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Objective: You are using the conclusion and stock & factor analysis to further expand on helping us. We need you to construct a quantitatively optimized portfolio for our client based on 8-10 stocks from the food, airline, financial, and medical industries, and conduct an in-depth analysis using coding and statistical methods.

Tools: Python/R (with libraries such as pandas, numpy, scikit-learn, statsmodels, matplotlib, seaborn), Excel, and financial data APIs.

Part 1: Portfolio Overview

Slide 1: Portfolio Asset Allocation

  • Data Collection: Use a financial API to programmatically download stock price data for the selected stocks for the past five years. Store this data in a dataframe for analysis.
  • Portfolio Metrics: Code custom functions or utilize libraries to calculate:
  • Portfolio returns for the past 1, 3, and 5 years.
  • Portfolio Sharpe, Beta, Treynor, and Information Ratio.
  • Benchmark Analysis: Select a relevant benchmark or index for your portfolio. Use the API to download this data and graph it against the portfolio performance.
  • Visualization: Use Python’s matplotlib or seaborn for visual representation, ensuring interactivity where possible.

Part 2: Stock Selection (16-20 slides)

Each stock will have one to two slides. Note: Combine quantitative analysis with qualitative insights.

  1. Problem Identification:
  • Why this sector? Support with coded quantitative trend analysis.
  • Why this stock? Use statistical summaries.
  • Why now? Highlight timing or cyclicality.
  1. Sector Analysis:
  • Code a trend analysis of the sector over the past decade. Visualize the sector’s growth, volatility, and other key metrics.
  • Use quantitative data to support why the sector is attractive right now.
  1. Industry Trends:
  • Programmatic retrieval and analysis of recent news articles or financial reports about the sector using NLP (Natural Language Processing) tools to identify prevalent trends.
  1. Valuation & Share Performance:
  • Automate data extraction for key valuation statistics.
  • Plot stock price history and relevant share statistics.
  1. Revenue Drivers:
  • Historical highlights from 2019-2023 – programmatically compare to sector averages.
  • 2024 Forecast using regression or time-series prediction models.
  1. Valuation Football Field:
  • Automate retrieval for:
  • 52 Week Price Range
  • Analyst Estimates
  • Comparables
  • Precedents
  1. Technical Analysis Highlights:
  • For each stock, use Python libraries like TA-Lib to compute:
  • Bollinger Bands, Chaikin A/D Line, On Balance Volume, etc.
  • Visualize these metrics and highlight anomalies or significant patterns.
  • Provide coded analysis for 3-5 technical indicators per stock. Comment on the implications of each.

Part 3: Factor Investing Analysis (4-6 slides)

Factor investing involves selecting assets based on attributes that are associated with higher returns. Common factors include size (small-cap vs. large-cap), value (cheap vs. expensive), and momentum (stocks that are trending).

Objective: Identify and quantify the impact of chosen factors on the returns of the stocks in your portfolio.

  1. Factor Selection:
  • Choose 3-5 factors you believe might be influencing the stocks in your portfolio. Some common factors include:
  • Size (Market Capitalization)
  • Value (Price-to-Book ratio, Price-to-Earnings ratio)
  • Momentum (Past 6-12 month returns)
  • Quality (Return on Equity, Debt-to-Equity ratio)
  • Volatility
  1. Factor Performance:
  • Analyze how each factor has performed over the past 5 years. This will help in understanding which factors have been rewarding investors.
  1. Factor Exposure:
  • Quantify how much of the stock returns can be attributed to its exposure to the chosen factors. Use regression analysis for this.
  1. Factor Diversification:
  • Examine how adding factor-based assets to the portfolio could impact its diversification and potential returns.


import pandas as pd

import statsmodels.api as sm

import yfinance as yf

# Download stock data

stock_data =‘AAPL’, start=’2018-01-01′, end=’2023-01-01′)

# Compute returns

stock_data[‘returns’] = stock_data[‘Close’].pct_change().dropna()

# Let’s say we are considering Size and Momentum as factors. For simplicity, we’ll create mock data for these factors.

# In a real-world scenario, you’d fetch or compute factor data.

stock_data[‘size’] = (stock_data[‘Close’] * stock_data[‘Volume’]).rolling(window=50).mean()

stock_data[‘momentum’] = stock_data[‘Close’].rolling(window=50).mean()

# Regression analysis to find exposure to factors

X = stock_data[[‘size’, ‘momentum’]].dropna()

X = sm.add_constant(X)

y = stock_data[‘returns’].loc[X.index]

model = sm.OLS(y, X).fit()


# This will give you the beta values for each factor, telling you about the stock’s exposure to each factor.


Four Basic Methodologies you may use on the stock selection period –

  • Comparable Company Analysis
  • Precedent Transaction Analysis
  • Discounted Cash Flow Analysis
  • Leveraged Buyout/ Recap Analysis

Methodologies Reference

Part 1. Comparable Company Analysis

A comparable company analysis (CCA) is a process used to evaluate the value of a company using the metrics of other businesses of similar size in the same industry. Comparable company analysis operates under the assumption that similar companies will have similar valuation multiples, such as EV/EBITDA.

