FIN6123 Investment Management and Analysis
Lecture 3: Equity Valuation and Return Prediction
Xiao (Shaun) Ren
Shenzhen Finance Institute
The Chinese University of Hong Kong, Shenzhen
Fall 2025
1
Equity Investment Analysis
• Fundamental analysis: The analysis which considers macro and
micro fundamentals that may impact future price changes
• Top-down approach: Forecasts price movements based on overall economic
environment
• Bottom-up approach: Forecasts price movements based on a company’s
financial metrics
• Technical analysis: The analysis which forecasts price movements
based on past market data
2
Fundamental Analysis (Top-down)
• The macroeconomy affects firms’ earnings
• Stock prices tend to move along with earnings 3
Fundamental Analysis (Top-down)
• Questions about the top-down approach
• What are some reliable indicators for macroeconomy condition?
• Which industries are procyclical? Which ones are countercyclical?
• Why does monetary policy affect stock returns?
• What types of firms are more sensitive to monetary policy shocks?
• Is the top-down approach useful for predicting stock returns?
• We will discuss the relationship between macroeconomy, monetary
policy, and stock returns in detail in Week 9
4
Fundamental Analysis (Bottom-up)
• The purpose of fundamental analysis (the bottom-up approach) is to
identify stocks that are mispriced relative to some measure of “true”
value that can be derived from observable financial data
• Fundamental analysis methodologies
• Valuation by comparables
• Dividend discount models
• Free cash flow models
5
Valuation by Comparables
• Compare financial metrics of a company with those of “comparable
companies” (usually use industry/market average, etc.). For example:
• Price to earnings ratio (P/E ratio): Share price divided by earnings per share
• Price to book ratio (market to book ratio): Share price divided by book value
per share
• Price/earnings to growth ratio (PEG ratio): P/E ratio divided by earnings
growth rate
6
Valuation by Comparables (Example)
• P/E ratio and Price/book ratio of Microsoft seem to suggest that Microsoft is “undervalued”
• But can we be confident about this inference? 7
Expected Return vs. Required Rate of Return
• Assume a one-year holding period on ABC stock
• The stock has an expected dividend per share, E(D1), of $4
• The current price of a share, Po, is $48
• The expected price at the end of a year, E(P1), is $52
• The expected holding-period return on the stock is calculated as
𝐸 𝐷1 + 𝐸 𝑃1 − 𝑃0 4 + 52 − 48
𝐸 𝑟 = = = 16.7%
𝑃0 48
• Suppose that the risk-free rate, rf, is 6%, the expected market return, E(rM), is 11%, and
the beta of ABC is 1.2. We can calculate the required rate of return for ABC using the
CAPM equation
𝑘 = 𝑟𝑓 + 𝛽𝑀 𝐸 𝑟𝑀 − 𝑟𝑓 = 6% + 1.2 × 5% = 12%
• The expected return of ABC exceeds its required rate of return. ABC should be included
in an actively managed portfolio. 8
Intrinsic Value vs. Market Price
• Another way to interpret these numbers is to compare the intrinsic value of a share of
stock to its market price
• The intrinsic value, V0, is the present value of all cash flows to the stockholder, including
dividends as well as the proceeds from sale of the stock, discounted at the appropriate
risk-adjusted discount rate, k.
• If the intrinsic value of a stock exceeds the market price, the stock is considered undervalued and a
good investment
• The intrinsic value of ABC is calculated as
𝐸 𝐷1 + 𝐸(𝑃1 ) $4 + $52
𝑉0 = = = $50
1+𝑘 1.12
• Since the current market price of ABC is $48, ABC is undervalued
• The market consensus value of k is often referred to as the market capitalization rate
9
Dividend Discount Model
• Dividend discount model (DDM):
• Suppose an investor holds a stock for a period of time and sells it in the future
• The investor receives dividend payment at the end of every period
• Price of the stock should be the total present value of the projected dividend
payments and the expected selling price
𝐷𝑡 𝑃𝑇
• 𝑉0 = σ𝑇𝑡=1 +
(1+𝑘)𝑡 (1+𝑘)𝑇
• 𝑉0 : Stock price at time 0
• 𝑇: Number of periods forecasted
• 𝐷𝑡 : Dividend payment at time t
• 𝑃𝑇 : Expected stock price at time T
• k: Required rate of return
10
Dividend Discount Model (Example)
• For example, if a company’s cost of equity is 12%. Given the
following projected dividends and expected stock price, calculate the
stock price at the end of 2020.
