Capital Asset Pricing
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Capital Asset Pricing
A simple model
Background
The Capital Asset Pricing Model (CAPM) is an important financial modeling tool where simple linear regression can be applied. This model is used to assess the risk of a security in terms of its contribution to the risk of a portfolio of stocks.
Ten years of quarterly data are available in the R data file capm .Rda, containing data on the following four variates:
● Year - the year of measurement, beginning at 1, the first year of available data.
● Quarter - the quarter (3 month period) for which summary measurements were made.
● PortfolioRate - the quarterly rate of return, as a percentage, for an entire portfolio (collection) of stocks.
● StockRate - the quarterly rate of return, as a percentage, for one particular stock in the portfolio.
In this question, you will investigate the dependency of the particular stock rate on that of the whole portfolio’s rate of return. Of interest is how the specific stock returns change relative to overall movements of
stock market returns. This reflects the stock’s volatility relative to that of an average stock. directory <- " . ./data" # directory where you have saved "chips .Rda" load(file .path(directory, "capm .Rda"))
Important note: In all cases where numerical calculation or plotting is required, include the R code used to produce the results.
11 marks
a. (2 marks) Produce a scatterplot of the data with StockRate as the vertical or y axis, and Quarter as the horizontal or z axis (use cex = 2). Make sure the axes are meaningfully labelled and give the plot a meaningful title as well.
● Show the plot
● Does a simple straight line model appear appropriate for this data? Explain.
b. (2 marks) Produce a scatterplot of the data with StockRate as the vertical or y axis, and PortfolioRate as the horizontal or z axis (use cex = 2). Make sure the axes are meaningfully labelled and give the plot a meaningful title as well.
● Show the plot
● Does a simple straight line model appear appropriate for this data? Explain.
c. (2 marks) Fit a simple straight model and provide the equation of the fitted line. What financial implication does the value of the estimate of 81 have?
d. (3 marks) A stock might be considered to be of average risk with respect to the portfolio it is part of, if its rate of return moves lock step with the rqte of return of the entire portfolio. That is, it is average
risk if its rate changes by one percentage point every time the rate of the portfolio changes by one percentage point.
Construct a 99% confidence interval for 81 and use this to assess whether it is plausible that the stock has average risk with respect to this portfolio. Explain your reasoning.
e. (2 marks) It is estimated that the return rate of the entire portfolio in the next quarter would be 8%. Construct a 95% prediction interval for the particular stock’s return when the entire portfolio returns 8%. What point estimate would you give for the predicted return of this stock?
2023-02-18
A simple model