Company Information –

  • This includes Company Name, Ticker, and Price. The ticker is a unique symbol given to the company to identify publicly listed companies.
  • You may take Bloomberg, Reuter’s tickers as well. Also, note that the prices that we take here are the most recent prices.
  • We make the table in such a way that these prices are linked to the database where they would get updated automatically.

Size of the company –

  • This includes Market Capitalization and Enterprise Value.
  • We normally sort the table on the basis of Market Capitalization. Market Capitalization also provides us pseudo for the size of the company.
  • Enterprise Value is the current Market-based valuation of the firm.
  • We may not want to compare a small market capitalization company with a large capitalization company.

Valuation Multiples –

  • This should include 2 to 3 appropriate valuation tools for comparison
  • We should ideally show one year of historical multiple and two years of forwarding multiples (estimated)
  • Choosing an appropriate valuation tool is the key to successfully valuing the company.

Operating Metrics –

  • This may include fundamental ratios like Revenue, growth, ROE, etc
  • This is important so that we can understand the fundamentals of the company at once.
  • You may include Profit Margins, ROE, Net Margin, Leverage, etc to make this comp more meaningful.

Summary –

  • This is a simple mean, median, low and high of the above metrics
  • Mean and Median provides core insights to the fair valuation
  • If a company’s multiple is above the mean/median, we tend to infer that the company may be
  • overvalued
  • Likewise, if the multiple is below the mean/median, we may infer undervalued.
  • High and Low also helps us in understanding the outliers and a case to remove those if they are too far away from the Mean/Median.

Part 2. Precedent Transaction Analysis

Precedent transaction analysis is a method of company valuation where past M&A transactions are used to value a comparable business today.

Precedent transaction analysis relies on publicly available information to create a reasonable estimate of multiples or premiums that others have paid for a publicly traded company. The analysis looks at the type of investors that have purchased similar companies under similar circumstances in the past and examines whether the companies making the acquisitions are likely to make another acquisition soon.

One of the most important components of precedent transaction analysis is identifying the transactions that are the most relevant. First, companies should be chosen based on having similar financial characteristics and for being in the same industry. Second, the size of the transactions should be similar in size to the transaction that is being considered for the target company. Third, the type of transaction and the characteristics of the buyer should be similar. Transactions that occurred more recently are considered more valuable in terms of usefulness for analysis.

Commonly referred to as “precedents”, this method of valuation is common when trying to value an entire business as part of a merger/acquisition and is commonly prepared by analysts working in investment banking, private equity, and corporate development.

Steps to Perform Precedent Transaction Analysis:

#1 Search for relevant transactions

The process begins by looking for other transactions that have happened in (ideally) recent history and are in the same industry.

The screening process requires setting criteria such as:

  • Industry classification
  • Type of company (public, private, etc.)
  • Financial metrics (revenue, EBITDA, net income)
  • Geography (headquarters, revenue mix, customer mix, employees)
  • Company size (revenue, employees, locations)
  • Product mix (the more similar to the company in question the better)
  • Type of buyer (private equity, strategic/competitor, public/private)
  • Deal size (value)
  • Valuation (multiple paid i.e. EV/Revenue, EV/EBITDA, etc.)
  • The above criteria can be set in a financial database, such as Bloomberg or CapIQ, and exported to Excel for further analysis.

#2 Analyze and refine the available transactions

Once the initial screen has been performed and the data is transferred into Excel then it’s time to start filtering out the transactions that don’t fit the current situation.

In order to sort and filter the transactions, an analyst has to “scrub” the transactions by carefully reading the business descriptions of the companies on the list and removing any that aren’t a close enough fit.

Many of the transactions will have missing and limited information if the deal terms were not publicly disclosed. The analyst will search high and low for a press release, equity research report, or another source that contains deal metrics. If nothing can be found, those companies will be removed from the list.

#3 Determine a range of valuation multiples

When a shortlist is prepared (following steps 1 and 2) the average, or selected range, of valuation multiples can be calculated.

The most common multiples for precedent transaction analysis are EV/EBITDA and EV/Revenue.

