Finance 300 Financial Markets Lecture 3 Professor J. Petry, Fall, 2002©

2 Housekeeping Keep your eyes on the calendar from the web-site. mid-term is 9/17 covering chapters 1-3—a week from Tuesday! equity analysis project begins soon. Teams on Tuesday. You should be doing ALL the “Things to Do” with variations on the theme—think exam questions We will NOT cover Arbitrage Pricing Theory Pages 65-66, TTD II-22. Last time I promised you the calculator key strokes for the IRR question at the end of our notes from Lecture 2....

4 Chapter II-Portfolio Theory 1.Measuring Portfolio Risk & Return 2.Diversification 3.Capital Asset Pricing Model (CAPM)

5 Risk Rational investors are risk averse—they must be compensated to take on risk. Risk in financial markets is quantified using standard deviation: Which provides a measure of the average distance of the observations from their mid-point—how dispersed the data points are around the mid-point. Our calculators can easily calculate the standard deviation for us:

6 Things To Do: II-12

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8 Interpreting Standard Deviation In our example, what percentage of the observations fall within the expected interval for 1, 2 and 3 standard deviations?

9 Benefits of Diversification Harry Markowitz demonstrated beginning in the 1950s that risk can be greatly reduced by holding a number of assets, in place of just one. This won him the 1990 Nobel Prize.

10 Benefits of Diversification An investor has two alternative investments Stocks return 17% w/ standard dev of 25% Bonds return 10% w/ standard dev of 12% She can choose any combination of these two investments in selecting her portfolio The return and risk characteristics of this portfolio are found by: 1.R p = w 1 R 1 + w 2 R 2   p = w 1 2    + w 2 2   2 +2w 1 w 2    1  2

11 Benefits of Diversification Using these two rules, find the risk and return for a portfolio that is 40% bonds and 60% stocks. Assume correlation coefficient of 1. Stocks return 17% w/ standard dev of 25% Bonds return 10% w/ standard dev of 12% R p = w 1 R 1 + w 2 R 2   (R p ) = w 1 2    + w 2 2   2 +2w 1 w 2    1  2

12 Benefits of Diversification

13 Benefits of Diversification Correlation Coefficient = 1

14 Benefits of Diversification Correlation Coefficient = 0

15 Benefits of Diversification Correlation Coefficient = -1

16 Benefits of Diversification As should be apparent, the extent of diversification depends upon the correlation coefficient between the assets incorporated. Correlation coefficient is a measure of the strength linear assocation between variables, and ranges from – 1 to +1. –-1 suggests perfectly negatively related variables, 0 suggests no linear association, and +1 suggests perfectly positive linear assocation. –Correlation coefficeint is calculated using the Data and Stat functions, just as for the standard deviation. Enter P&G data as Y variable and calculate the standard deviation between the S&P 500 and P&G:

17 Benefits of Diversification The choice of portfolio will vary by individual, and would be enhanced by inclusion of a risk free alternative, but there are specific portfolios of particular interest. Minimum variance portfolio is one such choice w B(min) = (   s –  BS  B  S )/(  B 2 +  S 2 -2  BS  B  S ) Calculate each of the weights for the minimum variance portfolio weights with r = +1, 0 and –1, and identify on the respective graph.

18 Benefits of Diversification Unsystematic, residual or specific risk: –Reflects industry or firm specific forces –Can be entirely eliminated by diversification Evidence shows that the risk of a portfolio can be reduced by about 60% by holding from stocks compared to the risk of holding a single stock. There is a limit to diversification benefits however. Systematic or Market Risk: –Reflects economy or market wide forces –Cannot be eliminated through diversification