Lesson 7 of 7 11–14% of the exam

By Daniil Tarakanov Updated Oct 22, 20262027 curriculum

Estimating beta with a CAPM regression

Q: How do you estimate beta with a regression?

Collect the asset's returns, a market index's returns and a short-term government bill rate. Subtract the bill rate from both returns, regress the asset's excess returns on the market's by ordinary least squares, and read the slope. Monthly returns over three to five years or weekly returns over one to three years are typical.

Q: What does R-squared mean in a CAPM regression?

It is the share of the variance of the asset's excess returns that the market's excess returns explain: the systematic part. An R² of 0.54 means 54% systematic and 46% idiosyncratic. It is not beta: a stock can be very sensitive to the market and still have a low R².

Q: How do you build a confidence interval for beta?

Take the slope and add and subtract the critical t-value times its standard error, with n − 2 degrees of freedom. A slope of 1.24 with a standard error of 0.15 and 58 degrees of freedom gives 1.24 ± 2.002 × 0.15, about 0.94 to 1.54.

The capital asset pricing model (CAPM) says only market risk, measured by beta, earns a premium. To estimate beta, regress the asset's excess returns on the market's excess returns: the slope is beta. Then the expected return is the risk-free rate plus beta times the market risk premium.

7 min cram, 34 min full read. Based on the 2027 CFA® Program Level I curriculum, Quantitative Methods, Learning Module 10.

Tailor this to you: take the self-assessment

Before this: Goodness of fit and testing the regression coefficients, From the capital allocation line to the capital market line and the CAPM

On the exam

Calculate and interpret the variable estimates of the capital asset pricing model (CAPM)

Calculate and interpret the estimates of a CAPM regression. Expect to pick beta out of a regression output, read R² as the share of the asset's excess-return variance the market explains, test beta against zero or one, build a confidence interval for beta, compute an expected return or the change in expected excess return when the market risk premium moves, and name the data needed.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

What does the capital asset pricing model say?

The capital asset pricing model (CAPM) links an asset’s expected return to its systematic risk , the risk it shares with the whole market, measured by beta. It is a one-factor model: the only reward for risk is beta times the market risk premium , $E[r_m] - r_f$ , where $r_f$ is the risk-free rate and $E[r_m]$ is the expected return on the market. Idiosyncratic risk (also called non-systematic risk) can be diversified away, so it earns nothing.

Capital asset pricing model Memorize

E[r_i] = r_f + \beta_i\left(E[r_m] - r_f\right)

Learning Module 8 derives the model; this lesson estimates beta from data. By using only the market, the CAPM ignores other factors such as size, value and momentum, which multifactor models add in Equities.

How do you turn the CAPM into a regression?

Expected returns cannot be observed, so use realized returns. Subtract the risk-free rate from both sides and the CAPM becomes a straight line in excess returns: regress the asset’s excess return on the market’s excess return, and the slope estimates beta.

An excess return is a return minus the risk-free rate, period by period.

Excess returns Memorize

Z_{i,t} = r_{i,t} - r_{f,t}, \quad Z_{m,t} = r_{m,t} - r_{f,t}

The CAPM regression then fits a line through the pairs of excess returns.

CAPM regression Memorize

Z_{i,t} = b_0 + b_1 Z_{m,t} + \varepsilon_{i,t}

The CAPM itself has no intercept; the regression adds one, $\hat{b}_0$ , to soak up any average excess return the market does not explain. Step 4 below uses only the slope.

The four steps

Memorize

Gather data. The asset’s returns, a broad market index’s returns (the proxy for the market portfolio) and a short-term government bill rate (for example one- or three-month) as the risk-free rate, all for the same period. Typical choices are monthly returns over three to five years or weekly returns over one to three years; the estimation window and the frequency change the estimate.
Compute excess returns $Z_i$ and $Z_m$ for every period.
Run the regression of $Z_i$ on $Z_m$ by ordinary least squares (OLS); the slope is the beta estimate.
Estimate the expected return: $E[r_i] = r_f + \hat{\beta}(E[r_m] - r_f)$ .

