In the general case, if financial capital W is invested in common stock with price-to-book ratio P/B at moment *t*, the owner of the stock gets equity ownership according to the following formula:
$$ \sf BV_t = \frac{W_t}{({P/B})_t} $$
For example, if $10,000 are invested in a company with price-to-book ratio of 0.5 (due to Mr Market being pessimistic about the future of the company and/or stocks in general), the buyer would get equity ownership calculated as follows:
$$ \sf BV_t = \frac{10,000}{0.5} = 20,000 $$
---
# Quick Test
In the general case, if the owner of a common stock that sells with price-to-book ratio P/B at moment *t+1*, the owner of the stock can dispose of it by selling at market price <span><i>P<sub>t+1</sub></i></span> and get financial capital as follows:
$$ \sf W\_{t+1} = BV\_{t+1} \times ({P/B})\_{t+1} $$
For example, if in moment *t+1* Mr Market becomes more optimistic about the future prospects of the company and/or stocks in general, resulting in the P/B ratio increasing from 0.5 to 0.6, the stock owner can liquidate his position and get financial capital as follows:
$$ \sf W\_{t+1} = 20,000 \times 0.6 = 12,000 $$
**NB:** This example assumes lack of positive or negative changes to the book value of the company's equity due to profits or losses for the period!
---
# Quick Test
What is the financial capital that will be received if the owner of a common stock with a book value of $30,000 sells it at a price-to-book ratio of 1.2?
---
<!-- Another quick test, this time assuming that Warren invests $10,000 in common stock at price to book ratio of 0.5 and sells them at price to book ratio of 2. What will be the profit? -->
# Quick Test
What will be the profit if Warren invests $10,000 to buy equity stake at price-to-book ratio of 0.5 and sells it soon afterwards at price-to-book ratio of 2?
---
# Profitability Overcomes Pessimism
Even, if in moment *t+1* Mr Market remains pessimistic about the future prospects of the company and/or stocks in general, resulting in the P/B ratio remaining 0.5, the investment operation would still be successful if the underlying business was profitable in the period between *t* and *t+1* — it would either pay dividend to the stock owner or retain the earnings, increasing the book value of equity. In the latter case, the owner can liquidate her position and get financial capital as follows:
$$ \sf W\_{t+1} = BV\_{t+1} \times ({P/B})\_{t+1} = (BV\_{t} + \pi\_{t, t+1})\times ({P/B})\_{t} $$
For example, if the book value of the company's equity increases from $20,000 to $22,000 due to retained profits for the period, the investor's wealth will increase with $1,000:
$$
\sf W\_{t+1} = (20,000 + 2,000)\times 0.5 = 11,000
$$
---
# Quick Test
What will be the financial capital that will be received by Warren for his equity with book value of $20,000 that can be sold at a price-to-book ratio of 0.5 if the retained profit for the holding period is $5,000?
---
# Optimism Prevails Despite Losses
Even, if the business loses money in the period between *t* and *t+1*, the investment operation can still be successful if Mr Market becomes optimistic about the future prospects of the company and/or stocks in general, resulting in a price-to-book ratio increasing to 0.75. In the latter case, the owner can liquidate his position and get financial capital as follows:
$$ \sf W\_{t+1} = BV\_{t+1} \times ({P/B})\_{t+1} = (BV\_{t} + \pi\_{t, t+1})\times ({P/B})\_{t+1} $$
For example, if the book value of the company's equity decreases from $20,000 to $18,000 due to losses for the period, the investor's wealth will increase by $3,500:
$$
\sf W\_{t+1} = (20,000 - 2,000)\times 0.75 = 13,500
$$
---
# Quick Test
What will be the financial capital that will be received by Warren for his equity with book value of $20,000 that can be sold at a price-to-book ratio of 0.8 if the loss for the holding period is $4,000?
---
# Justified Optimism
In the best case scenario, the underlying fortune of the business will reverse and the company will become profitable in the period between *t* and *t+1*, increasing the book value of equity from $20,000 to $22,000. In addition, Mr Market will become more optimistic about the future prospects of the company and/or stocks in general, resulting in a price-to-book ratio increasing to 0.75. In the latter case, the owner can liquidate his position and get financial capital as follows:
$$ \sf W\_{t+1} = BV\_{t+1} \times ({P/B})\_{t+1} = (BV\_{t} + \pi\_{t, t+1})\times ({P/B})\_{t+1} $$
For example, if the book value of the company's equity increases from $20,000 to $22,000 due to retained profits for the period, the investor's wealth will increase by $6,500:
$$ \sf W\_{t+1} = (20,000 + 2,000) \times 0.75 = 16,500 $$
---
# Quick Test
What will be the profit that will be received by Warren on his $10,000 investment at P/B ratio of 0.5 if the retained profit for the holding period is $5,000 while the P/B ratio increases to 1?