An analyst may exclude any extreme outliers such as transactions that had EV/EBITDA multiples much lower or much higher than the average (assuming there is a good justification for doing so).

#4 Apply the valuation multiples to the company in question

After a range of valuation multiples from past transactions has been determined, those ratios can be applied to the financial metrics of the company in question.

For example, if the valuation range was:

5x EV/EBITDA (low)

0x EV/EBITDA (high)

And the company in question has EBITDA of $150 million,

The valuation ranges for the business would be:

$675 million (low)

$900 million (high)

#5 Graph the results (with other methods) in a football field

Once a valuation range has been determined for the business that’s being valued it’s important to graph the results so they can be easily understood and compared to other methods.

The Football field chart is the best way to illustrate the various methods on one page in a simple way.

The main valuation methods included in the chart are:

Comparable company analysis

Precedent transactions analysis

DCF analysis

Ability-to-pay analysis

52-week hi/lo (if a public company)

Part 3. DCF analysis

Only needed if your target firm is public

The discounted cash flow (DCF) analysis represents the net present value (NPV) of projected cash flows available to all providers of capital, net of the cash needed to be invested for generating the projected growth. The concept of DCF valuation is based on the principle that the value of a business or asset is inherently based on its ability to generate cash flows for the providers of capital. To that extent, the DCF relies more on the fundamental expectations of the business than on public market factors or historical precedents, and it is a more theoretical approach relying on numerous assumptions. A DCF analysis yields the overall value of a business (i.e. enterprise value), including both debt and equity.

Some info about DCF

1. Cash Flow (CF) DCF Formula – Cash Flow

Cash Flow (CF) represents the free cash payments an investor receives in a given period for owning a given security (bonds, shares, etc.)

When building a financial model of a company, the CF is typically what’s known as unlevered free cash flow. When valuing a bond, the CF would be interest and or principal payments.

To learn more about the various types of cash flow, please read CFI’s cash flow guide.

2. Discount Rate (r) DCF Formula – Discount Rate

For business valuation purposes, the discount rate is typically a firm’s Weighted Average Cost of Capital (WACC). Investors use WACC because it represents the required rate of return that investors expect from investing in the company.

For a bond, the discount rate would be equal to the interest rate on the security.

3. Period Number (n) DCF Formula – Period

Each cash flow is associated with a time period. Common time periods are years, quarters, or months. The time periods may be equal, or they may be different. If they’re different, they’re expressed as a decimal.

What is the DCF Formula Used For?

The DCF formula is used to determine the value of a business or a security. It represents the value an investor would be willing to pay for an investment, given a required rate of return on their investment (the discount rate).

Examples of Uses for the DCF Formula:

To value an entire business

To value a project or investment within a company

To value a bond

To value shares in a company

To value an income-producing property

To value the benefit of a cost-saving initiative at a company

To value anything that produces (or has an impact on) cash flow

Part 4. Leveraged buyout analysis/ Recap Analysis

No valuation needed here, only rationales and selecting candidate for LBO

A leveraged buyout is the acquisition of a company, either privately held or publicly held, as an independent business or from part of a larger company (a subsidiary), using a significant amount of borrowed funds to pay for the purchase price of the company. The leveraged buyout transaction is orchestrated by a private equity firm (also called a financial sponsor) or group of private equity firms (also called a private equity group or a consortium), which will take ownership (own the equity of) the business after the acquisition has been completed.

The purchase of the company comes from a combination of equity capital (contributed by the sponsor/consortium, plus potentially some tag-along investors, such as management) and debt instruments (financed through banks and other lenders). Generally speaking, the debt will constitute a majority of the purchase price—after the purchase of the company, the debt/equity ratio is typically around 2.0x or 3.0x (i.e., usually the total debt will be about 60-80% of the purchase price).

In an LBO, the cash flow generated by the acquired company is used to service (pay interest on) and pay down (pay principal on) the outstanding debt. For this reason, while companies of all sizes and industries can be targets of LBO transactions, companies that generate a high amount of cash flow are the most attractive (more on this later).

The overall return for the sponsor or consortium in an LBO is determined by a number of factors:

Growth in the operating profit/cash flow of the company (EBIT or EBITDA) over the life of the investment;

The exit multiple on EBIT/EBITDA relative to the entry or acquisition multiple; and

The amount of debt that is paid off over the time horizon of the investment.