Estimating beta in four steps

CAPM regressionexcess returns on excess returns

1. Gather data Memorize asset, market index, bill rate; monthly 3–5 years or weekly 1–3 years
2. Excess returns Memorize Z_i = r_i − r_f, Z_m = r_m − r_f
3. Regress Z_i on Z_m Memorize slope = beta
4. Expected return Memorize r_f + β̂ × market risk premium

The data you need are the risk-free rate, the asset’s total returns and the market’s total returns. Not inflation, not dividend yields on their own.

Worked example Step 2: three months of excess returns

The stock is Halvard Logistics, an invented company. The one-month bill yields 3.0% a year, which is 0.25% a month.

Month	Stock return	Index return	Bill	Z_i	Z_m
1	3.10%	2.20%	0.25%	2.85%	1.95%
2	−1.40%	−0.60%	0.25%	−1.65%	−0.85%
3	0.90%	1.30%	0.25%	0.65%	1.05%

For month 1: 3.10 − 0.25 = 2.85 for the stock and 2.20 − 0.25 = 1.95 for the index.

Month 1 on your calculator

3.1−0.25= 2.85
2.2−0.25= 1.95

3.1ENTER0.25− 2.85
2.2ENTER0.25− 1.95

ENTER enter (on the HP, puts the number on the stack)

Go deeper Why the risk-free rate is treated as known

Over a month the bill rate barely moves and carries no default risk, so the estimate treats it as fixed for each period. Subtracting it from both returns is what turns the CAPM into a line through excess returns.

How do you read a CAPM regression output?

The slope on the market’s excess return is the beta estimate . Its t-statistic tests whether beta differs from zero (or, subtracting 1 first, from one). The R-squared of a CAPM regression is the share of the variance of the asset’s excess returns explained by the market’s: the systematic share. What is left, $1 - R^2$ , is idiosyncratic.

Worked example Halvard Logistics: 60 months

Here is the output for 60 monthly excess returns of Halvard Logistics on the index’s excess returns (all in percent). The abbreviation df stands for degrees of freedom.

Regression statistics
R²	0.540
Standard error of the estimate, s_e	4.62
Observations	60

Source	df	Sum of squares	Mean square	F
Regression	1	1,452.2	1,452.2	68.15
Error	58	1,236.0	21.31
Total	59	2,688.2

	Coefficient	Standard error	t-statistic	p-value
Intercept	0.18	0.60	0.30	0.77
Market excess return	1.240	0.150	8.26	< 0.001

Read it:

Beta is 1.24: when the market’s excess return rises by 1 percentage point, Halvard’s tends to rise by 1.24 points. It is more sensitive than the market.
Is beta different from zero? t = 8.26 (software divides the unrounded beta by its unrounded standard error; 1.240 ÷ 0.150 would give 8.27) against a two-tailed 5% critical value of 2.002 (58 degrees of freedom): reject. The p-value says the same.
Is beta different from one? $t = (1.24 - 1) \div 0.15 =$ 1.60, below 2.002: fail to reject. The data cannot tell Halvard’s beta apart from the market’s.
$R^2 = 1{,}452.2 \div 2{,}688.2 =$ 0.540, the regression sum of squares over the total: the market explains 54% of the variance of Halvard’s excess returns (its systematic share), and 46% is idiosyncratic. The correlation of the two excess returns is $\sqrt{0.540} =$ 0.735 (positive, like the slope).
The intercept, 0.18% a month, has t = 0.30: not significantly different from zero.

Steps 3 and 4 on your calculator

1.24−1=÷0.15= 1.6
1452.2÷2688.2= 0.5402
√x 0.735

√x square root

1.24ENTER1−0.15÷ 1.6
1452.2ENTER2688.2÷ 0.5402
g√x 0.735

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · √x square root

Exam tip R² is not beta. A stock can have a high beta and a low R² (very sensitive, but with lots of company-specific noise) or the reverse.

InteractiveRegress excess returns, read the beta

Try this 0 of 3

Keep beta positive and make its 95% interval leave out 1. Watch t vs 1.
Keep beta near 1.2 but push R² below 0.25.
Load the hedge and find its CAPM expected return.

One month
Least-squares line, slope 1.24
Slope 1 (moves with the market)

	Coefficient	Std error	t	p-value
Intercept	0.18	0.60	0.30	0.765
Market excess return	1.240	0.150	8.26	< 0.001

R² 0.540 · standard error of the estimate, s_e 4.62 · observations 60. Monthly excess returns in percent.