---
# Worst Case Scenario: Double Whammy
In the worst case scenario, the underlying fortune of the business will reverse and the company will lose money in the period between *t* and *t+1*, decreasing the book value of equity from $20,000 to $18,000. In addition, Mr Market will, rightly, become more pessimistic about the future prospects of the company and/or stocks in general, resulting in the price-to-book ratio decreasing to 0.4. In the latter case, the owner can liquidate his position and get financial capital as follows:
$$ \sf W\_{t+1} = BV\_{t+1} \times ({P/B})\_{t+1} = (BV\_{t} + \pi\_{t, t+1})\times ({P/B})\_{t+1} $$
For example, if the book value of the company's equity decreases from $20,000 to $18,000 due to losses for the period, the investor's wealth will decrease by $2,800:
$$
\sf W\_{t+1} = (20,000 - 2,000)\times 0.4 = 7,200
$$
---
# Quick Test
What will be the profit that will be received by Warren on his $10,000 investment at P/B ratio of 0.5 if the loss for the holding period is $5,000 while the P/B ratio decreases to 0.25?
---
# Table Completion Task
<!-- Create an HTML table of class="none" where the first column contains the names of the four companies from above, the second column contains their BV as of Sep 30, 2019, the third column is P as of Sep 30, 2019, the fourth column is their P/BV as of Sep 30, 2019, the fifth column is their BV as of Sep 30, 2019, the sixth column is their P as of Sep 30, 2024, the seventh column is the P/BV as of Sep 30, 2024, the eighth column is %Δ BV and the last column is %ΔP -->
<table class="none">
<tr>
<th style="vertical-align: top;">Company</th>
<th>BV<sub>19</sub></th>
<th>P<sub>19</sub></th>
<th>P/BV<sub>19</sub></th>
<th>BV<sub>24</sub></th>
<th>P<sub>24</sub></th>
<th>P/BV<sub>24</sub></th>
<th>%ΔBV</th>
<th>%ΔP</th>
</tr>
<tr>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
<td style="text-align: right; height: 0.3em;"></td>
</tr>
<tr>
<td>Berkshire</td>
<td style="text-align: right">402B</td>
<td style="text-align: right">539B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right">632B</td>
<td style="text-align: right">1,030B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
</tr>
<tr>
<td>Apple</td>
<td style="text-align: right">91B</td>
<td style="text-align: right">1,180B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right">57B</td>
<td style="text-align: right">3,520B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
</tr>
<tr>
<td>NVIDIA</td>
<td style="text-align: right">11B</td>
<td style="text-align: right">132B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right">66B</td>
<td style="text-align: right">3,331B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
</tr>
<tr>
<td>Innodata</td>
<td style="text-align: right">0.03B</td>
<td style="text-align: right">0.03B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right">0.05B</td>
<td style="text-align: right">1.32B</td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
<td style="text-align: right" class="can-edit"></td>
</tr>
</table>
*Notes:* <br>
The book value (BV) of equity is measured is USD for the company as a whole and not per share. <br>The market price (P) of equity is measured in USD for the company as a whole (market capitalization).
---
<!-- \begin{frame}{Conclusion} -->
<!-- \epigraph{There are many ways to make money and lose money on Wall Street}{Benjamin Graham} -->
<!-- \end{frame} -->
# Conclusion
.pull-right-2[
_There are many ways to make money and lose money on Wall Street_
Benjamin Graham
]
---
class: clear, middle, no-scribble
.font200[
Model Of Long-Term Investment
]
---
class: clear, middle
.pull-right-2[
_Over the long term, it’s hard for a stock to earn a much better return than the business which underlies it earns._
Charlie Munger
]
.pull-right-2[
_Charlie made me focus on the merits of a great business with tremendously growing earning power, but only when you can be sure of it—not like Texas Instruments or Polaroid, where the earning power was hypothetical._
Warren Buffett
]
---
# Modelling Growing, Profitable Business
In the general case, if some financial capital W is invested in common stock with price-to-book ratio P/B at moment *t* for *n* periods (e.g. years), and the underlying business reinvests all its earnings with average return on equity *ROE<sub>a</sub>* the market value of the financial capital would grow according to the following formula:
$$
\sf W\_{t+n} = \frac{W\_t}{({P/B})\_t}\times (1 + ROE\_a)^n \times (P/B)\_{t+n}
$$
---
# Quick Test
.panelset.sideways.right[
.panel[
.panel-name[Problem]
A company that had a book value of equity amounting to $19 per share in 1964 reinvested the earnings for 57 years at average rate of return on equity amounting to 18.71% per year. How much was its book value at the end of the holding period?
