

Strike price of the call is $145 and the underlying stock’s current price is $129.93.

The representative risk-free annual interest rate is 3.95%, which also represents the risk-free borrowing rate.

In your binomial model, the stock price can take only one of two possible values at the end of the year: $163.26 or $110.87.

What should be the current price of the call? How many shares of the stock do you need to buy? How much do you need borrow/invest in the risk-free asset?

Businesses built around Network Effects Part 1: A guide to understand the strategy and compare some contemporary examples (both good and bad ones)

A company that is built around network effects has a demand-side comparative advantage. Some companies have also the ability to combine this demand-side benefit with supply-side capabilities (do you know who they are?).

In today’s digital environment, a proprietary technology complemented by network effects is deemed a sure winner-take-all model (until it is not as is the case with all these financially unviable business models).

Think of a social media platform whose sole monetization tool is advertising.

It has both great proprietary technology boosting targeted advertising metrics and returns and enviable fortress built upon network effects.

However, the prospect of success may still be uncertain even if it is a monopoly.

Proprietary tech can monetize through how frequently the platform is being used and how many monthly active users the platform has command over.

Regardless of whether you run analog, digital, or a hybrid business; capitalizing fully on network effects traditionally requires both frequent usage and number of users. Nonetheless, some companies, after reaching a critical mass of users, may think that usage is more important than the number of users (which companies are they?) and they promote regular use evolving into habit and addictions.
This article is intended to be the first chapter of a thorough guide helping you understand the network effect strategies of different contemporary companies and focusing on both successes and failures of network-effects-driven businesses.

Solution to Management Science Series #186: Shareholders of a highly leveraged firm choosing a negative-NPV and highly risky project!

Shareholders of a highly leveraged firm choosing a negative-NPV and highly risky project âť—

Mazingo is a globally prominent toy company producing and marketing high-quality robot toys. Details concerning the company’s current situation is shared.

Calculate the market value of equity and debt for this company.

Additionally investigate the following scenario in which Mazingo considers a project that must be taken now or never and also affects both the market value of the firm’s assets and the firm’s asset return standard deviation.

It is a negative-NPV project that would reduce the market value of firm’s assets by $1.75M while changing firm’s cumulative asset return standard deviation to 77%.

Calculate the market value of equity and debt for Mazingo if it were to take on this project. Whom will the project benefit the most; shareholders or the debtholders?

On Machine Learning Techniques: Interpretability vs More Insight

On Machine Learning Techniques
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Ability to predict a categorical response more reliably is what machine learning techniques are after.

A data scientist may rely on classification and regression trees because the focus is more on prediction than on how each descriptor will contribute to the response.

However, in some special cases, you want to see how a change in the descriptor will change the response and to what extent.

Classification and regression trees facilitate interpretation, but this clear interpretation always comes at the expense of less insight into how each descriptor contributes to the response you are trying to predict.

In this article, I will analyze which method to use and under what condition each method trumps another method.

Solution to Management Science Series #185: Options and Capital Budgeting

Options and Capital Budgeting

Arkham Games is a game studio creating video games for console manufacturers. The following information is shared for the firm.

Calculate the market value of equity and debt for Arkham Games.

Additionally, the firm has two mutually exclusive investments under consideration. The projects will impact both the market value of the firm’s assets and standard deviation of the return on firm’s assets as was shared.

Calculate the market value of equity and debt if Arkham Games chooses Project A? What if it were to choose Project B? Which project would benefit the stockholders the most?

On investment decision rules in finance and why using payback period method misleads you

On investment decision rules in finance ⚠️

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There are many decision and investment rules in finance.

Although there is only one rule that trumps every other, inferior methods are still being used by many companies, even by the most successful ones.

Granted, regardless of whatever investment rule your company is using, estimating future cash flows is an uncertainty for each method.

However, this reality does not change the fact that there is still only one superior investment rule through which you can make sound decisions.

For example, which project would you choose if you were to use payback period method?

Project A requiring an initial investment of $100MM is projected to yield $20MM, $30MM, $50MM, and $35MM for the next four years.

Project B requiring an initial investment of $100MM is projected to yield $50MM, $30MM, $20MM, and $35MM for the next four years.

While solving the question above, I will also demonstrate why payback period may not be reliable in assessing financial viability of projects and what method you should have used given these inherent problems of the payback period.