Source	df	Sum of squares	Mean square	F
Regression	1	1,452.2	1,452.2	68.15
Error	58	1,236.0	21.31
Total	59	2,688.2

The interval 0.94 to 1.54 contains 1: beta is not significantly different from 1 at 5%. R² 0.540: the market explains 54% of the variance (systematic); 46% is idiosyncratic.

Beta1.24

s.e. of beta0.150

t vs 08.26

t vs 11.60

95% interval0.94 to 1.54

R²0.540

1 − R²0.460

Monthly excess returns

Correlation, ρ0.735

Stock σ, monthly6.75%

Market σ, monthly4.00%

Show working

Excess returns: Z_i = r_i − r_f for the stock and Z_m = r_m − r_f for the market, each month. n = 60; Z̄_m = 0.45, Z̄_i = 0.7381.

β̂ = r × s_Zi ÷ s_Zm = 0.735 × 6.75 ÷ 4.00 = 1.2403 (the same as Cov(Z_i, Z_m) ÷ Var(Z_m) = 19.845 ÷ 16.000).

Intercept b̂₀ = Z̄_i − β̂ × Z̄_m = 0.7381 − 1.2403 × 0.45 = 0.180. Not part of the CAPM.

SST = 2,688.19; SSR = 1,452.23; SSE = 1,235.96. R² = SSR ÷ SST = 0.5402 (= r²): the systematic share. 1 − R² = 0.4598 is idiosyncratic.

MSE = SSE ÷ (n − 2) = 1,235.96 ÷ 58 = 21.310; s_e = √MSE = 4.616. F = MSR ÷ MSE = 68.15.

s_β̂ = s_e ÷ √Σ(Z_m − Z̄_m)² = 4.616 ÷ √944.0 = 0.1502.

t vs 0 = 1.2403 ÷ 0.1502 = 8.26; t vs 1 = (1.2403 − 1) ÷ 0.1502 = 1.60. Critical t (df 58, 5%, two-tailed) = 2.0017.

95% interval: β̂ ± t_c × s_β̂ = 1.2403 ± 2.0017 × 0.1502 = 1.2403 ± 0.3007 = 0.9396 to 1.5411.

CAPM: E[r] = r_f + β̂ × (E[r_m] − r_f) = 3.0 + 1.2403 × 5.5 = 9.82%. Premium change +0.5: 1.2403 × 0.5 = +0.62 points.

95% interval for beta

2.0017×0.1502=STO10.3007
1.2403−RCL1=lower 0.9396
1.2403+RCL1=upper 1.5411

STO store · RCL recall a stored number

2.0017ENTER0.1502×STO10.3007
1.2403RCL1−lower 0.9396
1.2403RCL1+upper 1.5411

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Display: 0.94 to 1.54

CAPM expected return

8.5−3=×1.2403+3=9.8217

8.5ENTER3−1.2403×3+9.8217

ENTER enter (on the HP, puts the number on the stack)

Display: 9.82%

Beta is the slope of excess returns on excess returns; R² tells you how much of the risk is the market's.

Reading a CAPM regression output

Outputcoefficients, R², analysis of variance table

Slope Memorize beta: sensitivity to the market
t of the slope Use it beta ≠ 0? subtract 1 first for beta ≠ 1
R² Memorize systematic share of the variance; 1 − R² idiosyncratic
Intercept Know the idea not part of the CAPM; usually tested against 0

How sure is the beta? A confidence interval

Beta is an estimate, so give it a range: the confidence interval for beta is $\hat{\beta} \pm t_c \times s_{\hat{\beta}}$ , with the t critical value for $n-2$ degrees of freedom. If 1 lies inside a 95% interval, beta is not significantly different from 1 at 5%; if 0 lies inside, beta is not significant at all.

Confidence interval for beta Use it

\hat{b}_1 \pm t_c \times s_{\hat{b}_1}

With many observations the t critical value is close to 1.96, which is why outputs built on long samples are often read with it; when the question gives a t value, use that.