]
.panel[
.panel-name[Blackboard]
A company that had a book value of equity amounting to $19 per share in 1964 reinvested the earnings for 57 years at average rate of return on equity amounting to 18.71% per year. How much was its book value at the end of the holding period?
]
.panel[
.panel-name[Solution]
$$ \sf BV\_{t+57} = BV\_t \times (1 + ROE\_a)^n $$
$$ \sf BV\_{t+57} = 19 \times (1+0.1871)^{57} $$
$$ \sf BV\_{t+57} = 334,603 $$
]
]
---
# Quick Test
.panelset.sideways.right[
.panel[
.panel-name[Problem]
Warren invested $100 in a company with a price-to-book ratio of 0.7 in 1964. The company reinvested all its earnings at an average rate of return on equity amounting to 18.71% per year. At the end of the period the price to book ratio was 1.4. How much was the market value of Warren's investment at the end of the holding period?
]
.panel[
.panel-name[Blackboard]
Warren invested $100 in a company with a price-to-book ratio of 0.7 in 1964. The company reinvested all its earnings at an average rate of return on equity amounting to 18.71% per year. At the end of the period the price to book ratio was 1.4. How much was the market value of Warren's investment at the end of the holding period?
]
.panel[
.panel-name[Solution]
$$ \sf W\_{t+n} = \frac{W\_t}{({P/B})\_t}\times (1 + ROE\_a)^n \times (P/B)\_{t+n} $$
$$ \sf W\_{t+n} = \frac{100}{0.7} \times (1+0.1871)^{57} \times 1.4 $$
$$ \sf W\_{t+n} = 100 \times 17,611 \times 2 $$
$$ \sf W\_{t+n} = 3,522,200 $$
]
]
---
class: clear, middle
.pull-right-2[
_Return on beginning equity capital... We believe the latter yardstick to be the most important measure of single-year managerial performance. Informed use of that yardstick, however, requires an understanding of many factors, including accounting policies, historical carrying values of assets, financial leverage, and
industry conditions._
Warren Buffett
]
---
# Understanding The Price-To-Book Ratio
<br>
$$ (P/B)\_t = \frac{P\_t}{B\_t}$$
$$ (P/B)\_t = \frac{P\_t}{B\_t} \times \frac{\pi\_{t+1,t}}{\pi\_{t+1,t}} $$
$$ (P/B)\_t = \frac{P\_t}{\pi\_{t+1,t}} \times \frac{\pi\_{t+1,t}}{B\_t} $$
$$ (P/B)\_t = {P/E^e}_{t} \times ROE\_t^e $$
---
# DuPont Identity
<br>
$$ \sf \text{ROE} = \frac{\text{net income}}{\text{shareholder equity}} $$
$$ \text{ROE} = \frac{\text{net income}}{\text{sales revenue}}\times \frac{\text{sales revenue}}{\text{shareholder equity}} $$
$$ \text{ROE} = \frac{\text{net income}}{\text{sales revenue}}\times \frac{\text{sales revenue}}{\text{total assets}} \times \frac{\text{total assets}}{\text{shareholder equity}} $$
$$\text{ROE} = \text{profit margin} \times \text{total asset turnover} \times \text{financial leverage} $$
---
# Hendrik Bessembinder Research
Professor Bessembinder used the Center for Research in Security Prices (CRSP) daily common stock database to measure compound returns for all publicly-listed U.S. common stocks, and to identify the stocks that generated the highest compound rates of return, during the ninety-eight years spanning December 31, 1925 to December 31, 2023.
--
As of December 2023, CRSP reported returns for 29,078 distinct common stocks.
