In this question, with the data provided we estimate each portfolio’s security characteristic line (SCL) and obtain an estimate of its true beta coefficient; then we use the findings to estimate and plot the Security Market Line (SML). In doing so, we have two purpose to fulfill. First, demonstrating the fact that the total variance of a portfolio approaches the systematic variance as diversification increases, which means diversifying across industries offer benefit over diversifying within a given industry. Second, using the figures estimated to testify that the CAPM works in practice. The capital asset pricing model (CAPM) provides us with an insight into the relationship between the risk of an asset and its expected return. This relationship serves two significant functions. First, it provides a benchmark rate of return for evaluating possible investments. Second, the model helps us to make an educated guess as to the expected return on asset that have not yet been traded in the marketplace. Although the CAPM is widely used because of the insight it offers, it does not fully withstand empirical tests. CAPM is a one-period model that treats a security’s beta as a constant, but beta can be changed in respond to firms investment in new industry, change in capital structure and so on. If betas change over time, simple historical estimates of beta are not likely to be accurate. Mismeasuring of betas will not reflect stocks’ systematic risk, so in this case the CAPM does not compute the risk premium correctly. Furthermore, the systematic risk, the source of risk premiums, cannot be confined to a single factor. While the CAPM derived from a single-index market cannot provide any insight on this. The data we used provides us with 5-year period (60 observations) monthly returns for 48 industry portfolios, the excess return on a broad market index and the one-month (risk-free) Treasury bill rates. In order to better illustrate the methodological approach, we take the agriculture industry portfolio which is listed in the first place for example. As a first step, the excess returns on the industry portfolio for 60 observations are computed, which can be achieved by subtracting risk-free rate from monthly returns. The excess return on a broad market index is already available. In order to estimate the portfolio's security characteristic line, we apply the index model regression equation, which is stated as following.
Since represent firm-specific, zero-mean residual, the risk premium can be written as
As for expression of the CAPM, the most familiar one which is named as expected return-beta relationship can be stated as
From the two equation above, it can be found that the expression of CAPM expects to be zero. We are going to talk about this in detail later. The regression analysis can be conducted by Excel, the output include SCL for agriculture industry portfolio with intercept and slope, as well as regression statistics of it. Conducting the same procedure for all the industry portfolios we can get each portfolio’s security characteristic line and obtain an estimate of its beta. The CAMP states that the risk premium equals. Consequently, the expected return-beta relationship can be portrayed graphically as the Security Market Line (SML). We can portray SML by connecting the point on the horizon axis where with another point on the horizon axis where. The readings on the vertical axis of the two points are excess market return and risk-free rate respectively. Average excess market return and risk-free rate over 60 months are used to generate SML, the actual return of 48 industry portfolios and their beta are also plotted on the graph. Following are the results derived from the data available.
Since there are too many industry portfolios, we just take the agriculture portfolio and food portfolio to illustrate the outcomes.
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