Rearrange itConfidence interval for beta: solve for any one

The question asks for

A regression of a stock's excess returns on the market's gives a beta estimate of 1.24 with a standard error of 0.15. With a critical t-value of 2.002, the upper bound of the confidence interval for beta is closest to:

Beta estimate (slope), β̂Standard error of the slope, s_β̂Critical t-value, t_c

upper = b^_{1} + t_{c} \times s_{b^_{1}}

1.24 + 2.002 × 0.15 = 1.5403

Upper bound1.5403

On your calculator

2.002×0.15+1.24=

2.002ENTER0.15×1.24+

ENTER enter (on the HP, puts the number on the stack)

From beta to an expected return

Step 4 plugs the beta estimate into the CAPM: $E[r_i] = r_f + \hat{\beta}(E[r_m] - r_f)$ . Beta has no units, so a beta estimated from monthly returns works with annual rates.

Rearrange itCAPM expected return: solve for any one

The question asks for

The risk-free rate is 3.00%, the expected return on the market is 8.50% and a stock's estimated beta is 1.24. Its expected return under the CAPM is closest to:

Risk-free rate, r_f%Beta estimate, β̂Expected market return, E[r_m]%

E [r] = r_{f} + β^(E [r_{m}] - r_{f})

3.00% + 1.24 × (8.50% − 3.00%) = 9.82%

Expected return, E[r]9.82%

On your calculator

8.5−3=×1.24+3=

8.5ENTER3−1.24×3+

ENTER enter (on the HP, puts the number on the stack)

A fitted value is a different question

“What does the regression predict for the excess return when the market’s excess return is 2%?” uses the whole fitted line, intercept included. “What is the CAPM expected return?” uses only beta, the risk-free rate and the market risk premium.

What if the market risk premium changes?

If the market risk premium rises and the risk-free rate does not move, the expected excess return changes by beta times that change.

Change in expected excess return Use it

\Delta E[r_i - r_f] = \hat{\beta}_i \times \Delta\left(E[r_m] - r_f\right)

What do high, low and negative betas mean?

A beta above 1 amplifies the market: in a downturn a beta-1.5 stock is expected to fall more than a beta-0.5 stock, and in a rally to rise more. A beta below 1 dampens the market.

A negative beta means the asset tends to move against the market: if the market’s excess return is −6% in a month, an asset with $\hat{\beta} = -0.30$ is expected (from the slope) to gain 1.8 points. That makes it a hedge, not a riskier asset. Under the CAPM its expected return is below the risk-free rate, the price of that protection.

How good is the CAPM?

The evidence is mixed: some studies support the model, others find returns it cannot explain. It is still widely used for portfolio management, performance evaluation, the cost of capital and project valuation, because it is simple and ties expected return to the risk that cannot be diversified away. Market data services publish betas estimated the same way; their numbers differ with the window, the return frequency and the index they use.

Go deeper Why different windows give different betas

A company’s business and leverage change over time, so its beta does too. A longer window gives a steadier estimate but reflects the old business; weekly data give more observations but more noise. Neither choice is right in general; state which one you used.

Memorize this

MemorizeCAPM regression

Item	Formula or rule
CAPM	$E[r_i] = r_f + \beta_i(E[r_m] - r_f)$
Excess returns	$Z_i = r_i - r_f$ , $Z_m = r_m - r_f$
Regression	$Z_{i,t} = b_0 + b_1 Z_{m,t} + \varepsilon_{i,t}$ ; slope = beta
R²	share of excess-return variance explained by the market (systematic); $1 - R^2$ idiosyncratic
Interval for beta	$\hat{b}_1 \pm t_c\, s_{\hat{b}_1}$ , $n - 2$ degrees of freedom
Premium moves	$\Delta E[r_i - r_f] = \hat\beta \times \Delta$ premium
Data	bill rate, asset returns, index returns; monthly 3–5 years or weekly 1–3 years

Memory hook Subtract the bill from both, regress, read the slope. Slope = beta, R² = how much is market.

Know it cold Expected return uses the premium E[r_m] − r_f, never E[r_m] alone, and only the slope, not the intercept.