Year 2021 2022 2023
Projected dividend ($) 2 2.5 3
Expected stock price ($) 20
2 2.5 3+20
• 𝑉2020 = + + = $20.15
(1+12%) (1+12%)2 (1+12%)3
11
Constant-growth DDM
• Constant-growth DDM (Gordon model):
• Suppose an investor holds a stock indefinitely
• Dividend payment grows at a constant growth rate
𝐷1
• 𝑉0 =
𝑘−𝑔
• g: Constant dividend growth rate
• Example: Suppose a company paid a $3.81 dividend per share at the end of
2020. The company has a cost of equity of 12% and a constant dividend
growth rate of 5%. Calculate the share price at the end of 2020.
3.81×(1+5%)
• 𝑉2020 = = $57.15
12%−5%
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Two-stage DDM
• A DDM that involves a non-constant-growth stage and a constant-
growth stage
• Expected price of the stock at the end of the non-constant growth stage
estimated using constant DDM
𝐷𝑇+1
𝑇 𝐷𝑡 𝑘−𝑔
• 𝑉0 = σ𝑡=1 +
(1+𝑘)𝑡 (1+𝑘)𝑇
13
Two-stage DDM (Example)
• For example, if a company’s cost of equity is 12%. Given the following
projected dividends and a constant dividend growth rate at 5% after 2023,
calculate the stock price at the end of 2020.
Year 2021 2022 2023
Projected dividend ($) 2 2.5 3
3×(1+5%)
2 2.5 3+ 12%−5%
• 𝑉2020 = + + = $37.94
(1+12%) (1+12%)2 (1+12%)3
14
Stock Prices and Investment Opportunities
• Consider two companies, Cash Cow, Inc., and Growth Prospects, Inc.
• Each company has expected earnings in the coming year of $5 per share
• Both companies pay out all their earnings as dividends
• Neither company will have growth in earnings (and therefore dividends)
• If the market capitalization rate is 12.5%, both companies would be
𝐷1 $5
valued at = = $40 per share
𝑘 12.5%
15
Stock Prices and Investment Opportunities
• Suppose that Growth Prospects, Inc. has a project that will generate a
return on investment of 15%
• The return on investment is higher than the required rate of return on
equity, the company should invest earnings in the project
• Suppose that Growth Prospects chooses a lower dividend payout
ratio (dividend divided by earnings) at 40%
• 60% of earnings will be reinvested in the project (plowback ratio or
earnings retention ratio)
• The dividend of Growth Prospects will be $2 instead of $5
16
Stock Prices and Investment Opportunities
• Since Growth Prospects reinvest part of its earnings, its future earnings (and therefore dividends)
will grow over time
• The growth rate of dividends can be calculated as return on investment multiplied by plowback
ratio:
𝑔 = 𝑅𝑂𝐸 × 𝑏 = 15% × 60% = 9%
• Now the stock price of Growth Prospects will be
𝐷1 $2
𝑃0 = = = $57.14
𝑘 − 𝑔 12.5% − 9%
• The value of a firm can be seen as the sum of the value of assets in place and the present value of
growth opportunities (PVGO)
𝐸1
𝑃0 = + 𝑃𝑉𝐺𝑂
𝑘
$5
• For Growth Prospects, $57.14 = + 𝑃𝑉𝐺𝑂, PVGO = $17.14
12.5%
17
Dividend Growth and Investment Opportunities
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P/E Ratio and Growth Opportunities
• Now let’s think more about using P/E ratio as a valuation metric
$40
• Cash Cow Inc.’s P/E ratio is =8
$5
$57.14
• Growth Prospects Inc.’s P/E ratio is = 11.4
$5
• This suggests that P/E ratio is a useful indicator of expectations for growth
opportunities
𝑃0 1 𝑃𝑉𝐺𝑂
= (1 + )
𝐸1 𝑘 𝐸 1
𝑘
𝐷1
• We can also rearrange the constant-growth DDM formula 𝑃0 =
𝑘−𝑔
𝐸1 (1−𝑏) 𝑃0 1−𝑏
𝑃0 = and then =
𝑘−𝑔 𝐸1 𝑘−𝑔
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P/E Ratio and Growth Opportunities
• Mature companies with low growth potential are often referred to as value
firms
• For example, utility companies
• These firms have lower P/E ratios (or lower market-to-book ratios)
• Young companies with high growth potential are often referred to as growth
firms
