Understanding Risk

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Chapter 5

• Understanding Risk

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• Would you rather have 10 with certainty or 20
  with a 50 probability?
• Note that the expected value is the same for both
• Would you rather have 1,000 with certainty or
  2,000 with a 50 probability?
• Would you rather have 100,000 with certainty or
  200,000 with a 50 probability?

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Risk

• Definition
• a measure of uncertainty about the future payoff
  of an investment
• Risk arises from uncertainty about the future.
• Risk has to do with the future payoff to an
  investment, which is unknown.
• If a future payoff is known there is no risk
• Risk must be measured over some time horizon.
• Using historical data, Is this problematic?

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Measuring Risk

• Measuring Risk requires
• Risk must be measured relative to some benchmark,
  not in isolation.
• Compare a stocks risk and return versus the SP
  500
• If you want to know the risk associated with a
  specific investment strategy use must use an
  appropriate benchmark (index) to compare the risk
  of your investment strategy
• Large Cap stock is compared to the SP 500 Index
• Small Cap stock is compared to the Russell 2000
  Index
• You would not compare a Large Cap stock to a
  Small Cap Index

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The Impact of Leverage on Risk

• Leverage is the practice of borrowing in order to
  finance part of an investment.
• Examples include mortgages, and credit cards and
  buying stock on margin.
• Leverage increases the expected return on an
  investment and also increases the risk.
• Leverage magnifies the effect of price changes on
  an asset.
• Leverage has at least as big of an impact on
  value as risk does because it compounds the worst
  possible outcome.

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Measuring Risk

• Case 1
• An Investment can rise or fall in value. Assume
  that an asset purchased for 1000 is equally
  likely to fall to 700 or rise to 1400

Expected Value ½ (700) ½ (1400) 1050
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Measuring Risk

• Case 2
• The 1000 investment might pay off 100
  (prob.1) or 2000 (prob.1)in addition to 700
  (prob.4) or 1400 (prob.4)

Expected Value .1(100) .4(700) .4(1,400)
.1(2,000) 1050
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Measuring Risk

• Both cases have the same expected return, 50 on
  a 1000 investment, or 5?
• Would you take Case 1 OR Case 2?
• What determines which investment you select?

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Risk Aversion

• Risk-averse investor
• Always prefers an investment with a certain
  return to one with the same expected return, but
  some amount of uncertainty.
• Investors will not take on any additional risk
  without being compensated with a higher expected
  return
• Given an expected return investors will only
  accept an investment with the least amount of
  risk
• Risk neutral
• Given Case 12, an investor is indifferent
  between the two
• Risk Loving or Risk Seeking
• Given Case 12, an investor will take the
  investment with the most risk

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Measuring Risk

• Back to Case 1 2
• Assume the risk-free return is 5 percent
• a 1,000 risk-free investment will pay 1050
• its expected value, with certainty.
• Now, which investment will a risk averse,
  neutral, and loving investor take?

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Variability of Stock Returns
Normal distribution can be described by its mean
and its variance.

• Variance (?2) - the expected value of squared
  deviations from the mean
• Standard deviation (?) the square root if
  variance
• The greater the standard deviation, the higher
  the risk.

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Measuring Risk

• CASE 1
• Compute the expected value (mean) (1,400 x ½)
  (700 x ½) 1,050
• Variance (?2) ½ (1,400-1,050)2 ½
  (700-1,050)2 122,500
• Standard deviation (?) v 122,500 325
• CASE 2
• Compute the expected value (mean)
• .1(100) .4(700) .4(1,400) .1(2,000)
  1,050
• Variance (?2)
• .1(100-1,050)2 .4(700-1,050)2
  .4(100-1,050)2 .1(2,000-1,050)2 278,784
• Standard deviation (?) v 278,784 528

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Formulas
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Value of 1 Invested in Equities, Treasury Bonds
and Bills, 1900 - 2003
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Volatility of Asset Returns
Asset classes with greater volatility pay higher
average returns.

• Average return on stocks is more than double the
  average return on bonds, but stocks are 2.5 times
  more volatile.

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Percentage Returns on Bills, Bonds, and Stocks,
1900 - 2003
Difference between average return of stocks and
bills 7.6 Difference between average return
of stocks and bonds 6.5
Risk premium the difference in returns offered
by a risky asset relative to the risk-free return
available
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Risk Premium

• The riskier an investment
• the higher the compensation that investors
  require for holding it
• Thus, the higher the risk premium.
• There is a trade-off between risk and expected
  return
• you cant get a high return without taking
  considerable risk.

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Risk and Expected Return
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Risk and Return

• Investment performance is measured by total
  return.
• Trade-off between risk and return for assets
  historically, stocks had higher returns and
  volatility than bonds and bills.
• One measure of risk standard deviation
  (volatility)
• Unsystematic (idiosyncratic) and systematic risk
  risk that can (cannot) be eliminated through
  diversification, respectively

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Systematic and Unsystematic Risk
Systematic risk the volatility of the portfolio
that cannot be eliminated through diversification.
Unsystematic risk the proportion of risk of
individual assets that can be eliminated through
diversification
What really matters is systematic risk.how a
group of assets move together.
Diversification reduces portfolio volatility, but
only up to a point. Portfolio of all stocks still
has a volatility of 21.
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Systematic and Unsystematic Risk
Standard deviation contains both systematic and
unsystematic risk.
Because investors can eliminate unsystematic risk
through diversification, market rewards only
systematic risk.
What really matters is systematic risk.how a
group of assets move together.
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Reducing Risk through Diversification

