Sources and References

Primary textbook — Zvi Bodie, Alex Kane, and Alan Marcus, Essentials of Investments, 13th Edition (McGraw-Hill, 2024). [BKM]

Supplementary — Jonathan Berk, Peter DeMarzo, and David Stangeland, Corporate Finance, 5th Canadian Edition (Pearson Canada, 2022), Chapter 4–5 (Time Value of Money). [BDS]

Online resources — MIT OpenCourseWare 15.401 (Finance Theory I); Python for Finance open tutorials (Yves Hilpisch, Python for Finance, O’Reilly, 2nd ed.); CFA Institute introductory materials.

Chapter 1: Investments — Background and Issues

Why Study Investments?

The study of investments addresses a central economic problem: individuals accumulate savings over their working lives and need those savings to generate returns sufficient to fund future consumption (retirement, education, housing). Firms require capital to fund operations and growth, and they obtain it by issuing financial securities. Financial markets match these two groups, and the study of investments examines how securities are priced, how portfolios should be constructed, and how markets behave.

The risk-return tradeoff is the fundamental principle: rational investors require higher expected returns to compensate for bearing higher risk. This tradeoff permeates every investment decision.

The Investment Process

A structured investment process involves:

1. Setting investment policy — defining objectives (target return, risk tolerance), constraints (time horizon, liquidity needs, regulatory restrictions, tax status), and benchmark.
2. Security analysis — evaluating individual securities to identify mispriced assets (top-down or bottom-up analysis).
3. Portfolio construction — combining securities to achieve the target risk-return profile through diversification.
4. Portfolio revision — periodically rebalancing as market conditions and investor circumstances change.
5. Performance evaluation — measuring realized returns against benchmarks and attributing performance to skill vs. luck.

Participants in Financial Markets

Households are the ultimate owners of financial wealth. Firms, governments, and financial intermediaries are conduits through which household savings flow to productive investments.

Institutional investors — pension funds, insurance companies, endowments, sovereign wealth funds — manage large pools of capital on behalf of beneficiaries. Their scale allows access to illiquid investments (private equity, infrastructure, real estate) that are impractical for individual investors.

Market makers post bid and ask prices at all times, providing liquidity in exchange for the bid-ask spread. Arbitrageurs exploit price discrepancies across markets, driving prices toward consistency. Speculators take on risk in hopes of profit, providing liquidity and aiding price discovery.

Chapter 2: Financial Instruments

The Asset Class Taxonomy

Financial instruments are typically organized into three broad asset classes: equities (ownership claims), fixed income (debt claims), and derivatives (contingent claims). Alternative assets — real estate, commodities, private equity, hedge funds — constitute a fourth growing category.

Money Market Instruments

Money market instruments are short-term, highly liquid debt securities with maturities under one year. Their low default risk and high liquidity make them near-cash equivalents used for cash management.

Treasury bills are quoted on a bank discount basis:

where \(d\) is the discount yield, \(F\) is face value, \(P\) is purchase price, and \(n\) is days to maturity. The equivalent bond-equivalent yield is higher because it uses the purchase price as the base and a 365-day year.

Capital Market Instruments — Fixed Income

Government of Canada bonds are the benchmark for domestic fixed income, backed by the full faith and credit of the federal government. Provincial bonds carry modest additional spread due to lower creditworthiness than the federal government but remain investment grade. Corporate bonds carry credit spreads that reflect the issuing firm’s probability of default and expected recovery in default.

Structured products — mortgage-backed securities (MBS), asset-backed securities (ABS), collateralized loan obligations (CLOs) — pool individual loans into securities with varying risk tranches. These instruments played a central role in the 2007–2009 global financial crisis when credit ratings proved inaccurate.

Capital Market Instruments — Equities

Common shares entitle holders to residual earnings (dividends if declared) and a vote in corporate governance. The dividend yield is the annual dividend per share divided by the current stock price; capital gain arises when the selling price exceeds the purchase price.

Preferred shares pay fixed dividends with priority over common shares but typically without voting rights. They exhibit bond-like pricing when dividends are fixed, but with added risks (dividends can be omitted without triggering default).

Chapter 3: Securities Markets — How Trading Works

Market Organization

Securities markets are organized along two dimensions: exchange-traded vs. OTC and order-driven vs. quote-driven.

Exchange-traded markets (TSX, NYSE) use formal listing requirements, centralized price discovery, and standardized contracts. Over-the-counter (OTC) markets consist of dealer networks; trades are negotiated bilaterally. Most bonds, forex, and derivatives trade OTC.

Order-driven markets match buyers and sellers based on submitted orders without a designated market maker. The Toronto Stock Exchange uses a continuous electronic order-matching system. Quote-driven markets rely on dealers who continuously post bid and ask quotes.

Order Types

A market order executes immediately at the best available price. Execution is guaranteed but price is not — in illiquid markets, large market orders can move prices unfavorably (market impact).

A limit order specifies a maximum buying price or minimum selling price. Execution is not guaranteed if the market does not reach the limit price. Limit orders accumulate in the limit order book, visible to market participants (depth of market).

