adms3530_-_lecture_9_-_in

Finance ADMS 3530 - Winter 2012 – Professor Lois King Lecture 9 – Introduction to Risk and Efficient Markets – Mar 6 9.1 Overview of Cost of Capital  The discount rate ‘r’ has many different names: o Cost of capital o Market interest rate o Opportunity cost of funds o Yield to maturity (bonds) o Internal rate of return (if NPV=0)  Definitions o Cost of capital – the rate of return that shareholders could expect to earn if they invested in equally risky securities. o Market risk premium – the compensation for taking on the risk of common stock ownership, and can be shown as follows:  Rate of return on common stocks = rate of return on treasury bills + market risk premium.  3 components o Real rate of return in the economy. o Rate of inflation  Note: 1 + 2 = the nominal risk-free rate of return or the return you would expect to receive from investing in a risk-free security such as a Canadian treasury bill. o Risk premium – which is the return above and beyond the nominal risk-free rate. The third component is the most difficult to figure out.  How can we calculate the cost of capital? o Using historical returns to help calculate cost of capital:  If the project has no risk  use the expected T-bill rate of return as our cost of capital.  If the project has a risk level equivalent to the market portfolio of common stock  use the expected common stock rate of return as your cost of capital.

9.2 Return & Risk for Individual Securities  Definitions from Statistics:

o Risk – An increased dispersion of possible outcomes. Where increased volatility => increased risk. o Variance – Probability-weighted average of squared deviations around the expected return. o Expected (or mean) return – Probability-weighted average of possible outcomes.  Two types of variance: o Population variance – Includes all possible outcomes and probabilities are assigned. The divisor for population variance is ‘n’, versus ‘n-1’, as in sample variance. o Sample variance – Which is used to measure variance in stock returns and sample populations (no probabilities assigned as probabilities are not usually known).

9.3 Correlation & Diversification  Volatility (as measured by variance or standard deviation) is a good measure of total risk of individual securities. However those measures (as calculated for individual securities) are not good for assessing the risk of a portfolio.  Covariance of two securities: o The probability-weighted average of the product of each security’s difference from its mean, for each possible future event. o Covariance quantifies the degree to which securities, I and j vary together.  Correlation coefficient: o Measures how closely two variables move together. o Is always a number between +1 and -1  +1  Means the two securities are perfectly positively correlated.  -1  Perfectly negatively correlated.  0  no correlation – a change in one variable tells you nothing about likely change in other variable. o The correlation coefficient will thus tell you the incremental risk of adding a security to an existing portfolio of securities.  If the correlation between the stock and the portfolio: o Highly positive (close to +1)  Too little or no diversification benefit of the added stock. o Negative, Zero or lowly positive  The addition of the stock lowers the portfolio standard deviation (lowers the risk!)  Studies have shown that this diversification benefit tends to be maximized with between 20 and 30 stocks in a portfolio.

9.5 Market Risk versus Unique Risk  Types of Risk: o Total risk – measured by Variance or Standard Deviation.  Unique or Unsystematic Risk  Can be diversified away.  Caused by factors within a company’s operations (Debt levels, dividend yield, firm size, etc.)  Market or Systematic Risk  Non-diversifiable risk.  Caused by macroeconomic factors (inflation, interest rates, GDP growth, etc.)  Total risk of a portfolio is not; however, the weighted average of the standard deviations of the individual securities. For a portfolio of securities, we must analyze how each security’s returns vary with every other security in the portfolio.  The correlation coefficient is a measure of how closely two variables move together.  Diversification: o We can see from the analysis of randomly chosen stock portfolios that we can eliminate a great deal of risk by adding securities to a portfolio. o The additional benefits of adding securities diminishes after we have around 15 – 20 stocks in a portfolio. o As well, we cannot eliminate all risk.  The risk that we cannot eliminate is called market risk or systematic risk whereas,  The risk we can diversify away is called unique risk or unsystematic risk.