Estimating beta in four steps

CAPM regressionexcess returns on excess returns

1. Gather data Memorize asset, market index, bill rate; monthly 3–5 years or weekly 1–3 years
2. Excess returns Memorize Z_i = r_i − r_f, Z_m = r_m − r_f
3. Regress Z_i on Z_m Memorize slope = beta
4. Expected return Memorize r_f + β̂ × market risk premium

Reading a CAPM regression output

Outputcoefficients, R², analysis of variance table

Slope Memorize beta: sensitivity to the market
t of the slope Use it beta ≠ 0? subtract 1 first for beta ≠ 1
R² Memorize systematic share of the variance; 1 − R² idiosyncratic
Intercept Know the idea not part of the CAPM; usually tested against 0

Capital asset pricing model

E[r_i] = r_f + \beta_i\left(E[r_m] - r_f\right)

Quick example

r_f = 2.0%, E[r_m] = 7.5%, β = 0.9: 2.0 + 0.9 × 5.5 = 6.95%.

On your calculator

7.5−2=×0.9+2= 6.95

7.5ENTER2−0.9×2+ 6.95

ENTER enter (on the HP, puts the number on the stack)

Excess returns

Z_{i,t} = r_{i,t} - r_{f,t}, \quad Z_{m,t} = r_{m,t} - r_{f,t}

Quick example

A stock returns 1.8% in a month, the index 1.1% and the bill 0.3%: Z_i = 1.8 − 0.3 = 1.5%, Z_m = 1.1 − 0.3 = 0.8%.

On your calculator

1.8−0.3= 1.5
1.1−0.3= 0.8

1.8ENTER0.3− 1.5
1.1ENTER0.3− 0.8

ENTER enter (on the HP, puts the number on the stack)

CAPM regression

Z_{i,t} = b_0 + b_1 Z_{m,t} + \varepsilon_{i,t}

Quick example

Regress 60 monthly stock excess returns on the index's: the slope b̂₁ is the beta estimate, here 1.24.

Confidence interval for beta

\hat{b}_1 \pm t_c \times s_{\hat{b}_1}

Quick example

β̂ = 0.75, standard error 0.10, t_c = 2.01: 0.75 ± 0.201 = 0.55 to 0.95.

On your calculator

2.01×0.1=STO1 0.201
0.75−RCL1= 0.549
0.75+RCL1= 0.951

STO store · RCL recall a stored number

2.01ENTER0.1×STO1 0.201
0.75RCL1− 0.549
0.75RCL1+ 0.951

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Change in expected excess return

\Delta E[r_i - r_f] = \hat{\beta}_i \times \Delta\left(E[r_m] - r_f\right)

Quick example

β̂ = 0.8 and the market risk premium falls by 1.0 point: 0.8 × (−1.0) = −0.8 point.

On your calculator

0.8×1+|-= −0.8

+|- change sign

0.8ENTER1CHS× −0.8

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

How it is asked

Which number is beta?

Output: intercept 0.004, slope 0.92 (standard error 0.11), R² 0.61.

Beta = 0.92, the slope. Traps: 0.61 is R², 0.11 the standard error.
Confidence interval for beta

β̂ 0.68, standard error 0.14, t_c 2.002.

0.68 ± 0.280 = 0.40 to 0.96. Trap: ± one standard error, 0.54 to 0.82.
Expected return from the regression beta

β̂ 1.35, r_f 1.8%, E[r_m] 7.0%.

1.8 + 1.35 × 5.2 = 8.82%. Trap: 1.8 + 1.35 × 7.0 = 11.25% uses the market return.
Premium changes

β̂ 1.3; the market risk premium rises 0.8 point, r_f unchanged.

Expected excess return rises 1.04 points. Trap: 0.8 (beta ignored).

Exam traps

Plugging the expected market return instead of the market risk premium into the CAPM.
Reading R² as beta, or as the unsystematic share. R² is the share the market explains; 1 − R² is idiosyncratic.
Adding the regression intercept to a CAPM expected return. The fitted line includes it; the CAPM expected return uses only beta.
Regressing the market on the asset (swapping X and Y), or regressing raw returns on excess returns.
Building the interval with ± one standard error, or with 1.96 when the question gives a t critical value.
Calling a negative-beta asset riskier than the market. It moves against the market and hedges it.

Checkpoint

3 exam-style questions. About 90 seconds each.

