ECO14 SY 15-16 - Assignment for SIM - Instructions

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ECO14 S.Y. 2015-2016

Assignment for Single Index Model

Please follow these instructions as you complete the requirements for this assignment.

Note:

Chapters 8 and 9 of Investments by Bodie, Kane and Marcus may be referred to.

Data are in the MS Excel files ECO14 SY15-16 – Assignment for SIM – DATA (specifically in the ‘Raw data’ worksheet)This sheet contains monthly adjusted closing prices of 10 firms, market index (S&P 500 index) as well as the monthly

risk free rate of return and (yield on the 13 week treasury bill) covering the period December 2010 to Decembe

2015.

You may use MS Excel or other statistical software for coming up with the regression results for your homework.

1.

Convert the monthly adjusted closing prices of the 10 firms and the market index into monthly continuously

compounded returns. The covering period shall now be from January 2011 to December 2015 with a total of 60

observations for each data series.

2.

Obtain the mean, variance and standard deviation for the monthly return data of the 10 firms, market index and

risk free rate. Use the variance and standard deviation for sample data set (with formula VAR.S and STDEV.S in

MS Excel).

Note: From here, you can determine the variance of the market index ( σ2

m )

3.

Using the monthly return data on the 10 stocks and the market index covering January 2011 to December 2015,

estimate by OLS regression the parameters and of the Single Index Model (SIM) regression

.

where is the return of the stock i in period t and

where is the return on the market index in period t

Assume that the return/movement on the stock market index represents the single source of systematic risk o

all stocks.

4.

In the worksheet, ‘Summary of Results – Individual’, the report the estimated regression results in a table with

the following format:

Stock i

Alpha

Beta

Estimate T-stat p-value Conclusion Estimate T-stat p-value Conclusion

PRU

SBUX.

.

.

INTC

MARKET

Note: Report your conclusion for the and estimate whether the parameter estimate is statistically

significant or statistically insignificant given the corresponding p-values and t-statistic values. Is the stoc

undervalued or overpriced? Is it an aggressive stock or otherwise?



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5.

Report the expected returns, average returns, r-squares, standard error of the regression for each stock in a

table using the following format:

Stock i

Expected

Return

Average

Return

R-square

Standard Error

of the

Regression

PRU

SBUX

.

.

.

INTC

MARKET

Note: For reporting purposes, the appropriate which is the adjusted .

6.

Based on the SIM regression results, decompose the total risk of each stock to the systematic risk component

, and firm specific risk component, . Report these in the abovementioned worksheet in tabular form

in a format, as follows:

Stock i

Systematic

Risk

Firm

Specific

Risk

Total

Risk

PRU

SBUX

.

.

.

INTC

MARKET

Note: Total risk is computed as =

+

. Firm specific risk is computed as the square of the standard

error of the regression.

7.

Using the 10 stocks, form an equally weighted portfolio (call it P), i.e., the weight of each stock in the portfolio is

. Construct the portfolio return variable for this equally weighted portfolio for the period January

2011 to December 2015.

8.

Estimate by OLS the parameters of the SIM regression: . Report in tabular form the

estimates in a separate worksheet named ‘Summary of Results – Porfolio’, as follows:

Portfolio,

P

Alpha BetaAdjusted

R-squareEstimate T-stat p-value Conclusion Estimate T-stat p-value Conclusion



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9.

Determine the proportion of the total risk that is systematic risk and the portion that is firm specific in the

equally weighted portfolio. To do this, use the adjusted for the 10 individual stocks that you have previously

obtained from the regression results. Compute for the proportion of total risk that is systematic and the

proportion that is firm specific for each stock. For the portfolio, sum up the individual proportions pertinent to

each stock. Report and tabulate the results in the same worksheet, as follows:

Proportion of total risk that is

systematic (adjusted )

Proportion of total risk that is

firm specific (1 - )

PRU.

.

.

INTC

Portfolio, P

Is the proportion of systematic risk for the portfolio greater than the proportion of systematic risk for each of

the 10 stocks? What do the results suggest?

ECO14 SY 15-16 - Assignment for SIM - Instructions

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