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CAPM Guide - Capital Asset Pricing Model

📐 What is CAPM?

CAPM stands for Capital Asset Pricing Model. It's a formula that calculates the expected return on an investment based on its risk level compared to the overall market.

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                Key Point: CAPM helps investors answer the question: "What return should I expect from this investment given how risky it is?" The riskier the investment, the higher the expected return should be to compensate you for taking that risk.
            

The CAPM Formula

Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)

or more simply:

Expected Return = Risk-Free Rate + Beta × Market Risk Premium

Let's break down each component:

Component 1: Risk-Free Rate (Rf)

This is the return you could get from a completely safe investment with zero risk. Think of it as your baseline or starting point.

What to use: Typically the yield on government bonds (10-year Treasury bonds)
Why government bonds? They're considered the safest investment because governments can print money to pay debts
Current example: If NZ 10-year government bonds yield 4.5%, your risk-free rate is 4.5%

Component 2: Beta (β)

Beta measures how volatile or risky a stock is compared to the overall market. It answers: "How much does this stock move relative to the market?"

Beta Value	Meaning	Example
Beta = 1.0	Moves with the market	Market index fund
Beta > 1.0	More volatile than market	Tech stocks, growth companies (Beta 1.5 means 50% more volatile)
Beta < 1.0	Less volatile than market	Utility companies, consumer staples (Beta 0.7 means 30% less volatile)
Beta = 0	No correlation to market	Risk-free assets (government bonds)
Negative Beta	Moves opposite to market	Gold, some defensive stocks (rare)

💡 Real-World Beta Examples

Tesla might have a beta of 2.0 (twice as volatile as the market), while a utility company like Contact Energy might have a beta of 0.6 (40% less volatile). If the market goes up 10%, Tesla might go up 20%, while Contact Energy might only go up 6%.

Component 3: Market Return (Rm)

This is the expected return of the overall stock market, usually measured by a major index.

What to use: Historical average return of a broad market index
For NZ: NZX 50 historical average (approximately 8-10% annually)
For US: S&P 500 historical average (approximately 10-11% annually)
Time period: Typically use 10-20 year averages

Component 4: Market Risk Premium

This is the extra return investors demand for taking on market risk instead of keeping money in safe government bonds.

Market Risk Premium = Market Return - Risk-Free Rate

Example: 10% - 4% = 6% market risk premium

Why CAPM Matters

Investment decisions: Helps determine if a stock's expected return justifies its risk
Portfolio management: Guides asset allocation based on risk tolerance
Company valuation: Used to calculate the cost of equity for businesses
Performance evaluation: Compare actual returns to what CAPM predicts
Fair pricing: Identify overvalued or undervalued securities

Simple Example

You're considering buying shares in a tech company. Here's what you know:

Risk-free rate (NZ government bonds): 4%

Market return (NZX 50 historical average): 9%

Beta of the tech stock: 1.3

CAPM Calculation:

Expected Return = 4% + 1.3 × (9% - 4%)

Expected Return = 4% + 1.3 × 5%

Expected Return = 4% + 6.5%

Expected Return = 10.5%

Interpretation: Given this stock's risk level (beta of 1.3), you should expect approximately 10.5% annual return. If the stock is currently offering less than 10.5%, it might be overpriced. If it's offering more, it might be a good buy.

⚠️ Important Limitations

CAPM is a theoretical model with assumptions that don't always hold in real markets. It assumes investors are rational, markets are efficient, and all investors have the same information. Use CAPM as one tool among many, not the only decision-making factor.

🔢 Step-by-Step CAPM Calculations

Let's work through detailed examples to master CAPM calculations.

Example 1: Basic CAPM Calculation

Scenario: You're analysing Fisher & Paykel Healthcare shares.

Given Information:

Risk-free rate (NZ 10-year bonds): 4.2%

Expected market return (NZX 50): 8.5%

Fisher & Paykel beta: 0.85

Step 1: Calculate Market Risk Premium

Market Risk Premium = Market Return - Risk-Free Rate

= 8.5% - 4.2%

= 4.3%

Step 2: Apply CAPM Formula

Expected Return = Risk-Free Rate + Beta × Market Risk Premium

= 4.2% + 0.85 × 4.3%

= 4.2% + 3.66%

= 7.86%

Interpretation: Given Fisher & Paykel's beta of 0.85 (less volatile than the market), the expected return is 7.86%. This is less than the overall market return of 8.5% because the stock carries less risk.

Example 2: High-Beta Tech Stock

Scenario: Analysing a high-growth tech company.