• Two ways to diversify your investments. You can
• hedge risks
• reducing overall risk by making two investments
  with opposing risks.
• When one does poorly, the other does well, and
  vice versa.
• So while the payoff from each investment is
  volatile, together their payoffs are stable.
• spread them among the many investments.
• A combination of risky investments is often less
  risky than any one individual investment.
• find investments whose payoffs are completely
  unrelated.
• You can lower risk by simply spreading it around
  and finding investments whose payoffs are
  completely unrelated

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Reducing Risk through Diversification
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Reducing Risk through Diversification

• Lets compare three strategies for investing
  100, given the relationships shown in the table
• 1. Invest 100 in GE
• 2. Invest 100 in Texaco
• 3. Invest half in each company 50 in GE
  and 50 in Texaco

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Reducing Risk through Diversification
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Reducing Risk through Diversification

• Consider three investment strategies
• GE only
• Microsoft only
• half in GE and half in Microsoft.
• The expected payoff on each of these strategies
  is the same 110.
• For the first two strategies, 100 in either
  company, the standard deviation is still 10, just
  as it was before.
• But for the third strategy, 50 in GE and 50 in
  Microsoft, the analysis is more complicated.
• There are four possible outcomes, two for each
  stock

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Reducing Risk through Diversification
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Reducing Risk through Diversification
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Average Return and St. Dev. for Individual
Securities, 1994-2003
For various asset classes, a trade-off arises
between risk and return. Does the trade-off
appear to hold for all individual securities?
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Average Return and St. Dev. for Individual
Securities, 1994-2003
Average Return ()
Wal-Mart
Anheuser-Busch
American Airlines
Archer Daniels Midland
Standard Deviation ()
No obvious pattern here
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Probability Distribution

• Presents a graphical representation of all
  expected returns
• Assumes returns are Normally Distributed
• 68 of returns are -1 ?
• 95 of returns are -2 ?
• Riskier securities have wider distributions

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Annual Total Returns,1926-1998
Average Standard Return Deviation Distribution
Small-companystocks 17.4
33.8 Large-companystocks
13.2 20.3 Long-termcorporate bonds
6.1 8.6 Long-termgovernment
5.7 9.2 Intermediate-termgovernme
nt 5.5 5.7 U.S.
Treasurybills 3.8
3.2 Inflation 3.2
4.5
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Diversification

• Why is an asset held as part of a portfolio
  generally less risky than being held by itself?
• Because stocks that are truly diversified are not
  perfectly positively correlated, therefore adding
  a stock would reduce risk
• This is true diversification

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Diversification

• Investors are concerned with the riskiness of
  their portfolio, not each security separately
• As securities in a portfolio increase the s
• Decreases, moving closer to the Market s
• Investors are concerned only with a securities
  risk and return relative to the market
• All other risk can be diversified away

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Portfolio Risk

• Correlation
• Tendency of two variables to move together
• Most stocks are positively correlated. rk,m
  0.65.
• s 35 for an average stock.
• Combining stocks generally lowers risk.
• Measure by
• Correlation Coefficient ( r )
• Between -1 and 1

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Index correlation

• Indices are highly correlated portfolios remove
  idiosyncratic risk, therefore different indices
  are simply comparing different measure of
  systematic risk in the market
• DJIA is systematic risk in industrial firms
• NASDAQ 100 measure the systematic risk in high
  tech
• SP500 measures the systematic risk as a broader
  market measure.
• Dow Jones 30 correlation with other indices
• 74 with Nasdaq composite
• 95 with NYSE composite
• 93 with Russell 1000
• 95 with SP500
• 87 with value line
• 92 with Wilshire

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Returns Distributions for Two Perfectly
Positively Correlated Stocks (r 1.0) and for
Portfolio MM
Stock M
Portfolio MM
Stock M
25
15
0
-10
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Returns Distribution for Two Perfectly Negatively
Correlated Stocks (r -1.0) and for Portfolio WM
Stock W
Stock M
Portfolio WM
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25
25
25
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15
15
15
0
0
0
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-10
-10
-10
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The Impact of Additional Assets on the Risk of a
Portfolio
Portfolio Standard Deviation
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The Importance of Diversification

• One impact of Enrons demise is likely to be the
  impact on their workers retirement funds.
• Like many other companies, Enron offered its
  employees 401(k)s (defined-contribution
  retirement savings accounts)
• which included, among other options, the
  possibility of investing in the companys own
  stock.
• Enron matched employee contributions to their own
  retirement accounts with company stock rather
  than cash,
• by the end of 2000, 60 of the plan was invested
  in Enron shares
• a higher proportion than would be considered
  prudent diversification by most investors.
• Some of the blame for the lack of diversification
  can be put on the employees (who were not forced
  to choose Enron stock)

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The Importance of Diversification

• The company did compound the problem by not
  allowing employees to sell Enron shares out of
  their plan.
• Thousands of other companies, including many of
  the Fortune 500 companies, run their plans in a
  similar manner.
• The bankruptcy of Enron has not lead to a
  fundamental restructuring of the U.S. retirement
  savings system
• But, it does point out the importance of
  diversification.

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Lesson of the Enron

• Dont put all of your eggs in one
  basketdiversify.
• Diversification is especially important for
  retirement savings.
• But Enron employees lost more than just their
  investment in Enron stock they lost their jobs
  too.
• Almost every aspect of their financial well-being
  was tied up in the same company.
• The real lesson is that you shouldnt buy stock
  in the company you work for. If the company goes
  bankrupt, as Enron did, youre in bad enough
  shape.
• You dont want your savings to go down the drain
  along with your job.