Case: Capital Asset Pricing Model

Case: Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) describes the relationship between returns on a speculative asset (typically returns on stock) and returns on the whole stock market. The underlying theory describes the risk of owning an asset, where risk refers to variation in returns over time. Part of the risk of owning an asset is associated with overall movements in the market as a whole and so is called market risk. The remaining idiosyncratic risk is unique to the asset. The underlying theory promises that markets will pay investors for taking market risk, but not for assuming idiosyncratic risk, which it treats as a gamble.

According to the CAPM, a simple regression model describes the returns   Rt   on a stock  over some time period as  Rt = α + βMt + Ɛt     where  Mt   is the return on the market and  Ɛt    denotes the effects of other factors on the stock return. The intercept α is called the alpha of the stock, and the slope β is called the beta of the stock.  The data capm.jmp for this example give monthly returns on Berkshire Hathaway and the overall stock market since January 1980. Use these data to fit the CAPM regression and check whether the simple regression model is appropriate. Answer the following questions:

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1. If β = 0, do movements in the market influence the value of the stock?

• No, if the stock’s Beta equals zero then that means it is not correlated with the market.

2.  If β = 1, does the stock tend to move up and down with changes in the market?

• Yes, if the stock’s beta is 1 that indicates that the portfolio will move in the same direction and will have the same volatility as the market and is sensitive to systematic risk.

3. What kinds of stocks have stock beta: β • 1, β < 1, or β < 0? Give some examples.

• A beta less than 0 indicates that it moves in the opposite direction of the market.

• Examples: Stocks of debt collection companies, SH (ProShares Short S&P 500), SPXU (ProShares UltraPro Short S&P 500).

• A beta between 0 and 1 signifies that it moves in the same direction as the market, with less volatility.

• Examples:

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• A beta greater than 1 indicates that the portfolio will move in the same direction as the market, with a higher magnitude, and is very sensitive to systematic risk.

• Examples: Apple, Amazon

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Sources: http://www.abg-analytics.com/stock-betas.shtml

https://www.investopedia.com/ask/answers/031715/how-does-beta-reflect-systematic-risk.asp

4. The claim of CAPM that investors are not compensated for taking idiosyncratic risk implies that α =?

• CAPM shows that the cost of equity capital is determined only by beta (β); hence, α = 0. “An alpha of zero would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any value” (https://www.investopedia.com/terms/a/alpha.asp)
• Idiosyncratic risk refers to the risk directly associated with the stock and that is not a result of changes in the market. (https://www.investopedia.com/terms/i/idiosyncraticrisk.asp).

5. What is risk?

• Risk takes on many forms but is broadly categorized as the chance an outcome or investment's actual return will differ from the expected outcome or return. Risk includes the possibility of losing some or all of the original investment. It can also be defined as variations in returns over time.

6. What is variation?

• Variation tells you how far a data set is spread out and is the fluctuation in price or returns of stocks. It can include both common variation (normal, random) and specific variation (trend or pattern).
• A range is one of the most basic measures of variation. It is the difference between the smallest data item in the set and the largest. For example, the range of 73, 79, 84, 87, 88, 91, and 94 is 21, because 94 – 73 is 21.

7. What is market risk?

• Market risk, also called "systematic risk,” is the possibility of an investor experiencing losses due to factors that affect the overall performance of the financial markets in which he or she is involved.
• Sources of market risk include recessions, political turmoil, changes in interest rates, natural disasters and terrorist attacks.

8. How can we measure association?

• Association can be measured by using correlation analysis (when having both the variables as random one), regression analysis (when out of the two variables one is a fixed variable) (https://math.tutorvista.com/statistics/correlation-and-regression.html), Pearson’s correlation coefficient or Spearman rho (to measure the strength of the association), Chi-Square Test (to measure the significance of the association), and Relative risk or odds ratio (to measure the strength of the association considering the incidence of multiple events), among others. (https://www.britannica.com/topic/measure-of-association)
• The measures of association refer to a wide variety of coefficients (including bivariate correlation and regression coefficients) that measure the strength and direction of the relationship between variables; these measures of strength, or association, can be described in several ways, depending on the analysis.

9. What is idiosyncratic risk?

• Idiosyncratic risk, also referred to as unsystematic risk, is the risk that is endemic to a particular asset such as a stock and that is not a result of changes in the market. Idiosyncratic risk can be mitigated through diversification in an investment portfolio. This is the risk that remains from owning an asset, after accounting for market risk.

10. What is the alpha of the stock?

• Alpha is perceived as a measurement of a portfolio manager's performance. The alpha of the stock is determined by the intercept in this model: Rt = α + βMt + Ɛt. Alpha is used for mutual funds and all types of investments. It's often represented as a single number (like 3 or -5), but this refers to a percentage measuring how the portfolio or fund performed compared to a benchmark index (i.e., 3% better or 5% worse).

11. What is the beta of the stock?

• Beta is a measure used in fundamental analysis to determine the volatility of an asset or portfolio in relation to the overall market. Beta is often used as a risk-reward measure meaning it helps investors determine how much risk their willing to take to achieve the return for taking on that risk. A stock's price variability is important to consider when assessing risk. If you think of risk as the possibility of a stock losing its value, beta has appeal as a proxy for risk. The beta of the stock is determined by the slope in this model Rt = α + βMt + Ɛt.

12. What is CAPM? According to this theory, will investors be compensated for taking market risk? Will investors be compensated for taking idiosyncratic risk? What does this theory treat idiosyncratic risk really as?

• The capital asset pricing model (CAPM) is a model that calculates expected return based on expected rate of return on the market, the risk-free rate and the beta coefficient of the stock.
• Yes, according to this model investors will be compensated for the market risk but not for the idiosyncratic risk. Within this theory, idiosyncratic risk would be considered as gambling. However, although the impact of the idiosyncratic risk cannot be completely eliminated, within this theory it can be significantly minimized through diversification (https://www.investopedia.com/articles/06/capm.asp).

13. Hedge funds often claim that they are able to pick investments for which alpha>0. What are they claiming about these investments?