Given Information:

Risk-free rate: 3.5%

Market return: 10%

Tech stock beta: 1.8

Calculation:

Expected Return = 3.5% + 1.8 × (10% - 3.5%)

= 3.5% + 1.8 × 6.5%

= 3.5% + 11.7%

= 15.2%

Interpretation: The high beta of 1.8 means this stock is 80% more volatile than the market. Investors should demand 15.2% return to compensate for the extra risk. This is significantly higher than the market return of 10%.

                Key Insight: Notice how higher beta leads to higher expected returns. Beta of 1.8 pushed the expected return from 10% (market) to 15.2%. This extra 5.2% compensates investors for the additional volatility.
            

Example 3: Defensive Stock (Low Beta)

Scenario: Analysing a utility company.

Given Information:

Risk-free rate: 4%

Market return: 9%

Utility company beta: 0.6

Calculation:

Expected Return = 4% + 0.6 × (9% - 4%)

= 4% + 0.6 × 5%

= 4% + 3%

= 7%

Interpretation: The low beta of 0.6 reflects the stable, predictable nature of utility companies. The expected return of 7% is below the market return of 9%, reflecting lower risk. Utility stocks are often called "defensive" stocks for this reason.

Comparing Investment Options with CAPM

Let's compare three different investment options:

Investment	Beta	Expected Return (CAPM)	Risk Level
Government Bonds	0.0	4.0%	Very Low
Utility Stock	0.6	7.0%	Low
Market Index Fund	1.0	9.0%	Average
Growth Stock	1.5	11.5%	High
Tech Startup Stock	2.0	14.0%	Very High

Assumes: Risk-free rate = 4%, Market return = 9%

💡 Risk-Return Trade-off

This table clearly shows the fundamental principle of investing: higher risk demands higher expected returns. You can't expect tech startup returns (14%) if you're only taking utility stock risk (7%).

Using CAPM for Investment Decisions

Decision Framework:

If Actual Expected Return > CAPM Expected Return:

Stock might be undervalued
Potentially good buying opportunity
You're getting more return than the risk justifies

If Actual Expected Return < CAPM Expected Return:

Stock might be overvalued
Consider avoiding or selling
You're not being compensated enough for the risk

Example Decision:

Stock Beta: 1.2

CAPM Expected Return: 4% + 1.2(9% - 4%) = 10%

Stock's Actual Forecast Return: 12%

Decision: Consider buying (12% > 10%)

Finding Beta Values

Where do you get beta values for stocks?

Financial websites: Yahoo Finance, Bloomberg, MarketWatch
Broker platforms: Most trading platforms show beta
Company reports: Annual reports often include beta
Calculate yourself: Regression analysis of stock returns vs market returns (advanced)

⚠️ Beta Can Change

A company's beta isn't fixed. It can change as the company matures, changes strategy, or if market conditions shift. Check beta values regularly and use recent calculations (typically based on 2-5 years of data).

CAPM in Portfolio Management

You can also use CAPM to calculate the expected return of an entire portfolio:

Portfolio Beta Formula:

Portfolio Beta = Weighted Average of Individual Betas

Example Portfolio:

Stock	Weight	Beta	Weighted Beta
Stock A	40%	1.2	0.48
Stock B	30%	0.8	0.24
Stock C	30%	1.5	0.45
Portfolio Beta			1.17

Now use the portfolio beta (1.17) in CAPM to find the portfolio's expected return.

🌍 Real-World Examples

Let's explore practical scenarios showing how CAPM applies in real investment situations.

Comparing Two NZ Companies

Situation: Sarah wants to invest $20,000 in either Company A or Company B and wants to know which offers better value given the risk.

Market Conditions:

NZ 10-year government bond yield (risk-free rate): 4.5%

NZX 50 historical return (market return): 8.8%

Market risk premium: 8.8% - 4.5% = 4.3%

Company A - Established Retailer:

Beta: 0.9

Analyst forecast return: 7.5%

CAPM Expected Return:

= 4.5% + 0.9 × 4.3%

= 4.5% + 3.87%

= 8.37%

Company B - Tech Startup:

Beta: 1.6

Analyst forecast return: 12%

CAPM Expected Return:

= 4.5% + 1.6 × 4.3%

= 4.5% + 6.88%

= 11.38%

Analysis:

Company	CAPM Expected	Forecast Return	Verdict
Company A	8.37%	7.5%	Overvalued (7.5% < 8.37%)
Company B	11.38%	12%	Undervalued (12% > 11.38%)

                    Sarah's Decision: Company B appears to be the better value. Even though it's riskier (beta 1.6 vs 0.9), the forecast return of 12% exceeds what CAPM suggests should be required (11.38%). Company A's forecast of 7.5% doesn't compensate for its risk level.
                

Building a Balanced Portfolio

Situation: Mike wants to build a $50,000 portfolio with a target expected return of 9.5%.