1A CAPM regression of a stock's monthly excess returns on the market's excess returns has a slope of 1.10 and an R² of 0.36. The R² is best interpreted as:
2A regression of 60 monthly excess returns of a stock on the market's excess returns gives a slope of 0.86 with a standard error of 0.12. The two-tailed 5% critical t-value is 2.002. The 95% confidence interval for the stock's beta is closest to:
3A CAPM regression of a stock's monthly excess returns gives an intercept of 0.20% and a slope of 1.15. The risk-free rate is 2.5% and the expected return on the market is 9.0%. The stock's expected return under the CAPM is closest to:

Key takeaways

The CAPM prices only systematic risk: E[r_i] = r_f + β(E[r_m] − r_f).
Estimate beta by regressing the asset's excess returns on the market's excess returns; the slope is beta.
R² is the share of the excess-return variance the market explains (systematic); 1 − R² is idiosyncratic.
A confidence interval for beta is β̂ ± t_c × s_β̂; if it contains 1, beta is not significantly different from 1.
A change in the market risk premium changes the expected excess return by beta times that change.

Capital asset pricing model

E[r_i] = r_f + \beta_i\left(E[r_m] - r_f\right)

Quick example

r_f = 2.0%, E[r_m] = 7.5%, β = 0.9: 2.0 + 0.9 × 5.5 = 6.95%.

On your calculator

7.5−2=×0.9+2= 6.95

7.5ENTER2−0.9×2+ 6.95

ENTER enter (on the HP, puts the number on the stack)

Excess returns

Z_{i,t} = r_{i,t} - r_{f,t}, \quad Z_{m,t} = r_{m,t} - r_{f,t}

Quick example

A stock returns 1.8% in a month, the index 1.1% and the bill 0.3%: Z_i = 1.8 − 0.3 = 1.5%, Z_m = 1.1 − 0.3 = 0.8%.

On your calculator

1.8−0.3= 1.5
1.1−0.3= 0.8

1.8ENTER0.3− 1.5
1.1ENTER0.3− 0.8

ENTER enter (on the HP, puts the number on the stack)

CAPM regression

Z_{i,t} = b_0 + b_1 Z_{m,t} + \varepsilon_{i,t}

Quick example

Regress 60 monthly stock excess returns on the index's: the slope b̂₁ is the beta estimate, here 1.24.

Confidence interval for beta

\hat{b}_1 \pm t_c \times s_{\hat{b}_1}

Quick example

β̂ = 0.75, standard error 0.10, t_c = 2.01: 0.75 ± 0.201 = 0.55 to 0.95.

On your calculator

2.01×0.1=STO1 0.201
0.75−RCL1= 0.549
0.75+RCL1= 0.951

STO store · RCL recall a stored number

2.01ENTER0.1×STO1 0.201
0.75RCL1− 0.549
0.75RCL1+ 0.951

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Change in expected excess return

\Delta E[r_i - r_f] = \hat{\beta}_i \times \Delta\left(E[r_m] - r_f\right)

Quick example

β̂ = 0.8 and the market risk premium falls by 1.0 point: 0.8 × (−1.0) = −0.8 point.

On your calculator

0.8×1+|-= −0.8

+|- change sign

0.8ENTER1CHS× −0.8

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

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Simple Linear Regression on 4 pages

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Questions about this lesson?

Where this comes back

The CAPM, the Market Model and Factor Models Equities
Portfolio Risk and Return: Part II (CAPM and Performance Measures) Portfolio Construction

Questions candidates ask

How do you estimate beta with a regression?

Collect the asset's returns, a market index's returns and a short-term government bill rate. Subtract the bill rate from both returns, regress the asset's excess returns on the market's by ordinary least squares, and read the slope. Monthly returns over three to five years or weekly returns over one to three years are typical.

What does R-squared mean in a CAPM regression?

It is the share of the variance of the asset's excess returns that the market's excess returns explain: the systematic part. An R² of 0.54 means 54% systematic and 46% idiosyncratic. It is not beta: a stock can be very sensitive to the market and still have a low R².

How do you build a confidence interval for beta?

Take the slope and add and subtract the critical t-value times its standard error, with n − 2 degrees of freedom. A slope of 1.24 with a standard error of 0.15 and 58 degrees of freedom gives 1.24 ± 2.002 × 0.15, about 0.94 to 1.54.

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