Although the study spans ninety-eight calendar years only 31 stocks are present in the data across all ninety-eight years. This is 0.11% of the total number of stocks in the database.
--
The median cumulative compound return across stocks is -7.41%, as 51.64% of
stocks realized negative compound returns over their full lives in the CRSP database.
---
# Hendrik Bessembinder Research
The mean outcome across stocks is a cumulative compound return of 22,840%, or equivalently, final wealth of $229.40 per dollar initially invested.
--
Therefore, a small number of stocks account for the majority of the wealth creation in the U.S. stock market. The best-performing 4% of listed companies account for the entire wealth creation of the U.S. stock market since 1926.
--
Are the best performers some super exciting high tech companies? No, the best performers are boring companies that have been around for a long time.
---
# Hendrik Bessembinder Research
<!-- Company Name (Most Recent) -->
<!-- First -->
<!-- Return -->
<!-- Date -->
<!-- Last -->
<!-- Return -->
<!-- Date Years -->
<!-- Cumulative -->
<!-- Gross -->
<!-- Wealth Per -->
<!-- Dollar -->
<!-- Cumulative -->
<!-- Compound -->
<!-- Return (%) -->
<!-- Annualized -->
<!-- Compound -->
<!-- Return (%) -->
<!-- ALTRIA GROUP INC 31-Dec-25 29-Dec-23 98.00 2,655,290 265528900.62% 16.29% -->
<!-- VULCAN MATERIALS CO 31-Dec-25 29-Dec-23 98.00 393,492 39349084.13% 14.05% -->
<!-- KANSAS CITY SOUTHERN 31-Dec-25 13-Dec-21 95.95 361,757 36175578.11% 14.27% -->
<!-- GENERAL DYNAMICS CORP 28-Jan-26 29-Dec-23 97.92 220,850 22084880.36% 13.39% -->
<!-- BOEING CO 5-Sep-34 29-Dec-23 89.32 212,206 21220526.33% 14.72% -->
<!-- Make an HTML table with class none using the data above -->
<table class="none">
<tr>
<th style="vertical-align: top">Company Name (Most Recent)</th>
<th style="vertical-align: top">Years</th>
<th style="vertical-align: top">Cumulative Gross Wealth Per Dollar</th>
<th style="vertical-align: top">Annualized Compound Return (%)</th>
</tr>
<tr>
<td>ALTRIA GROUP INC</td>
<td style="text-align: right">98.00</td>
<td style="text-align: right">2,655,290</td>
<td style="text-align: right">16.29%</td>
</tr>
<tr>
<td>VULCAN MATERIALS CO</td>
<td style="text-align: right">98.00</td>
<td style="text-align: right">393,492</td>
<td style="text-align: right">14.05%</td>
</tr>
<tr>
<td>KANSAS CITY SOUTHERN</td>
<td style="text-align: right">95.95</td>
<td style="text-align: right">361,757</td>
<td style="text-align: right">14.27%</td>
</tr>
</table>
---
<!-- \begin{frame}{Key Takeways} -->
<!-- By now YOU should have learned the importance of profitability and the growth prospects of the underlying business (measured by return on equity!) for the performance of investments in common stocks. However, what determines the profitability and the growth prospects of a business? -->
<!-- There are two major theoretical frameworks: -->
<!-- \begin{list}{\faChevronCircleRight}{\leftmargin=3.9em \labelsep=1.5em} -->
<!-- \item the structure-conduct-performance framework; -->
<!-- \item the resource-based view of the firm; -->
<!-- \end{list} -->
<!-- By the end of this course we will be studying business economics which mostly explains the structure-conduct-performance framework. -->
<!-- \end{frame} -->
# Key Takeaways
By now YOU should have learned the importance of profitability and the growth prospects of the underlying business (measured by return on equity!) for the performance of investments in common stocks. However, what determines the profitability and the growth prospects of a business?
--
There are two major theoretical frameworks:
- the structure-conduct-performance framework;
- the resource-based view of the firm;
By the end of this course we will be studying business economics which mostly explains the structure-conduct-performance framework.
---
# Questions?
<br>
<br>
<html>
<head>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
</head>
<body>
<i class="fa fa-question" style="font-size:240px; position: absolute; right: 250px; width: 300px;"></i>
</body>
</html>
---
# Thank You!
<br>
<br>
<i class="fa fa-smile-o" style="font-size:240px; position: absolute; right: 250px; width: 300px;"></i>