Finance
Chapter 5
Risk & rates of return
No pain no gain
 What is risk?
 How is risk measured?
 How can risk be minimized or at least
compensated for bearing it?
 Investors like returns and dislike risk
 Investors will invest in risky assets only if they
expect to receive higher returns
Risk in perspective
 The riskiness of an asset can be considered in
two ways:
 Stand-alone—an assets cash flows are analyzed by
themselves
 Portfolio context—cash flows from a number of
assets are combined (consolidated) and analyzed
Risk analysis considerations
 Portfolio context
 Diversifiable risk—risk that is eliminated through
diversification (irrelevant)
 Market risk—cannot be eliminated thru
diversification (relevant)
 An asset with a high degree of market risk
(relevant) must provide a high rate of return to
attract investors
 Remember that investors are averse to risk
Investment returns
 Measuring rates of return problem:
 Scale (size of investment)
 Timing problem
 Solution:
 Rates of return or percentage of return for a one
year investment
 ROR = (amount rec’d - amount invested) /
amount invested
Stand-alone risk
 Risk—the chance that some unfavorable event
will occur
 Stand-alone risk—the risk an investor would face
if s/he held only one asset
 Probability—the chance an event will occur
 Probability distribution—a listing of all possible
outcomes (events) with a chance of occurrence
(probability) assigned to each outcome
 Probabilities must add up to 100%
 See Table 5-1, pg. 172
Expected rate of return
 Expected rate of return, k (k-hat)—the rate of
return expected to be realized from an
investment; the weighted average of the
probability distribution of possible results (payoff
matrix)
Stand-alone risk
 The tighter the probability distribution of
expected future returns, the smaller the risk of a
given investment (see figure 5-2, page 174)
 Standard deviation (sigma)—the smaller the
standard deviation, the tighter the probability
distribution, and the lower the riskiness of a stock.
 Standard deviation is essentially a weighted
average of the deviations from the expected
value.
Stand-alone risk
 Coefficient of variation (CV)—the standard
deviation divided by the expected return.
 CV = Standardized measure of the risk per unit of
return used for investments that have the same
expected returns but different standard
deviations.
Risk Aversion
 Most investors are risk averse.
 The higher a security’s risk the lower its price and
the higher its required return.
 Risk Premium (RP)—the difference between the
expected rate of return on a given risky asset
and that on a less risky investment = increased
compensation required for a risky investment
Portfolio returns & risk
 Expected return on a portfolio kp (k-hat p)= the
weighted average of the expected returns on
assets held in the portfolio
 Realized rate of return k (k-bar) = the return that
was actually earned during some past period. Kbar usually is different from the expected (k-hat)
except for riskless assets.
Correlation coefficients
 Correlation = the tendency of 2 variables to
move together
 Correlation coefficient, r = measures the degree
of relationship between 2 variables (the
tendency to correlate movements)
 r can range from +1.0 (perfectly positive
correlation - move up and down together) to 1.0 (perfectly negative correlation - move in
opposite directions) while 0 means they are
independent of one another.
 Diversification means nothing if all stocks are
perfectly correlated
Diversifiable risk vs. market risk
 Almost half the riskiness of an average stock can
be eliminated if the stock is held in a diversified
portfolio containing at least 40 stocks
 Market risk—that part of security’s risk that
cannot be eliminated by diversification.
 Capital Asset Pricing Model (CAPM)—a stock’s
required ROR is equal to the risk-free rate of
return plus a risk premium that reflects only the
risk remaining after diversification.
 Relevant risk—the risk remaining after
diversification that cannot be diversified away
(aka, market risk)
The concept of Beta (b)
 Beta coefficient, b—a measure of market risk,
which is the extend to which the returns on a
given stock move with the stock market.
 b measures the volatility of a stock, e.g., 1.0 (high
beta)stocks will move up and down with the
broad market averages. 0.5 (low beta) stocks
are half as volatile as the market averages. A
negative b means the stock will move in the
opposite direction as the market average.
Market risk premium
 RPm –the additional return over the risk-free rate
needed to compensate investors for assuming
an average amount of risk.
 Security Market Line (SML)—the relationship
between a security’s market risk and its required
rate of return. The return required for any security
is equal to the risk-free rate plus the market risk
premium times the security’s beta:
ki = krf + (km – krf )bi
Factors effecting RROR
 Risk-free rate change (real rates or inflation)
 Change in a stock’s beta
 Investors’ aversion to risk can change
 Global diversification may result in lower risk for
multinational companies and globally diversified
portfolios.