FINANCE IN A CANADIAN SETTING Sixth Canadian Edition Lusztig, Cleary, Schwab

CHAPTER SEVEN CHAPTER SEVEN Risk, Return, and Portfolio Theory

Learning Objectives 1.Define the term “risk” and explain how it is related to expected return. 2.Define and discuss expected return and risk with regards to individual securities and a portfolio as a whole. 3.Explain the meaning of correlation coefficient, and discuss how it compares to covariance. 4.Identify the main aims of diversification, and explain the principle benefits of international versus domestic diversification.

What is Risk? Risk – the chance that the actual outcome from an investment will differ from the expected outcome Risk – the chance that the actual outcome from an investment will differ from the expected outcome

Estimating Risk and Return n Investors are concerned with total returns whether one is measuring realized returns or estimating future returns Total return – consists of two components: yield and capital gain or loss Total return – consists of two components: yield and capital gain or loss Yield – is the periodic cash flows on an investment Yield – is the periodic cash flows on an investment Capital gain (loss) – is the appreciation (or depreciation) in the price of the assets Capital gain (loss) – is the appreciation (or depreciation) in the price of the assets

Estimating Risk and Return n The general equation for calculating total return is : Where: CF t = cash flows during the measurement period t P E = price at the end of period t or sale price P B = purchase price of the asset PC = change in price during the period

Calculating Expected Return Expected return – is the average of all possible return outcomes, where each outcome is weighted by the probability of its occurrence Expected return – is the average of all possible return outcomes, where each outcome is weighted by the probability of its occurrenceWhere: E( R)= the expected return on a security R i = the i th possible return pr i = the probability of the i th return R i m = the # of possible returns

Calculating Risk n Variance or standard deviation is typically used to calculate the total risk associated with the expected return Variance = Standard deviation =

Portfolio Expected Return n The expected return is calculated as a weighted average of the individual securities’ expected returns n The combination portfolio must add up to be 100 percent Where: E(R p ) = the expected return on the portfolio w i = the portfolio weight for the i th security E(R i ) = the expected return on the i th security n = the # of different securities in the portfolio

Portfolio Risk n Portfolio risk is less than the weighted average of the risk of the individual securities in a portfolio of risky securities but

Portfolio Risk n Two factors must be considered in developing an equation that will measure the risk of a portfolio through variance and standard deviation 1.Weighted individual security risk 2.Weighted co-movements between securities’ returns as measured by the correlations between the securities’ returns weighted again by the percentage of investable funds placed in each security

Portfolio Risk Correlation coefficient – is a statistical measure of the relative co-movement between the return on securities A and B Correlation coefficient – is a statistical measure of the relative co-movement between the return on securities A and B n The relative measure is bound between +1.0 and –1.0 with  AB = +1.0 = perfect positive correlation  AB = +1.0 = perfect positive correlation  AB = = zero correlation  AB = = zero correlation  AB = -1.0 = perfect negative correlation  AB = -1.0 = perfect negative correlation

Portfolio Risk Examples of Security Returns that Are Positively Correlated, Negatively Correlated, and Uncorrelated (Independent)

Covariance n Covariance – is another measure of co- movement between security returns which is an absolute measure of the degree of association between returns for a pair of securities Covariance can be: 1.Positive – returns on the two securities move in the same direction 2.Zero – return of two securities are independent 3.Negative – returns on the two securities move in the opposite direction

Covariance n Formula for calculating Covariance is: Where  = covariance between securities A and B R A,I = one estimated possible return on security A E(R A ) = the most likely outcome for security A for the period m = the # of likely outcomes for a security for the period pr i = the probability of attaining a given return R A,i

Diversification n Helps investors reduce their exposure to risk to the greatest extent possible while still attempting to maximize their returns. n As more securities are added to a portfolio, the exposure to any particular source of risk becomes smaller and the risk of the portfolio declines rapidly as more securities are added.

Diversification n Through diversification non-systematic risk can be eliminated n Systematic risk cannot be eliminated Total risk = non-systematic risk + systematic risk n Diversification can be performed: 1.Domestically 2.Internationally

Summary 1.Uncertainly can be quantified in terms of probabilities, and risk is commonly associated with the variance or standard deviation of probability distributions. 2.When securities are combined, the combined risk of the resulting portfolio depends not only on the individual risk of the underlying securities but also on the statistical correlation that exists between the individual returns. 3.Correlation coefficients of +1, 0, and –1 indicate perfect positive correlation, statistical independence, and perfect negative correlation respectively.

Summary 4.Portfolio diversification reduces risk, and most investors hold diversified portfolios. 5.Diversification enables the reduction of risk through the elimination of company-specific or unique risk. Because the returns of most securities are related to the general state of the economy, they are positively correlated with each other. 6.International diversification offers additional benefits in terms of risk reduction.