A stop-loss order becomes a market order when price falls to a specified trigger. It limits downside but may execute at an unfavorable price in fast-moving markets.

Short Selling

Short selling allows investors to profit from price declines. The short seller borrows shares, sells them, and later buys them back (covers) to return to the lender. Profit = proceeds from initial sale minus cost to cover.

Risk is theoretically unlimited because prices can rise without bound. Short sellers must post margin and may face short squeezes when a stock price rises sharply, forcing mass covering that accelerates the price increase.

Margin Trading

Buying on margin means borrowing from a broker to purchase securities, using the securities themselves as collateral. The initial margin requirement (set by regulators) specifies the minimum equity the investor must put up. The maintenance margin is the minimum equity ratio before a margin call requires the investor to deposit more funds or liquidate positions.

Margin magnifies both gains and losses (financial leverage effect).

Chapter 4–5: Time Value of Money and Python Analytics

Review of TVM Fundamentals

The time value of money principles that underpin all of quantitative finance were established in AFM 121. In AFM 127, the emphasis is on applying these concepts computationally using Python.

The fundamental relationships:

For a stream of cash flows \(C_1, C_2, \ldots, C_n\):

Python for Financial Analytics

Python has become the dominant language for financial data analysis. Key libraries used in financial applications include:

Computing PV and FV in Python

A present value calculation using numpy:

import numpy as np

r = 0.06        # discount rate
n = 10          # periods
FV = 1790.85    # future value

PV = FV / (1 + r)**n
print(f"PV = ${PV:.2f}")

Computing the present value of a cash flow stream:

import numpy as np

cash_flows = np.array([0, 100, 200, 300, 400, 500])  # index 0 = now
r = 0.08
t = np.arange(len(cash_flows))
pv_factors = 1 / (1 + r)**t
PV = np.dot(cash_flows, pv_factors)
print(f"PV = ${PV:.2f}")

Working with Financial Data

The pandas library is essential for handling time series market data. A typical workflow retrieves price data, computes returns, and performs descriptive statistics:

import yfinance as yf
import pandas as pd

ticker = yf.Ticker("RY.TO")        # Royal Bank on TSX
hist = ticker.history(period="2y") # 2 years of daily data
hist["Return"] = hist["Close"].pct_change()

print(hist["Return"].describe())

Log returns are often preferred in quantitative analysis because they are additive across time:

Whereas simple returns compound multiplicatively, log returns can be summed across periods.

Chapter 7: Bond Prices and Yields

Pricing Bonds

A bond’s price is the present value of its cash flows. For a bond with face value \(F\), annual coupon \(C\), \(n\) periods to maturity, and yield to maturity \(y\):

Most Canadian and US government bonds pay coupons semi-annually, so coupon = (coupon rate × F) / 2, yield is the semi-annual yield, and n is the number of semi-annual periods.

The Term Structure of Interest Rates

The yield curve plots yields to maturity against time to maturity for bonds of the same credit quality. A normal (upward-sloping) yield curve means long-term yields exceed short-term yields — compensation for duration risk and inflation uncertainty. An inverted yield curve (short rates above long rates) has historically been a reliable predictor of recessions.

Three competing theories explain the yield curve’s shape:

1. Expectations theory: Long-term rates equal the geometric average of expected future short-term rates. No term premium.
2. Liquidity preference theory: Long-term rates include a liquidity (term) premium above the expectations component, compensating investors for bearing interest rate risk.
3. Market segmentation theory: Supply and demand in different maturity segments independently determine yields in each segment.

Forward rates are implied future short-term rates embedded in the current yield curve. The forward rate \(f_{n-1,n}\) between periods \(n-1\) and \(n\) is derived from spot rates:

Duration and Interest Rate Risk

Macaulay Duration is the weighted average time to receive a bond’s cash flows:

Modified Duration converts Macaulay Duration into a price sensitivity measure:

The approximate percentage price change for a small change in yield \(\Delta y\):

This approximation improves when combined with the convexity correction:

Convexity is always positive for non-callable bonds: prices rise more than duration predicts when yields fall, and fall less than duration predicts when yields rise.

Chapter 8: Macroeconomic and Industry Analysis

The Top-Down Approach

The top-down approach to security analysis begins with the macroeconomic outlook, then assesses industry prospects, and finally values individual securities. This sequencing reflects the empirical finding that macroeconomic conditions and industry membership explain a large fraction of stock return variation.

Macroeconomic factors that influence financial markets:

• GDP growth: Strong growth supports corporate earnings and equity valuations. Watch the business cycle.
• Inflation: Moderate inflation is consistent with healthy growth; high or rising inflation leads central banks to tighten monetary policy, raising discount rates and depressing asset prices.
• Interest rates: Central bank policy rates (Bank of Canada overnight rate; US Federal Funds rate) cascade through the yield curve, affecting all asset prices through the discount rate.
• Unemployment: A lagging economic indicator, but movements in employment affect consumer spending (personal consumption expenditures are ~60% of GDP in Canada).
• Currency exchange rates: A stronger Canadian dollar reduces competitiveness of exporters; weaker CAD boosts commodity exporters (energy, mining) but raises import costs.

