# Conditional CAPM analysis for stock-based investing

The previous article examined the performance of 303 stocks listed in the *Bombay Stock Exchange (BSE)* via assessment of average return, market return, and movement analysis. However, these methods only provide an overview of past movements and the performance of stocks. They do not shed light on the linkage between return and risk. ** CAPM** analysis helps in understanding the trade-off for each category of stock, i.e. growth, income and value stock.

Investor’s decision of investment depends on the relationship between risk and return. The existence of uncertainty and variability in the financial market build in the risk for investors. Investors invest in a diversified portfolio to minimise risk and maximise return. **The Capital Asset Pricing Model (CAPM)** was developed in 1964 for assessing the risk and return in stock and enable investors to invest optimally (Sukono et al., 2018). **CAPM** analysis in this article starts with descriptive statistics that explain the nature of the dataset. The previous article (Short term momentum analysis of growth, income and value stocks) grouped the dataset into 4 weeks, 8 weeks, 12 weeks, 3 months, and 6 months to understand the return possibility over a period of time. Therefore, the descriptive analysis herein is done for the same intervals. The time period under consideration is 1^{st} April 2000 to 31^{st} March 2020. The formula used for assessing the risk is:

This can be written as :

Wherein,

R_{i }– R_{f}: Excess return (Expected Return on investment – Risk-free rate of return)

(R_{m} – R_{f}): Market risk premium (Expected market return – Risk-free rate of return)

β: Systematic risk

The **CAPM** evaluates market risk in form of beta for measuring the fluctuations in the stock prices due to market movement. The analysis helps in determining whether the **CAPM** is applicable in *BSE* 500 companies or not. This below-stated hypothesis is tested at a 5% or 10% level of significance.

H

_{01}: There is no significant influence of market risk premium on the excess returnH

_{A1}: There is a significant influence of market risk premium on the excess return

## Descriptive analysis for the market return

The descriptive analysis for the different time intervals is shown in Table 1.

Statistics | 4 weeks | 8 weeks | 12 weeks | 3 months | 6 months |
---|---|---|---|---|---|

Mean | 1.59 | 3.38 | 5.27 | 5.70 | 12.22 |

Standard deviation | 8.89 | 12.90 | 16.65 | 17.40 | 26.60 |

Kurtosis | 5.83 | 7.82 | 5.05 | 5.04 | 5.55 |

Skewness | -0.25 | 0.67 | 0.65 | 0.67 | 0.91 |

Standard Error | 0.13 | 0.18 | 0.24 | 0.25 | 0.38 |

**Mean value:**Represents the performance of return on investment. The mean values above depict that there is not much difference in the performance of the*BSE*for the 4 weeks, 8 weeks, 12 weeks and 3 months period. There has been an improvement in the return earning capacity over time, but the major change is visible in the medium-term i.e. period for more than 3 months.**Standard deviation:**This represents the volatility in returns. With the return, volatility-based risk has increased for the investors and that too rapidly i.e. from 8.89 in the 4 week period to 26.60 in 6 months’ movement.**Kurtosis:**It represents the possibility of extreme variation. The Kurtosis value for the 4 and 8 weeks period is very high showing the occasional presence of extreme values. Though for the 12 weeks, 3 months, and 6 months period the Kurtosis value is comparatively less but still, the presence of value more than 5 depicts that there is the existence of Kurtosis risk wherein investors tend to have extreme variation in their returns.**Skewness:**Represents underestimation of risk. value for the 4 weeks is negative showing the presence of negative skewness risk while for all other periods the value is positive depicting positive skewness risk. However, as the value is below -1 or 1, thus the probability of having underestimation of skewness risk in the model is less.**Standard error:**Represents possibility in error while computation. For each time interval, the value is below 0.4, representing very fewer chances of error.

Hence, the descriptive analysis of the *BSE* 500 market shows that over time, the return earning capacity for the investors has increased but due to the presence of volatility in the market, the risk associated with investment too has risen.

**CAPM** analysis for a growth stock

Growth stocks are high risk and high return investment. The **CAPM** herein determines the risk-free rate of return via the 1-year Treasury bill yield. It derives the excess return and market premium, and the linkage between both. This helps identify the contribution of risk in influencing the decision of investors. The results of the analysis are shown in Table 2.

Excess Return | Coefficient | t-stat | p-value of t | R-square | Adjusted R-square | p-value of F-stat |
---|---|---|---|---|---|---|

Market Premium | 0.994 | 132.88 | 0.00 | 0.7802 | 0.7802 | 0.00 |

**CAPM**analysis results for growth stock

- The values of R
^{2 }and adjusted R^{2}are 0.7802, depicting a 78% variation in the excess return on a stock by market premium. - The P-value of F-stat is 0.00 which is less than the significance value of 0.05 or 0.10, showing more precision of excess return by including market premium as an independent variable.
- Systematic risk value is 0.994, showing that with a rise in market risk premium by 1%, the propensity of deriving excess return increase by 0.994%.
- The P-value for the t-stat test is 0.00 which is less than the required value of 0.05 or 0.10. Thus, the null hypothesis of no significant influence of market risk premium on excess return is rejected.