Investment bankers typically use LBO analysis to obtain an LBO market value for a company. This can act as a “floor” for company valuation, because it provides a reasonable amount that financial investors (sponsors) would be willing to pay to own the company, whereas other investors may be willing to pay more for a variety of reasons. Other typical uses of LBO modeling include:

Determining the equity returns (through IRR calculations) that can be achieved if a company is bought privately, improved, and then ultimately sold or taken public

Determining the effect of recapitalizing the company through issuance of debt to replace equity

Determining the debt service limitations of a company based on its cash flows

A company capable of successfully undergoing an LBO typically possesses the following characteristics:

· Mature industry and/or company: The stock price of the target company is trading at a lower multiple to free cash flow than new companies in high-growth industries. This enables the LBO purchaser to buy the company at a relatively low cost compared to the annual cash flow it produces; this cash flow will be a key ingredient in generating an attractive return for the investors.

· Clean balance sheet with no or low amount of outstanding debt: Buyers need the ability to be able to use new debt, or “leverage” as the name suggests, as part of the acquisition consideration. Companies with high levels of pre-existing debt limit the amount of new debt that it can withstand, and new debt is crucial for the LBO. (Note that if a company has existing debt, that existing debt will often need to be refinanced in an LBO, because the financial sponsor will need to remove pre-existing financial covenants and limitations to fit the new capital structure.)

· Strong management team and potential business improvement measures: Management is capable of running the company effectively, and capable of creating a more efficient company (lower costs) or expanding into new profitable markets or products.

· Strong competitive advantages and market position: It is ideal if the company is in a good position within its market space (relative to current and potential competitors)—this will help shield the company from competitive pressures that might reduce profit margins (and therefore cash flows) and will help provide possible growth opportunities for the business.

· Steady cash flows: Stable, recurring cash flows are necessary, as that cash flow is needed every year to service the large debt burden for the LBO (especially in the first several years post-acquisition). Cyclical or highly seasonal companies, therefore, can run into trouble quickly if a downturn occurs. Debt pay-down is also important in that it increases the equity/total assets ratio of the company, boosting investor returns.

· Low future capital expenditure and working capital requirements: Part of the return LBO investors seek will be generated from growing the business, and growth costs cash in the short-term: growth must be used to finance new capital expenditures and new working capital requirements for the business. Therefore businesses that have relatively high capital expenditure and working capital requirements will be less attractive for an LBO.

· Possible sale of underperforming/non-core assets: Some companies that are purchased via LBO will have divisions or side businesses that are performing weakly or are a distraction to management. Often, these businesses can be sold to raise cash to pay off outstanding debt that is used in the purchase of the company. Note that these assets should not represent a significant portion of the company’s current cash flow: selling the business means losing that future cash flow, and cash flow is needed to pay off debt and interest.

· Feasible exit options: Once the business has been improved and some of the debt used to purchase the business has been paid off, an LBO investor would generally like to exit—that is, sell—the company fairly quickly (a typical timeframe is 3-5 years after purchase). Holding the company beyond the optimal selling point will reduce the expected annual return on the investment, because leverage decreases every year. Therefore an analyst considering an LBO opportunity might want to consider how the company can be sold (typically via strategic sale to another company, an Initial Public Offering, or sale to another LBO investor). Any historical LBO, M&A, or IPO precedents in the LBO candidate’s industry might give an indicator as to how easily the company can be sold when it is ready for sale.

Recap Analysis

Recapitalization (“recap”) accounting refers to accounting for the repurchase, by a corporation, of its own common stock. The price paid for the common stock is booked as a decrease to shareholders’ equity, and the repurchased shares are held as treasury stock. The treasury shares may be reissued at a later date or retired. There is no adjustment to the basis of the assets or liabilities of the company.

Recap LBOs are transactions that are accounted for by the target company as the sale of equity securities, the issuance of new debt, the retirement of existing debt, and the purchase and retirement of treasury stock. The practice of using recap accounting in the context of an LBO offer a potential benefit to the acquirer to the extent that reported earnings are not burdened by the potentially higher depreciation associated with the excess of the purchase price over the book value of the net assets acquired. The higher reported earnings are typically viewed as beneficial for an eventual IPO of the acquired business.

The use of recaps to effectively increase earnings was more advantageous before the FASB eliminated the amortization of goodwill (SFAS 142). Recap accounting is still somewhat relevant, since non-goodwill intangibles, which may be significant for certain service and non-industrial businesses, continue to require amortization.


To avoid push-down accounting rules (asset write-ups and the creation of a new goodwill intangible asset), a residual equity interest must be maintained by some group of original shareholders. The amount of residual equity ownership required is not explicitly identified by the SEC, but it generally ranges from a minimum of 5% to 20%, subject to the specific facts and circumstances of the transaction.

No new company structure can be used in connection with the transaction; all activities must be effected by the existing company.


Recapitalization accounting is a method of avoiding “push-down” of purchase accounting adjustments (i.e. write-up of assets) into a target company’s standalone financial statements.

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