Industry Analysis

Industries differ substantially in their sensitivity to the business cycle:

• Cyclical industries (automobiles, industrials, discretionary consumer goods) see revenues and earnings amplify economic swings.
• Defensive industries (utilities, consumer staples, healthcare) maintain relatively stable earnings through economic cycles.

Porter’s Five Forces framework analyses competitive dynamics within an industry by examining: threat of new entrants, bargaining power of buyers, bargaining power of suppliers, threat of substitute products, and intensity of competitive rivalry. High competitive intensity depresses industry profitability.

The industry life cycle — startup, consolidation, maturity, decline — has valuation implications. Growth companies re-invest heavily and pay few dividends; mature companies generate stable cash flows suited to dividend discount models.

Chapter 9: Equity Valuation

Dividend Discount Models

The fundamental principle is that a share’s value equals the present value of all future dividends. The Gordon Growth Model for a firm with stable, perpetually growing dividends:

For firms with non-constant near-term growth, a multi-stage DDM is used: explicitly project dividends for the high-growth period, then apply the Gordon model as a terminal value.

The PVGO Framework

A stock’s price can be decomposed into the value of the firm as a no-growth perpetuity plus the Present Value of Growth Opportunities (PVGO):

where \(E_1 / k\) is the value if all earnings are paid out as dividends and no reinvestment occurs. PVGO is positive only if the firm invests in projects earning above the required return \(k\).

Free Cash Flow Valuation

An alternative to DDM uses Free Cash Flow to the Firm (FCFF) or Free Cash Flow to Equity (FCFE):

Firm value = PV of FCFF discounted at WACC. Equity value = Firm value minus net debt.

Chapter 10: Financial Statement Analysis (with Python)

Purpose and Framework

Financial statement analysis serves equity valuation (estimating intrinsic value), credit analysis (assessing debt repayment capacity), and managerial assessment (evaluating operational efficiency). The three primary statements — income statement, balance sheet, and cash flow statement — must be read together.

Key Financial Ratios

Profitability Ratios

The DuPont decomposition of ROE is analytically powerful:

This decomposition reveals whether high ROE stems from efficient operations, efficient use of assets, or aggressive use of debt financing.

Liquidity Ratios

Leverage (Solvency) Ratios

Market Value Ratios

Ratio Analysis with Python

import pandas as pd

# Hypothetical income statement data
data = {
    'Year': [2023, 2024],
    'Revenue': [5000, 5500],
    'Net_Income': [400, 462],
    'Total_Assets': [8000, 8500],
    'Total_Equity': [3500, 3800]
}
df = pd.DataFrame(data)

df['Net_Margin'] = df['Net_Income'] / df['Revenue']
df['ROA'] = df['Net_Income'] / df['Total_Assets']
df['ROE'] = df['Net_Income'] / df['Total_Equity']

print(df[['Year', 'Net_Margin', 'ROA', 'ROE']].round(4))

Quality of Earnings

Reported earnings are subject to accounting choices (revenue recognition, depreciation methods, inventory valuation). Analysts examine accruals — the difference between reported earnings and cash flow from operations — as a quality indicator. High accruals relative to assets signal aggressive accounting.

Firms with high accrual ratios tend to have lower subsequent earnings and lower stock returns (the accruals anomaly).

Chapter 11: Group Presentation and Applied Finance

Equity Research Process

A professional equity research report integrates top-down macro analysis, industry assessment, financial statement analysis, and intrinsic value estimation into an actionable investment recommendation (Buy/Hold/Sell) with a price target.

The structure of a standard equity research report:

1. Executive Summary — investment thesis, recommendation, price target, key risks.
2. Business description — what the company does, competitive positioning.
3. Industry outlook — Porter’s Five Forces, growth drivers, regulatory environment.
4. Financial analysis — historical financials, ratio trends, segment analysis.
5. Valuation — DDM, DCF, comparables analysis (using trading and transaction multiples).
6. Risks — downside scenarios, sensitivity analysis.

Scenario and Sensitivity Analysis

No valuation model is precise. The appropriate response is not to hide uncertainty but to model it explicitly:

• Scenario analysis: Define a base case, bull case, and bear case reflecting different economic outcomes. Compute intrinsic value under each.
• Sensitivity analysis: Change one input at a time (e.g., the discount rate or growth rate) and observe the resulting change in estimated price.

In Python, a sensitivity table for a Gordon Growth Model valuation can be generated using nested loops or pandas pivot tables, varying both \(k\) and \(g\) systematically.

Communication of Analytical Findings

Analytical work that cannot be communicated effectively has limited value. Investment presentations should lead with the conclusion (the recommendation), support it with evidence structured in a logical hierarchy, anticipate counterarguments, and quantify uncertainty. Data visualization (time series charts, bar charts for segment revenues, waterfall charts for earnings bridges) enhances comprehension when used purposefully rather than decoratively.