• For example, high-tech companies
• These firms have higher P/E ratios (or higher market-to-book ratios)
• On average, value firms have higher expected returns than growth firms
• This return spread (called the value premium) is not explained by the CAPM model
• However, value premium exists because value firms are riskier than growth firms, and
the risk is not captured by CAPM
20
Free Cash Flow Models
• Approach 1: Using free cash flow for the firm (FCFF)
• Estimate FCFFs for a projection period and terminal value
• Estimate enterprise value as the total present value of FCFFs and the terminal
value
• Imply equity value using enterprise value
• Approach 2: Using free cash flow to equity holders (FCFE)
• Estimate FCFEs to equity holders for a projection period and terminal value
• Estimate equity value as the total present value of FCFEs and the terminal
value
21
Valuation Using FCFF
• Step 1: 𝐹𝐶𝐹𝐹 = 𝐸𝐵𝐼𝑇 × 1 − 𝑇 + 𝐷&𝐴 − 𝐶𝐴𝑃𝐸𝑋 − 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑁𝑊𝐶
• EBIT: Earnings before interest and taxes
• T: Marginal tax rate
• D&A: Depreciation and amortization
• CAPEX: Capital expenditures
• NWC: Net working capital
𝐹𝐶𝐹𝐹
𝑇+1
• Step 2: 𝑇𝑉 = 𝑊𝐴𝐶𝐶−𝑔
• TV: Terminal value
• WACC: Weighted average cost of capital
• g: Perpetuity growth rate of free cash flow
𝐹𝐶𝐹𝐹 𝑇𝑉
• Step 3: 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑣𝑎𝑙𝑢𝑒 = σ𝑇𝑡=1 (1+𝑊𝐴𝐶𝐶)
𝑡
𝑡 + (1+𝑊𝐴𝐶𝐶)𝑇
𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑣𝑎𝑙𝑢𝑒−𝐷𝑒𝑏𝑡−𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑠𝑡𝑜𝑐𝑘−𝑁𝑜𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡+𝐶𝑎𝑠ℎ 𝑎𝑛𝑑 𝑐𝑎𝑠ℎ 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡𝑠
• Step 4: 𝑉0 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
22
Valuation Using FCFF (Example)
Year 2022 2023 2024
EBIT 1500 1600 1650
Taxes 450 480 495
D&A 100 150 200
CAPEX 100 100 150
Changes in NWC 200 250 300
FCFF 850 920 905
Marginal tax rate 30%
WACC 12%
Perpetuity growth rate 2%
Debt 3000
Preferred stock 500
Noncontrolling interest 200
Cash and cash equivalents 300
Number of shares outstanding 200
• Step 1: For example, 𝐹𝐶𝐹𝐹2022 = 1500 × 1 − 30% + 100 − 100 − 200 = $850
905×(1+2%)
• Step 2: 𝑇𝑉 = = $9,231
12%−2%
850 920 905+9231
• Step 3: 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑣𝑎𝑙𝑢𝑒 = + + = $8,706.95
1+12% (1+12%)2 (1+12%)3
8706.95−3000−500−200+300
• Step 4: 𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 = = $26.53
200
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Valuation Using FCFE
• Step 1: 𝐹𝐶𝐹𝐸 = 𝐹𝐶𝐹𝐹 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 × 1 − 𝑇 +
𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑠 𝑖𝑛 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡
𝐹𝐶𝐹𝐸𝑇+1
• Step 2: 𝑇𝑉 =
𝑟𝑒 −𝑔
𝐹𝐶𝐹𝐸𝑡 𝑇𝑉
• Step 3: 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = σ𝑇𝑡=1 +
(1+𝑟𝑒 )𝑡 (1+𝑟𝑒 )𝑇
𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒
• Step 4: 𝑉0 =
𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
24
Valuation Using FCFE (Example)
Year 2022 2023 2024
FCFF 850 920 905
Interest expense 200 200 250
Increases in net debt 100 50 50
FCFE 810 830 780
Marginal tax rate 30%
Cost of equity 15%
Perpetuity growth rate 2%
Number of shares outstanding 200
• Step 1: For example, 𝐹𝐶𝐹𝐸2022 = 850 − 200 × 1 − 30% + 100 = $810
780×(1+2%)
• Step 2: 𝑇𝑉 = = $6,120
15%−2%
810 830 780+6120
• Step 3: 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = + + = $5,869
1+15% (1+15%)2 (1+15%)3
5869
• Step 4: 𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 = = $29.3
200
25
Technical Analysis
• Technical analysis refers to the analysis to forecast price movements
based on past market data (returns, trading volume, volatility, etc.)
