Leveraging MBA Skills in a Capstone Project: A Derivative Portfolio Case Study

Applying Business Analytics to Investment Management: A Journey from Theory to Practice

Embarking on my MBA journey, I anticipated numerous group projects that would allow me to apply theoretical knowledge to practical business scenarios. Indeed, I had several opportunities to work on various projects, including case competitions and pro bono consulting for local businesses. Still, I considered the capstone project as the apex of practical learning in the MBA program. Thus, in this post, I'll recap the project and my collaboration with our project sponsor.

During my two-year MBA journey at Tepper, I'm proud to have discovered my strengths and passion. Initially, I was inclined towards finance, but I soon realized my genuine interest lies in analyzing diverse phenomena, whether it's financial data or generic business data. Recognizing this, I chose to pursue the business analytics track at Tepper, a pioneer in the field. My final assignment was a course project in collaboration with an investment management company, aligning perfectly with my newfound interest.

Our client aimed to enhance market exposure—essentially increasing leverage—while simultaneously capping downside risk. Their approach was twofold; firstly, they wanted to test the feasibility of their strategy through a quantitative model. Secondly, they aimed to survey potential clients' reactions. Thus, their approach integrated both quantitative and behavioral finance perspectives.

Applying Newfound Skills and Knowledge to the Project

Interestingly, the project was closely aligned with my past experience, having worked in financial engineering and as a commodity trading advisor. I had previously assisted clients with similar goals and conducted financial simulations for them. However, upon volunteering to work on portfolio building and testing the strategy, I realized how much I had grown during my MBA journey.

My post-MBA self is now much more proficient in handling large data sets, aided by an arsenal of advanced tools and enhanced Python skills. Coupled with my background in Machine Learning, I found it easier to tackle analytic challenges. For instance, I conducted all the analyses using a notebook file.

Tepper's diverse courses enhanced my analytical capabilities, helping me navigate data more efficiently and confidently. Not only did the finance courses solidify my understanding of derivative portfolios, but the analytic courses also equipped me to handle data anomalies, understand the characteristics of a good data set, and preempt potential issues during analysis. This knowledge greatly reduced the time and effort required for data preparation and pre-processing.

During my MBA journey, I learned the invaluable skill of simplification—a key competency for effective management. Simplification demonstrates a thorough understanding of a problem and facilitates effective communication of critical points to others.

A Simplified, Leveraged Portfolio

For the capstone project, I developed a derivative portfolio, simplifying the process by adding options to a market portfolio represented by the S&P500. The real challenge lay in determining various factors influencing option pricing. To reflect reality as closely as possible, I used implied volatility and consulted the project professor to utilize VIX as the best estimator for market volatility.

The quantitative simulation was based on Monte Carlo simulation, involving random sampling of data from a historical dataset. I incorporated historical data such as VIX and interest rates to ground the Black-Scholes model parameters in historical reality. The strike price was the only variable chosen randomly from a uniform distribution, indicating a slightly In-The-Money (ITM) options strategy.

The portfolio allocated only 10% to options, following industry norms to cap downside risk. This resulted in a risk reduction of 10% compared to a non-leveraged portfolio. Below are more details on the methodologies.

Black Scholes Model

The foundation of our approach lies in the Black-Scholes model. The Black-Scholes model is a method of estimating the price of an options contract. It provides a theoretical estimate of the price of European-style options and is widely used by options traders.

Here's an implementation of the Black Scholes Model:

import math
from scipy.stats import norm

def black_scholes(option_type, S, X, T, r, sigma, delta_flag=False):
    d1 = (math.log(S / X) + (r + 0.5 * sigma ** 2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)

    if option_type == 'call':
        option_price = S * norm.cdf(d1) - X * math.exp(-r * T) * norm.cdf(d2)
        delta = norm.cdf(d1)
    elif option_type == 'put':
        option_price = X * math.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
        delta = norm.cdf(d1) - 1
    else:
        raise ValueError("Option type must be either 'call' or 'put'")

    if delta_flag:
        return option_price, delta

    return option_price

(As I continue working on various projects, I plan to enrich this blog with additional features like 'code block'. Until then, you can check my GitHub for the code details.)

Random Sampling from Historical Data

The next step is to randomly select dates and their associated parameters such as returns, volatility, and risk-free rates. These parameters will be used in the Black-Scholes model to compute the option price and delta. Our simulation uses a 3-month timeframe, starting from the randomly chosen date.

Derivative Portfolio Simulation

I simulate the investment over a 25-year period. I begin by investing a certain amount into the equity and continue to invest a monthly amount into the portfolio.

A portion of the investment (defined by 'alpha') is allocated to call options, and the rest is allocated to the equity. This is the "leveraged" portion of our investment. For the equity portion, the investment grows by the randomly selected return. The call options portion of the investment grows by the return on the call option.

Here's an outline of the simulation process:

Initialize the simulation parameters.
Run the simulation for a specified number of times. For each simulation, it randomly samples returns for both equity and call options, and updates the investment value accordingly.
The simulation returns the final investment values for each run.

Implementing the Simulator

Our simulation runs for 25 years, with each year divided into months. In each month, a portion of the portfolio is invested in equity and a portion in options. The proportion invested in options is determined by the leverage plan, defined by the 'start_year' and 'end_year' parameters. If the current year falls within this range, a fraction (10% in our case) of the total portfolio is allocated to options.

Conclusion

In conclusion, I created a derivative portfolio that compared various scenarios to examine the differences between leveraged and non-leveraged strategies. While I won't reveal the final reconciliation of analytic and behavioral finance, I can attest that this capstone project showcased my skillset application and team collaboration abilities.