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.