Chapter 4. Pricing the Risk: Capital Asset Pricing Model (CAPM) and Beta

Welcome back. Previously, we learned how to eliminate unsystematic risk through portfolios. Today, we tackle one of the greatest formulas in modern finance: the Capital Asset Pricing Model (CAPM).

The CAPM starts with a bold question: ==“Exactly how much compensation does the market provide for risk?”== This model serves as a compass not only for individual stocks but also for evaluating corporate capital costs and project feasibility. Let’s dive into the world of logic that earned William Sharpe a Nobel Prize.

1. Prerequisites: The Ideal Market

The CAPM assumes a ‘clean’ market: rational investors, light-speed information, and zero taxes or transaction costs. While reality is different, this framework allows us to see the ==“fundamental skeleton of risk and return.”==

2. Beta ( $\beta$ ): Your Sensitivity to the Market

The star of the CAPM is Beta ( $\beta$ ). It ignores small, diversifiable risks and measures only how much you move when the market as a whole shakes.

Analyzing Character by Beta Value

Beta Value	Meaning	Character	Example Sectors
$eta = 1$	Moves exactly with the market	Market Average	Index Funds
$eta > 1$	Fluctuates more than the market	Aggressive Asset	IT/Tech, Semiconductors
$eta < 1$	Moves less than the market	Defensive Asset	Consumer Staples, Utilities

==The Philosophy of Beta==: A beta of 1.5 means if the index rises by 1%, your stock rises by 1.5%. Conversely, if the index drops 1%, yours drops 1.5%. It means: ==“If you want higher returns, endure a higher beta (market risk).”==

3. The CAPM Formula: The Price Tag of Risk

Here is the golden formula of finance:

$R_f$ (Risk-Free Rate): Interest rate on government bonds with zero risk (Compensation for waiting).
$[E(R_m) - R_f]$ (Market Risk Premium): Compensation for jumping into a risky market.
$\beta_i$ : The weight of how much you reflect that market risk.

Base Reward

Start with the Risk-Free Rate (Rf)

Market Premium

Calculate the extra return expected from the market (Rm - Rf)

Sensitivity Adjustment

Multiply the premium by your specific Beta (β)

Final Expected Return

Combine both to find the total required return

4. Security Market Line (SML): Where is Your Stock?

The graph of this formula is the Security Market Line (SML).

Points ABOVE the SML: Return is too high for the risk. ==“Undervalued”==—Time to Buy.
Points BELOW the SML: Risk is high but return is poor. ==“Overvalued”==—Time to Sell.

==Convergence of Efficient Markets==: If markets are efficient, all assets eventually move back to the SML as abnormal profits disappear quickly.

5. Conclusion: He Who Manages Beta Wins

Today, we learned how to put a price on risk. The CAPM teaches us that simply taking risks doesn’t guarantee returns; what matters is understanding the ==“Risk the market compensates for (Systematic Risk).”==

📚 Prof. Sean’s Selected Library

[Investments] - Bodie, Kane, Marcus: The legendary textbook covering everything in modern portfolio theory.
[The Psychology of Finance] - Lars Tvede: A critical look at why the ‘rational human’ assumed by CAPM often fails in reality.
[Empire of Wealth] - John Steele Gordon: The fascinating history of how mathematical models came to dominate Wall Street.

Next time, we will learn about the tool for deciding a company’s destiny—whether to build a new factory or launch a new product: ‘Capital Budgeting: The Battle of NPV vs. IRR.’

Pricing the Risk: Capital Asset Pricing Model (CAPM) and Beta