Goal: This case introduces simple regression analysis in the context of estimating the financial risk of a widely held stock. Specifically, this case introduces how to:

• Estimate a Simple Regression Model using FORECASTX^TM
• Evaluate the "Goodness-Of-Fit" of an Estimated Regression Model
• Generate Confidence Intervals for the OLS Slope Parameter
• Analyze the Financial 'Beta' of a widely held High-Tech Stock.

The spreadsheet for this problem is CH4_Case1.xls. It contains the following data:

From December 1994 through January 1995 we collected 37 daily observations on the NYSE composite stock index and the closing price of Intel stock (INTC), accounting for weekends, holidays and missing observations.

The series NYSE is the daily close on the New York Stock Exchange Composite Index.

The series INTC is the daily closing price for Intel stock.

We converted the data above into daily continuously compounded rates of return with the following using a spreadsheet:

This creates two new series %NYSE and %INTEL, which are the approximate percentage change each variable, respectively. These are the holding period returns on the NYSE and INTC labeled HPR NYSE and HPR Intel in the spreadsheet. We are now ready to examine the risk characteristics of Intel stock.

There are two important measures of the risk of holding any stock. The first measure called total risk is the variability of Intel's rate of return measured by the standard deviation. This total risk measure is appropriate for a portfolio in which Intel is the only stock; we are ignoring for now the effects of portfolio diversification.

In modern finance, the preferred measure of the risk associated with the return on a stock is volatility defined as standard deviation. Accordingly, volatility is the expected deviation from the mean rate of return. A classic proposition in finance is that portfolio diversification reduces risk!

To examine this, the following volatilities were calculated using the Statistics Menu in FORECASTX^TM.

A time-series plot of holding period returns on NYSE and INTEL is shown below.

Question #1: Based upon examination of the time-series plot of the holding period returns on INTC and NYSE and their respective estimated volatility, which is riskier? Explain.

ANSWER:

A second measure of risk is called Market Risk and measures the variability in Intel stock attributable to the economy (stock market) as a whole and not specific to Intel or its management. This risk measure is relevant when holding INTC as part of a well-diversified equity portfolio. Accordingly, the correlation between the rate of return on Intel and that of the NYSE composite is an important determinant of Intel’s market risk.

The estimated correlation matrix using FORECASTX^TM is:

Question #2: Based upon examination of the scatter plot between the holding-period returns on Intel and the NYSE, and the estimated correlation coefficient, how strong is the relationship between %Intel and %NYSE? Formally test the null hypothesis of no correlation between HPR Intel and HPR NYSE using a one-tailed alternative for level of significance of .05.

ANSWER:

The measure of market risk used by portfolio managers is the risk contribution of a single stock to a well-diversified portfolio and is called a "Financial Beta (b)." Betas have the following interpretation: A beta of one means the stock has the same risk as the overall market (benchmark) portfolio. Accordingly, a beta of .5 (1.5) indicates security risk of one-half (one and one-half) of that of the overall market. Specifically, it can be shown that the variance of Intel returns relate to the variance of the returns on the market as a whole by the following relationship:

Var(%INTEL) = b²Var(%NYSE)

Accordingly, market risk, defined as variability in Intel’s returns attributable to the market as a whole (as measured by beta), can be estimated by using the market model of finance.

Accordingly, to estimate Intel’s market risk (beta), we apply ordinary least squares to the following simple linear regression model:

R_Intel,t = a + b R_Market,t + e_t

Where:

R_Intel,t = Daily rate of return of Intel stock.

R_Market,t = Daily rate of return on Market Index (NYSE).

b = Intel’s financial beta measuring the market risk of Intel stock.

Using the multiple regression forecasting option in FORECASTX^TM, we generated the following tables:

Question #3: What is the estimated beta for Intel? What does this suggest about the market risk of Intel?

Answer:

Question #4: What is the 95% confidence interval for Intel’s beta? What does your answer suggest about the quality of this particular regression? Explain.

ANSWER:

Question #5: R2 measures the proportion of the total variance of Intel’s stock that can be explained by movements in the overall stock market. What percent of Intel's risk is attributable to the market as a whole? Does this result surprise you? Explain.

ANSWER:

Question #1: Go to the Internet and gather daily data for one year on INTC and either the NYSE Composite or the S&P 500 and redo the assignment. Contrast and compare your results. Did the presence of more data provide a substantial improvement in fit?