Risk and Rates of Return

1
Risk and Rates of Return

• Besley Chapter 5
• Pages 179-198

2
Risk and Investing

• The Rules
• Investing is risky.
• Risk is manageable.
• Types of Risk
• Diversifiable Risk Can be eliminated through
  diversification.
• Nondiversifiable Risk

3
Defining and Measuring Risk

• Risk is the chance that an outcome other than the
  expected outcome will occur.
• A Probability Distribution lists all possible
  outcomes and the probability of each outcome.
• The probabilities must sum to 1.0 (100)

4
Defining and Measuring Risk

• Stand-Alone Risk is that risk which is associated
  with an investment that which is held on its own.
• Portfolio Risk is that risk which is associated
  with an investment that which is maintained in a
  portfolio of investments.

5
Probability Distributions

• Flip a Coin
• Outcome Probability
• Heads 50
• Tails 50
• 100

• Chance of Snow
• Outcome Probability
• Snow 50
• Rain 30
• No Snow 20
• /Rain
• 100

Probability Distribution a listing of
all possible outcomes with the likelihood of
each possibility indicated.
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Probability Distributions
Martin Products and U. S. Electric
7
Expected Rate of Return

• The rate of return expected to be realized from
  an investment
• The mean value of the probability distribution of
  possible returns
• The weighted average of the outcomes, where the
  weights are the probabilities

8
Expected Rate of Return
9
Expected Rate of Return
10
Continuous versus Discrete Probability
Distributions

• Discrete Probability Distributionthe number of
  possible outcomes is limited, or finite

11
Discrete Probability Distributions
12
Continuous versus Discrete Probability
Distributions

• Continuous Probability Distributionthe number
  of possible outcomes is unlimited, or infinite

13
Continuous Probability Distributions
Probability Density
A tighter probability distribution is
representative of lower risk.
Martin Products
-60 0 15
110
Rate of Return ()
Expected Rate of Return
14
Measuring Risk The Standard Deviation
Calculating Martin Products Standard Deviation
15
Measuring Risk The Standard Deviation
s provides a definite value that represents the
tightness of the probability distribution.
A lower standard deviation indicates a tighter
probability distribution, and the less risk
associated with that particular stock.
16
Measuring Risk Coefficient of Variation

• Standardized measure of risk per unit of return
• Calculated as the standard deviation divided by
  the expected return
• Useful where investments differ in risk and
  expected returns

17
Risk Aversion

• Risk-averse investors require higher rates of
  return to invest in higher-risk securities

18
Risk Aversion and Required Returns

• Risk Premium (RP)
• The portion of the expected return that can be
  attributed to the additional risk of an
  investment
• The difference between the expected rate of
  return on a given risky asset and that on a less
  risky asset

19
Portfolio Returns

• Expected return on a portfolio, kp
• The weighted average expected return on the
  stocks held in the portfolio

20
Portfolio Risk Returns

• Unlike returns, portfolio risk is not a weighted
  average of the standard deviations of the
  individual stocks (the portfolios risk is
  usually smaller).
• Realized rate of return, k
• is the actual return earned, and usually differs
  from the expected return.

_
21
Returns Distribution for Two Perfectly Negatively
Correlated Stocks (r -1.0) and for Portfolio WM
Stock W
Stock M
Portfolio WM
25
25
25
15
15
15
0
0
0
-10
-10
-10
22
Returns Distributions for Two Perfectly
Positively Correlated Stocks (r 1.0) and for
Portfolio MM
Stock M
Stock M
Stock MM
25
25
25
15
15
15
0
0
0
-10
-10
-10
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Portfolio Risk

• Correlation Coefficient, r
• A measure of the degree of relationship between
  two variables
• Perfectly correlated stocks rates of return move
  together in the same direction (1.0)
• Negatively correlated stocks have rates of return
  that move in opposite directions (-1.0)
• Uncorrelated stocks have rates of return which
  move independently on one another (0.0)

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Portfolio Risk

• Risk Reduction
• Combining stocks that are not perfectly
  correlated will reduce the portfolio risk by
  diversification
• The riskiness of a portfolio is reduced as the
  number of stocks in the portfolio increases
• The smaller the positive correlation, the lower
  the risk

25
Actual Stock Prices and Returns SP 500 over 10
years