1. A stock's (or portfolio's) β(beta) is a measure of the volatility of that stock relative to the volatility of the market-therefore, the market has a β equal to one. For individual securities, β can take on any value, negative or positive.
Some basic facts about β:
• If an individual security has β= 1, then that security tends to move in line with the market.
• If β= 0 the returns on the security are uncorrelated with returns of the market.
• If 0 <β<1 the security tends to move in the same direction as the market, but is less volatile than the market.
• If β>1 the security tends to move in the same direction as the market, but is more volatile than the market.
• If β<0 the security tends to move in the opposite direction of the market. Above average returns on the market would tend to be associated with below average returns on the security and vice versa.
A stock's βis calculated from a least-squares regression of the returns of the stock on the returns of the market. IfRstis the return of the stock on day t,Rmtis the return of the market at time tandRfis a risk free return, then we ?t the linear regression model and use the estimate of the slope as the β for the stock.
In this exercise you will calculate β for "Intel stock" using all available data from September 25, 2014 to present. We will use the returns of the S&P 500 to serve as our "market returns" in the calculation and the return on three month treasury bonds as a risk free return. The steps below walk you through the calculation.
(a) Find and download the daily closing values of the S&P 500 and Intel stock for the time period starting Sep 25, 2014 and ending Sep 25, 2015 from the internet. Import both data sets into a spreadsheet. What website did you use to download the data?
(b) Calculate the daily percentage returns for the S&P 500 and Intel stock. The daily percentage return for day t is:
wherevtis the closing value of the security on day t. What was the daily percentage return of the S&P 500 on September 24, 2015?
(c) Create a new data series measuring excess market return and excess return on Intel stock .
(d) Produce a scatterplot of the excessreturn of Intel stock versus the excess market returns on S&P500. Com¬ment on the strength, direction, and form (e.g., linear, quadratic, non-linear) of the scatterplot. Copy and paste the scatterplot into your document.
(e) Use OLS regression to estimate the β for Intelstock. Include all relevant information about the regression equation. Interpret both αandβof Intel stock.
(f) Comment on statistical significance of estimated coefficients.
(g) Graph the data points and the estimated regression line.Does the regression error appear to be homoskedastic or heteroskedastic? Explain
(h) Compute the correlation coefficient between excess market return and excess return on Intel stock, and compare its square to the R2. How are the correlation coefficient and the R2 related?
(i) Use the information above to ?nd the predicted (?tted) percentage return ofIntel stock when the percentage excess market return on the S&P 500 is 1%.