SIM and the efficient frontier In Tutorial Library

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TITLE: SIM and the efficient frontier




Question: SIM and the efficient frontier

i.    Estimate the Single Index Model parameters for each of the following 5 stocks,
      using daily data for the period 8/09/2009 to 30/11/2009:

-     BHP (BHP Billiton)

-     WOW (Woolworths)

-     CSL

-     JHX (James Hardie)

-     AIO (Asciano)


You will need also to collect data for the market index (use the All Ordinaries Index)


Use DAILY closing stocks prices (NOTadjusted closing prices) from Yahoo Finance
( All Ords data can also be obtained from Yahoo Finance.
Use the 90 day bank bill rate as a proxy for determining the risk free rate.  Daily data is
available from the RBA website (
Table F1.

For your calculations of daily returns on the time series data (stocks, All Ords and 90 day bank bill rate) use daily continuously compounded returns (CCR).


a.         Report the following results in your Word document summary:


BHP       WOW    CSL       JHX       AIO                                                      AllOrds


(alpha t-stat)


(beta t-stat)


Residual Variance        i



Excess Return Variance        i




b.         Interpret and comment on your estimates of the alpha and beta

parameters. Which stocks would you judge to be ‘defensive’ and why?


ii.         What is the average daily excess continuously compounded return on the

market index?                                                                                


iii.        Select one of your stocks and plot the Security Characteristic line based on

your regression results at (i) above. (Insert the graph, with the regression

equation,  in your Word Document.)                     


iv.        For each of the 5 stocks, what  proportion of the total variance in each

stock’s excess return relates to the systematic risk component?


v.         What is the expected return and standard deviation of a portfolio that

comprises equal weights of the 5 stocks (i.e 20% each)? 

Assume that the expected excess return on the market index over the forthcoming period is the historical average excess return calculated at (ii)


vi.        Using the standard deviation estimated at (v), use Excel Solver to determine

the efficient portfolio for that level of risk. (Assume NO short-selling)


a. What are the weights of each stock in the portfolio? 

b. What is the annualised expected portfolio return and annualised

standard deviation?                                                                 


annualised E(r) = periodic expected return * number of periods in the year;

annualised variance= Period variance* number of periods in the year; annualised
standard deviation = period standard deviation *(number of periods in year)1/2

Your answer to (vi)(b) forms your first data point in mapping the efficient


vii.       Determine and plot the efficient frontier.                           

In Word insert:

a. a table of the datapoints (combinations of annualised standard deviation
      and annualised expected return determined using Excel Solver) and the
      weights of each stock (for this exercise, assume 365 day in a year)

b. the graph of your efficient frontier (ensure you label the axes)



HINTS: I will handout materials on the Single Index Model from the relevant chapter of
Yip, H. 


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1. Finance
2. Financial Management
3. Corporate Finance
4. Investment and Portfolio Management
5. Business Economics
6. Economics


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