• For example, relying on moving averages of stock prices to make investment
decisions is a form of technical analysis
26
Technical Analysis (Example)
• The moving average of a stock price is the average price over a given interval.
For example:
• Buy when price breaks through the moving average from below (Point A)
• Sell when price breaks through the moving average from above (Point B) 27
Fundamental/Technical Analysis
Technical analysis Fundamental analysis 28
Fundamental/Technical Analysis
Fundamental analysis
29
Efficient Market Hypothesis
• Can we really predict stock returns?
• Suppose there is a model that can really predict stock returns
• The model predicts that XYZ stock price, currently at $100 per share, will rise to $110 (10%
expected return)
• Investors would place a great wave of immediate buy orders, raising the stock price
immediately to $110
• Longing the stock will now generate a 0% return, instead of 10%
• Stock price immediately reflects the “good news” predicted by the model
• More generally, any information that could be used to predict stock returns should
already be reflected in stock prices
• Stock prices increase or decrease only in response to new information
• New information, by definition, must be unpredictable
• This is the essence of the argument that stock prices should follow a random walk
30
Efficient Market Hypothesis
• The notion that stock prices already reflect all available information is
referred to as the Efficient Market Hypothesis (EMH)
• Evidences supporting the EMH (examples)
• Most of the stock price response to corporate dividend or earnings announcements
occurs within 10 minutes of the announcement (Patell and Wolfson, 1984)
• Stock price response to positive/negative reports featured on CNBC’s “Midday Call”
segment occurs within 5 minutes after the program (Busse and Green, 2002)
• Three versions of the EMH:
• Weak-form, semistrong-form, and strong-form
31
Efficient Market Hypothesis
• Weak-form EMH: Stock prices already reflect all information that can be derived
by examining market trading data such as past prices, trading volume, short
interest, etc.
• Implies that technical analysis will not generate superior returns
• Semistrong-form EMH: Stock prices already reflect all publicly available
information regarding a firm
• Implies that fundamental analysis and technical analysis will not generate superior returns
• Strong-form EMH: Stock prices already reflect all information, either pubic or
private, regarding a firm
• Implies that fundamental analysis and technical analysis will not generate superior returns
• In addition, insider trading will not make superior returns
32
Efficient Market Hypothesis
• There are evidences which might imply that the market is not efficient
• For example, certain trading strategies can generate abnormal returns which
should not exist if the market is efficient:
• Value effect: Value firms (firms with high book-to-market ratio) have higher
expected returns than growth firms (firms with low book-to-market ratio) on average
• Size effect: Small firms have higher expected returns than large firms on average
• Momentum effect: Recent winners have higher expected returns than recent losers
• Post-earnings-announcement drift (PEAD): Firms with higher earnings surprises
have higher expected returns than those with lower earnings surprises
• *Details of these trading strategies to be discussed in Week 6
33
Visualization of PEAD
34
Behavioral Finance
• The EMH assumes that investors are rational. But in reality, investors are
not. These irrationalities fall into two broad categories:
• Information processing: Investors do not always process information correctly and
therefore infer incorrect probability distributions about expected stock returns
• Behavioral biases: Even when given the correct information, investors might make
inconsistent or systematically suboptimal decisions
• Behavioral finance explains investment decisions and stock returns within
the context of the impact of psychological factors
• Question to think about: Is the existence of irrational investors sufficient to
render capital markets inefficient?
