Regression Analysis of the Security Market Line: Beta and Expected Returns
Overview
This paper analyzes the relationship between Beta and expected returns using regression analysis to estimate the Security Market Line (SML). The study demonstrates a strong positive correlation between systematic risk (Beta) and expected returns, with Beta explaining 99.34% of the variance in expected returns, supporting the Capital Asset Pricing Model (CAPM) framework.
What this coursework covers
- Part A: Regression analysis presenting the relationship between Beta and expected return with statistical summary output and residual analysis
- Part B: Interpretation of regression results including discussion of Multiple R correlation coefficient, R-squared coefficient of determination, and ANOVA significance testing
- Explanation of SML as a CAPM tool for evaluating investment risk-return relationships and the role of Beta in measuring systematic risk
Preview
Econ and Accounting, Security Market Line
Student’s Name
Institutional Affiliation
Econ and Accounting, Security Market Line
The following data on the annual Beta and expected return on assets are used to estimate the “Security Market Line (SML).”
Beta | Expected return |
0.2 | 0.02 |
0.5 | 0.035 |
0.75 | 0.052 |
1.2 | 0.085 |
1.5 | 0.11 |
Part A: A Regression Line
The following is a regression showing the relationship between Beta and Expected return.
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.996688 | |||||||
R Square | 0.993387 | |||||||
Adjusted R Square | 0.991182 | |||||||
Standard Error | 0.003454 | |||||||
Observations | 5 | |||||||
ANOVA | ||||||||
| df | SS | MS | F | Significance F | |||
Regression | 1 | 0.005377 | 0.005377 | 450.6247 | 0.000229 | |||
Residual | 3 | 3.58E-05 | 1.19E-05 | |||||
Total | 4 | 0.005413 |
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| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% |
Intercept | 0.002315 | 0.003142 | 0.736772 | 0.514649 | -0.00768 | 0.012315 | -0.00768 | 0.012315 |
X Variable 1 | 0.069982 | 0.003297 | 21.22792 | 0.000229 | 0.05949 | 0.080473 | 0.05949 | 0.080473 |
RESIDUAL OUTPUT | ||||||||
Observation | Predicted Y | Residuals | ||||||
1 | 0.016311 | 0.003689 | ||||||
2 | 0.037306 | -0.00231 | ||||||
3 | 0.054801 | -0.0028 | ||||||
4 | 0.086293 | -0.00129 | ||||||
5 | 0.107288 | 0.002712 | ||||||
The following graph shows the estimated security market line.
Part B. Explaining the Regression Line
The regression line is presented as . Y is the expected annual returns, and x is the Beta. Therefore, the regression equation is . As such, when all other factors remain constant, a one-unit change in Beta results in a 0.06998 change in expected returns. Besides, expected returns are equal to 0.00232 when the value of Beta is zero. The SML shows a positive association between expected return and Beta.
The multiple R is defined as a correlation coefficient that examines how two variables are linearly related. The correlation coefficient is usually between -1 and 1. The absolute value of the correlation coefficient denotes the strength of the relationship. The summary output table shows that the value of the multiple R is 0.996688, which indicates that because the value is significant, the relationship between the values is strong.