Hence, the **CAPM** is applicable for growth stocks showing the presence of a relationship between expected return and risk associated with the stock.

**CAPM** analysis for income stock

Income stocks provide investors with a fixed source of income, are a more mature and less risky investment. Companies in income stocks group distribute most of their profits to investors as a dividend. Therefore, the influence of pricing factors is less on the return. The examination of the excess return and market risk premium relationship is shown by the **CAPM** in the table below. It shows the contribution of risk in influencing the excess return value of investor.

Excess Return | Coefficient | t-stat | p-value of t | R-square | Adjusted R-square | p-value of F-stat |
---|---|---|---|---|---|---|

Market Premium | 0.9998 | 405.28 | 0.00 | 0.9706 | 0.9706 | 0.00 |

**CAPM**analysis results for income stock

- The value of R2 and Adjusted R2 is 0.9706, showing a 97% variation in the excess return value represented by the market risk premium.
- A P-value of F-stat is 0.00 i.e. less than the significance level of 5% or 10%. This depicts that more precision in the computation of the excess return for the income stock is determined by the inclusion of market premium as the independent variable.
- The coefficient value of market premium depicts the systematic risk value i.e. 0.9998 which is slightly greater than the beta value for the growth stocks. As the value is approximately equal to 1, the volatility of income stocks is the same as the volatility present in the market.
- Beta value further states that the rise in market premium by 1% tends to raise the excess return possibility by 0.9998%.
- The P-value for the model is 0.00 which is also less than the significance value of 0.05 or 0.10. Thus, the null hypothesis of no significant linkage between the excess return and market premium is rejected.

Hence, in the case of income stocks, the **CAPM** is applicable and there is the presence of a relationship between expected return and risk.

**CAPM** analysis for value stock

Value stocks are cheap, undervalued stocks. They have good financial status but are less stable and perform poorly often, causing distress to investors. Considering the associated risk and the return possibility for the investors, the below table, represents the linkage between the excess return and market risk premium. **CAPM** is used to identify the contribution of risk in influencing the excess return of investors.

Excess Return | Coefficient | t-stat | p-value of t | R-square | Adjusted R-square | p-value of F-stat |
---|---|---|---|---|---|---|

Market Premium | 1.0015 | 1280.33 | 0.00 | 0.997 | 0.997 | 0.00 |

**CAPM**analysis results for value stock

- R
^{2 }and Adjusted R^{2}are 0.9970, showing 99.7% of the variation in the excess return of value stocks by the market risk premium. - P-value of F-stat as 0.00, depicting that the value is less than the required level of 0.05 or 0.10. Thus, the build in the
**CAPM**is more effective is stating the linkage between excess return and market premium. The computation of excess return is more precise when considering market risk premium as the independent variable for the model. - The coefficient value is 1.0015, showing the systematic risk of investors. Comparison of value with the growth and income stocks shows that since the beta value higher than the growth and income stocks, there is more risk associated based excess return earned by the investors in value stocks. Also, with a 1% increase in the market risk premium, there has been a rise in excess return by 1.0015%.
- Lastly, the p-value of t-stat is 0.00 which is less than the significance value of 0.05 or 0.10. Thus, the null hypothesis of no significant linkage between the excess return and market risk premium is not rejected.

Hence, the analysis shows that in the case of value stocks, the **CAPM** is applicable and there is a presence of a relationship between expected return and risk for the value stocks.

## Growth investing is an effective source of investment

Investors estimate the relationship between expected return and risk using the **CAPM** analysis to invest optimally. For this investors compare the investment with the market performance and select the stock wherein associated systematic risk due to volatility of the market is low. Examination of growth, income, and value stocks for the period 1st April 2000 to 31st March 2020 depicts that the **CAPM** model is applicable for all of the selected stocks. However, there is risk in growth stocks as compared to market risk, making it optimal for investment. Growth stocks issuing companies tend to provide a secured investment source to the investors. Although value stocks, in general, are considered to have low risk, herein, the risk intensity of the stocks is high. Due to this, investors who prefer high-risk instruments will invest in value stock for a higher return. Lastly, as income stocks risk association is similar to the *BSE* 500 market, the investors would be indifferent to either investing in income stocks or having a portfolio of different stocks.

#### References

- Chowdhury, E. K., & Chowdhury, T. U. (2015). Application of Capital Asset Pricing Model- Empirical evidences from Chittagong Stock Exchange.
*The Cost and Management*,*3*, 38–44. - Sukono, Susanti, D., Najmia, M., Lesmana, E., Napitupulu, H., Supian, S., & Putra, A. S. (2018). Analysis of stock investment selection based on CAPM using covariance and genetic algorithm approach.
*IOP Conference Series: Materials Science and Engineering*,*332*(1). https://doi.org/10.1088/1757-899X/332/1/012046

- Analysing annualized average returns from BSE listed stocks - May 13, 2021
- Predicting value stocks trend using ARIMA - May 11, 2021
- Forecasting income stocks trend with the ARIMA model - May 7, 2021

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