35
Information Processing Irrationalities (Examples)
• Memory bias: Investors give too much weight to recent experience compared to prior beliefs when
making forecasts
• For example, when a firm has favorable recent performance, P/E forecasts tend to be too high relative to the
objective prospects of the firm, which can partially explain the value effect
• Overconfidence: Investors tend to overestimate the precision of their beliefs or forecasts, and tend
to overestimate their abilities
• For example, high portfolio turnover, which correlates with overconfidence, leads to lower returns in general
• Conservatism: Investors are too slow in updating their beliefs in response to new evidence
• For example, investors tend to react slowly to earnings announcements, which can partially explain the post-
earnings-announcement drift
• Representativeness bias: People commonly do not take into account the size of a sample, acting
as if a small sample is just as representative of a population as a large one
• For example, a small sample of stocks with high P/E ratio followed by high returns may lead investors to
believe that high P/E ratio = high expected returns
36
Behavioral Biases (Examples)
• Regret avoidance: People who make decisions that turn out badly have more regret when that
decision was more unconventional
• For example, smaller, less well-known firms are also less conventional investments, which require more
“courage” on the part of the investor, which increases the required rate of return, which can partially explain
the size effect
• Affect: Other than risk and return, people also tend to consider affect, which is a feeling of “good”
or “bad” that people may attach to a potential investment
• For example, investors may prefer to invest in socially responsible stocks even though they do not provide
better risk-return trade-off
• Prospect theory: People are more risk-tolerant when facing losses than they are when facing gains
• For example, gamblers who are losing money always want to make “one last big bet” to “turn their luck
around”
• Disposition effect: Investors are reluctant to realize losses
• For example, people tend to hold on to losing investments, which slows down the convergence between stock
price and fundamental value, which can partially explain the momentum effect
37
Limits to Arbitrage
• The question we asked earlier: Is the existence of irrational investors
sufficient to render capital markets inefficient?
• Behavioral biases would not matter for stock pricing if rational
arbitragers could fully exploit the mistakes of irrational investors
• However, in practice, several factors limit the ability to profit from
mispricing
• Fundamental risk: Even if a stock is underpriced, buying it is not a risk-free
investment since the stock price might not converge to its intrinsic value
• Implementation costs: For example, short-selling an overpriced stock might
impose high trading costs and potential costs to cover the margin
• Model risk: It is possible that the model used to value a stock is incorrect
38
Efficient Market Hypothesis
• So, is the stock market really efficient?
• And what should investors do if it is?
• Unsolvable issues for this discussion:
• The magnitude issue:
• If an investment manager overseeing a $5 billion portfolio can improve the performance by
0.1% per year, that’s a $5 million improvement annually
• However, 0.1% annual contribution would be easily swamped by market volatility
• The selection bias issue:
• If an investor discovers a trading strategy that could really make money, he/she can either
publish the trading strategy or keep the strategy secret
• Most people would choose to keep it secret
• Therefore, it is not fair to draw conclusions about the EMH using the trading strategies that we
know of
• The lucky event issue:
• Even coin flips can generate consistent good returns if lucky enough
• Winners will say they win because of skill, losers will say it’s luck
39
Summary
• Equity investment analysis
• Fundamental analysis
• Top-down approach
• Bottom-up approach
• Technical analysis
• Efficient market hypothesis
• Three forms of efficient market hypothesis and their implications
• Evidences for and against efficient market hypothesis
• Behavioral finance
• Information processing
• Behavioral biases
• Limits to arbitrage
40
Suggested Reading
• Chapters 11, 12, and 18 of Bodie, Kane, and Marcus
41
References
• Barber, B.M. and Odean, T., 2001. Boys will be boys: Gender,
overconfidence, and common stock investment. The Quarterly Journal of
Economics, 116(1), pp.261-292.
• Busse, J.A. and Green, T.C., 2002. Market efficiency in real time. Journal
of Financial Economics, 65(3), pp.415-437.
• De Bondt, W.F. and Thaler, R.H., 1987. Further evidence on investor
overreaction and stock market seasonality. The Journal of Finance, 42(3),
pp.557-581.
• De Bondt, W.F. and Thaler, R.H., 1990. Do security analysts overreact?. The
American Economic Review, pp.52-57.
• Grinblatt, M. and Han, B., 2005. Prospect theory, mental accounting, and
momentum. Journal of Financial Economics, 78(2), pp.311-339.
• Patell, J.M. and Wolfson, M.A., 1984. The intraday speed of adjustment of
stock prices to earnings and dividend announcements. Journal of Financial
Economics, 13(2), pp.223-252. 42