Available Options:

Risk-free rate: 4%

Market return: 10%

Market risk premium: 6%

Investment Options with CAPM Expected Returns:

Asset	Beta	Expected Return
Government Bonds	0.0	4.0%
Defensive Stocks	0.7	8.2%
Market Index Fund	1.0	10.0%
Growth Stocks	1.4	12.4%

Mike's Portfolio Allocation:

30% Defensive Stocks (8.2% return) = $15,000

50% Market Index Fund (10% return) = $25,000

20% Growth Stocks (12.4% return) = $10,000

Portfolio Expected Return:

(0.30 × 8.2%) + (0.50 × 10%) + (0.20 × 12.4%)

= 2.46% + 5% + 2.48%

= 9.94%

Portfolio Beta:

(0.30 × 0.7) + (0.50 × 1.0) + (0.20 × 1.4)

= 0.21 + 0.50 + 0.28

= 0.99

💡 Portfolio Insight

Mike's portfolio has a beta of 0.99 (essentially market risk) and an expected return of 9.94%, exceeding his 9.5% target. The diversification across different risk levels helps balance risk and return.

Evaluating Company Cost of Equity

Situation: A NZ manufacturing company needs to calculate its cost of equity for a capital budgeting decision.

Company Information:

Company: Manufacturing Ltd

Industry beta: 1.1

Risk-free rate (NZ 10-year bonds): 4.3%

Expected market return (NZX 50): 9.2%

Cost of Equity Calculation (using CAPM):

Cost of Equity = 4.3% + 1.1 × (9.2% - 4.3%)

= 4.3% + 1.1 × 4.9%

= 4.3% + 5.39%

= 9.69%

Business Application:

The company is considering a $2 million factory expansion that will generate $250,000 annual profit.

Return on investment: $250,000 / $2,000,000 = 12.5%

Cost of equity (hurdle rate): 9.69%

12.5% > 9.69%

Decision: Proceed with expansion

                    Business Insight: The project's 12.5% return exceeds the 9.69% cost of equity, meaning it will create value for shareholders. This is a common application of CAPM in corporate finance.
                

Market Crash Scenario

Situation: During a market downturn, understanding how different beta stocks react.

Market Scenario:

Market drops: -15%

Expected Impact on Different Stocks:

Stock Type	Beta	Expected Change	Calculation
Defensive Utility	0.5	-7.5%	0.5 × -15% = -7.5%
Consumer Staples	0.8	-12%	0.8 × -15% = -12%
Market Index	1.0	-15%	1.0 × -15% = -15%
Growth Tech	1.5	-22.5%	1.5 × -15% = -22.5%
High-Risk Startup	2.0	-30%	2.0 × -15% = -30%

⚠️ Beta Works Both Ways

High beta stocks amplify gains in bull markets but also amplify losses in bear markets. A stock with beta 2.0 that rises 20% when markets rise 10% will also fall 20% when markets fall 10%.

💡 Defensive Strategy

This is why conservative investors favour low-beta stocks (utilities, consumer staples) during uncertain times. They sacrifice upside potential for downside protection.

🎯 Test Your Knowledge

Complete this 10-question quiz to check your understanding of CAPM

1. What does CAPM stand for?

Capital Asset Pricing Model

Current Asset Performance Model

Compound Annual Profit Measure

Capital Allocation Performance Metric

2. What does a beta of 1.5 mean?

The stock is 1.5 times more expensive than average

The stock will return 1.5% annually

The stock is 50% more volatile than the market

The stock moves opposite to the market

3. If the risk-free rate is 4%, market return is 10%, and beta is 1.2, what is the expected return?

7.2%

9.2%

14.4%

11.2%

4. What is typically used as the risk-free rate in CAPM?

Government bond yield (usually 10-year)

Average savings account interest

Corporate bond yield

Stock market dividend yield

5. If a stock has a beta of 0.7, what does this indicate?

The stock will lose 70% of its value

The stock is less volatile than the market

The stock will return 0.7% annually

The stock is more risky than average

6. What is the market risk premium if the market return is 9% and the risk-free rate is 3%?

12%

7. Which type of stock typically has the lowest beta?

Technology startups

Utility companies

Cryptocurrency stocks

Small-cap growth stocks

8. If a stock's forecast return is 12% and CAPM suggests 10%, what does this indicate?

The stock is overvalued

The stock is too risky

CAPM doesn't work for this stock

The stock might be undervalued (good buying opportunity)

9. What happens if the market goes up 10% and a stock has a beta of 2.0?

The stock goes up 10%

The stock goes down 10%

The stock goes up approximately 20%

The stock stays the same

10. What is the main limitation of CAPM?

It's too complicated to calculate

It relies on assumptions that don't always hold in real markets

It only works for New Zealand stocks

It can't be used for portfolio management

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