David KilgourLecture 11 Foundations of Finance Lecture 1 Portfolio Theory Read: Brealey and Myers Chapter 8

David KilgourLecture 12 Risk and Return What have we learnt so far? The stock market is risky! –There is a spread of outcomes The usual measure of spread is the variance. The risk of a stock can be broken down into two: –The unique risk »specific to the stock »diversifiable -can be eliminated by holding a portfolio –The market risk »due to market-wide variations »not diversifiable »all the risk a well-diversified portfolio bears!

David KilgourLecture 13 Portfolio Theory Markowitz (1952) JF –Combining stocks into portfolios can reduce standard deviation below the level obtained from a simple weighted average calculation. If they do not move exactly together –Correlation coefficients make this possible. If they are not perfectly positively correlated –Basic Principle of Portfolio construction: efficient portfoliosThe various weighted combinations of stocks that create lower standard deviations for a pre-specified level of expected return constitute the set of efficient portfolios.

David KilgourLecture 14 Distribution of Returns Price changes vs. Normal distribution Microsoft - Daily % change # of Days (frequency) Daily % Change Past rates of return on stocks usually conform to normal distribution Normal distribution can be defined by two numbers: mean/expected return standard deviation

David KilgourLecture 15 Example 1 Standard Deviation VS. Expected Return Investment A % probability % return The expected return on stock A is 20% and the standard deviation is 15%. If stock B had an expected return of 20% and standard deviation of 25% which one would you prefer A or B? If stock C had an expected return of 10% and standard deviation of 15% which one would you prefer A or C? Most investors dislike uncertainty and prefer A to B! Most investors like high expected return an prefer A to C! Most investors dislike uncertainty and prefer A to B! Most investors like high expected return an prefer A to C!

David KilgourLecture 16 Example 2 You can invest into one of the following companies: –McDonalds: Expected return = 20%,  = 20.8% –Bristol-Myers: Expected return = 10%,  =17.1% Which investment would you prefer? Why? Most investment alternatives are like that! The investment with the higher expected return is considerably more risky! BUT THERE IS NO REASON TO RESTRICT YOURSELF TO HOLDING ONLY ONE STOCK! YOU CAN MAKE A PORTFOLIO!

David KilgourLecture 17 Historically the correlation between Bristol-Myers and McDonalds has been The rest of the example is the same! Suppose you invest £55 in Bristol-Myers and £45 in McDonald’s. Example 2 (cont’d)

David KilgourLecture 18 Markowitz Portfolio Theory Bristol-Myers Squibb McDonald’s Standard Deviation Expected Return (%) 45% McDonald’s  Expected Returns and Standard Deviations of the Portfolio change as we hold different weighted combinations of the two stocks. 14.5% 14.2%

David KilgourLecture 19 Efficient Frontier Standard Deviation Expected Return (%) In practice we are not limited to holding only two stocks. We must find a way of identifying the best portfolios of … stocks! Each half egg shell represents the combinations for two stocks. The portfolios along the heavy line are called efficient portfolios. The composite of all efficient portfolios constitute the efficient frontier. If you like high expected returns and dislike high standard deviations you will prefer portfolios along the efficient frontier! But which specific portfolio? The set of efficient portfolios can be calculated by quadratic programming! If you like high expected returns and dislike high standard deviations you will prefer portfolios along the efficient frontier! But which specific portfolio? The set of efficient portfolios can be calculated by quadratic programming!

David KilgourLecture 110 Efficient Frontier-Lending and Borrowing Standard Deviation Expected Return (%) Suppose that you can Lend or Borrow money at the risk free rate ( r f ). What if you invest some of your money into T-bills and the remainder in common stock portfolio S? or T? What does portfolio T look like? rfrf Lending Borrowing T S

David KilgourLecture 111 Example 3 Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40% 21% Weighted Average of Standard Deviations = 33.6 Portfolio Standard Deviation = 28.1 [note that < 33.6] PortfolioReturn = Weighted average return = 17.4% Now, Let’s Add stock New Corp to the portfolio!

David KilgourLecture 112 Example 3 (cont’d) Correlation Coefficient =.3 Stocks  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Weighted Average of Standard Deviations = NEW Portfolio Standard Deviation = NEW Weighted Average Return = Portfolio Return = 18.20% Higher return & Lower risk!!! How did we do that? –BY DIVERSIFICATION!

David KilgourLecture 113 Efficient Frontier A B N Return Risk AB Goal is to move up and left. WHY? ABN

David KilgourLecture 114 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return