Economics 173 Business Statistics Lecture 16 Fall, 2001 Professor J. Petry

2 Project I: Finance Application Project simulates the job of professional portfolio managers. Your job is to advise high net-worth clients on investment decisions. This often involves “educating” the client. Client is Medical Doctor, with little financial expertise, but serious cash ($1,000,000). The stock market has declined significantly over the last year or so, and she believes now is the time to get in. She gives you five stocks and asks which one she should invest in. How do you respond?

3 Project I: Finance Application The project is divided into three parts 1.Calculate mean, standard deviation & beta for each asset. –gather 5 years of historical monthly returns for your team’s five companies, the S&P 500 total return index and the 3- month constant maturity Treasury bill. Calculate beta b/n each of your stocks and the market index. Put in table and explain to client. 2.Illustrate benefits of diversification with concrete example. –You are provided with average annual returns and standard deviations for the S&P 500 and the 3-month T-bill. You create a portfolio with these two instruments weighted differently to illustrate the impact on risk (standard deviation). 3.Analyze impact of correlations on diversification. –Create table of correlation coefficients between all assets, and explain. Select asset pair with r closest to –1. Explain. –Adjust graph in 2 with r = 1, and –1 instead of 0. Explain.

4 Part 1. Finding Beta (17.6 in text) One of the most important applications of linear regression is the market model. It is assumed that rate of return on a stock (R) is linearly related to the rate of return on the overall market. R =  0 +  1 R m +  Rate of return on a particular stockRate of return on some major stock index The beta coefficient measures how sensitive the stock’s rate of return is to changes in the level of the overall market.

5 Example 17.5 The market model Estimate the market model for Nortel, a stock traded in the Toronto Stock Exchange. Data consisted of monthly percentage return for Nortel and monthly percentage return for all the stocks. This is a measure of the stock’s market related risk. In this sample, for each 1% increase in the TSE return, the average increase in Nortel’s return is.8877%. This is a measure of the total risk embedded in the Nortel stock, that is market-related. Specifically, 31.37% of the variation in Nortel’s return are explained by the variation in the TSE’s returns.

6 Part 2. Diversification (Ex 6.8, sect 6.7) Investment portfolio diversification –An investor has decided to invest 60% of investable resources in Investment 1 (bond fund—conservative investment) and 40% in Investment 2 (stock fund, riskier but higher returns on average). –Find the expected return on the portfolio –If  = 0, find the standard deviation of the portfolio.

7 –The return on the portfolio can be represented by R p = w 1 R 1 + w 2 R 2 =.6(.15) +.4(.27) =.198 = 19.8% The relative weights are proportional to the amounts invested. –The variance of the portfolio return is  2 (R p ) =w 1 2  2 (R 1 ) + w 2 2  2 (R 1 ) +2w 1 w 2  1  2 =(.60) 2 (.25) 2 +(.40) 2 (.40) 2 +2(.60)(.40)(0)(.25)(.40)  2 (R p )=  (R p )=.2193 = 21.93%

8 Part 2. Diversification (cont’d) Investment portfolio diversification –Now assume your investor wants to see what kind of returns and risk she might assume is she invested 20% of investable resources in investment 1 (bond fund—conservative investment) and 80% in investment 2 (stock fund, riskier but higher returns on average). –Find the expected return on the portfolio –If  = 0, find the standard deviation of the portfolio.

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10 Part 2. Diversification (cont’d) Investment portfolio diversification –Maintaining this last assumption (she invested 20% in Investment 1, and 80% in investment 2), but the correlation coefficient between bonds and stocks is now 1, not 0. –Find the expected return on the portfolio –Find the standard deviation of the portfolio.

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Using the Regression Equation If we are satisfied with how well the model fits the data, we can use it to make predictions for y. Illustration –Predict the selling price of a three-year-old Taurus with 40,000 miles on the odometer (Example 17.1). Before using the regression model, we need to assess how well it fits the data. If we are satisfied with how well the model fits the data, we can use it to make predictions for y. Illustration –Predict the selling price of a three-year-old Taurus with 40,000 miles on the odometer (Example 17.1).

13 Prediction interval and confidence interval –Two intervals can be used to discover how closely the predicted value will match the true value of y. Prediction interval - for a particular value of y, Confidence interval - for the expected value of y. –The confidence interval –The prediction interval The prediction interval is wider than the confidence interval

14 Example 17.6 interval estimates for the car auction price –Provide an interval estimate for the bidding price on a Ford Taurus with 40,000 miles on the odometer. –Solution The dealer would like to predict the price of a single car The prediction interval(95%) = t.025,98

15 –The car dealer wants to bid on a lot of 250 Ford Tauruses, where each car has been driven for about 40,000 miles. –Solution The dealer needs to estimate the mean price per car. The confidence interval (95%) =

16 Example –Provide a 95% confidence interval for your Armani’s Pizza estimate from above. You are given the following: = 688.4