Risk and Return

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Risk and Return

• FIL 240 Business Finance
• Prepared by Keldon Bauer

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Risk and Return

• Risk is defined as uncertainty of outcomes.
• In a financial sense, we are uncertain of the
  outcome of any investment.
• Formally, uncertainty is measured by variability.
• Statistically that means variance or standard
  deviation.

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Risk and Return

• Return refers to the gain or loss on an
  investment.
• It is generally stated as a percent of the
  original investment, and annualized.
• The interest rate on a savings account is a form
  of return.

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Defining/Measuring Return

• Observed return, kt, is calculated as follows

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Defining/Measuring Risk

• Expected Return as defined in statistics is as
  follows

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Defining/Measuring Risk

• Risk in statistics (and financial economics) is
  measured by standard deviation, which measures
  the variability of the return.

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Defining/Measuring Risk

• If we assume that the return on two companies
  would be as follows

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Defining/Measuring Risk
Widget Manufacturing
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Defining/Measuring Risk
Bloomington Electric
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Defining/Measuring Risk
Using m and s to Approximate a Normal
Distribution
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Measuring Stand-Alone Risk

• If investors have invested everything in one
  investment, then standard deviation should be
  standardized by expected return.

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Measuring Stand-Alone Risk
The lower the CV the lower the return adjusted
risk.
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Risk Aversion

• Assuming that you need to live off of your
  investment, and you can only invest in one of the
  two companies from the previous slides, which
  would it be?
• Widget Manufacturing
• Bloomington Electric

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Risk Aversion

• If you chose Bloomington Electric, you are risk
  averse.
• Risk averse investors require higher rates of
  return to invest in riskier assets.
• It is assumed that all investors are risk averse
• If two assets offer the same return, they will
  opt for the less risky.

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Risk Premium

• The amount of additional return required by a
  riskier asset to make that asset equally
  desirable by the market in general is called a
  risk premium.
• When the market perceives that one asset is
  riskier than another, it requires that the
  expected return increase to compensate investors
  for the risk.

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Portfolio Returns

• In the real world, investors can hold more than
  one investment.
• But risk is still important in pricing assets
  given their expected return.

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Returns
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Returns
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Returns
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Return Variability
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Return Variability
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Return Variability
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Risk and Return
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Portfolio Returns

• Risk and return should not be evaluated in
  isolation. Each security should be evaluated in
  its risk/return trade-off to the portfolio.
• Portfolio expected return

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Portfolio Returns - Example

• Given the following portfolio of stocks

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Portfolio Risk

• Unlike portfolio return, which is just a weighted
  average return of all returns in the portfolio,
  portfolio standard deviation is much more
  complicated.

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Portfolio Risk

• It depends on the weight (wi) of the new asset to
  the overall portfolio.
• It depends on the standard deviation (si) of the
  new assets returns.
• It depends on the correlation (rij) between the
  new asset and all other assets in the portfolio.

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Correlation Coefficient

• rij is a measure of the degree of relationship
  between two variables.
• It ranges from -1 to 1.
• For rijlt1, overall portfolio risk decreases.
• Which is why risk goes down as number of stocks
  in a portfolio goes up.
• For rij-1, portfolio risk could be eliminated.

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Portfolio Risk Reduction

• Risk can only be reduced so far.
• Almost all stocks are positively correlated.
• As the number of stocks increase, the risk
  approaches sm.

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Portfolio Risk Reduction
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Portfolio Risk Reduction
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Capital Asset Pricing Model

• CAPM shows return is a function of only the
  systematic risk.
• Unsystematic risk can be reduced through
  diversification.
• CAPM is used to determine the required rate of
  return.
• Measured by degree of correlation with the
  market.

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Capital Asset Pricing Model

• bj is a measure of a stocks sensitivity to
  market fluctuations.
• When bj 1, equal volatility with market.
• Only measures systematic risk.

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Portfolio Risk/Return

• Term definitions
• RF Risk-free (US Treasury bill) rate of return.
• bj Beta coefficient for stock j.
• kM Expected return to the market portfolio.
• (kM RF) Risk premium on the market portfolio.

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Capital Asset Pricing Model

• Risk has two components
• Market and firm-specific risks.
• Firm specific risk can be eliminated through
  diversification.
• Market risk cannot be eliminated.
• Therefore, one must be compensated to hold market
  (systematic) risk.

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Capital Asset Pricing Model

• The greater the systematic risk, the higher
  return will be required by the market.
• The beta (regression) coefficient measures
  systematic risk.
• Because beta determines how the stock affects the
  riskiness of a diversified portfolio, beta is the
  most relevant measure of a stocks risk!

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Portfolio Beta Coefficients

• Like expected return, the portfolio beta, bp, is
  a weighted average of individual stock bs.

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Portfolio Beta Coefficients

• Given the following stocks

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Portfolio Risk/Return

• We have talked about expected return.

• Now we will talk of required return, required by
  efficient economic markets.

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Portfolio Risk/Return - Example

• If the market portfolio is expected to earn 14,
  the risk-free rate is 6 and Wasup Dot.com has a
  beta of 2.

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Portfolio Risk/Return - Example

• Earlier, we said that this stock had an expected
  return of 30.
• Based on a required return of 22, should you buy
  or sell?
• Buy - It is under-priced!!!

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The Security Market Line - SML

• If we allow the x-axis to represent bj, and the
  y-axis to represent the required return, kj, the
  resulting graph is called the Security Market
  Line - SML.
• Note that RF is the intercept.
• Note that (kM-RF), or market risk premium, is the
  slope.

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The Security Market Line - SML
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The Security Market Line - SML
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Impact of Inflation on SML

• We will find out next chapter that inflationary
  expectation are embedded in interest rates (as
  inflation is expected to go up - interest rates
  go up).
• The risk premium is expected to stay constant
  over time.

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Impact of Inflation on SML
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Impact of Inflation on SML
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Impact of Risk Aversion on SML

• If there were no risk aversion, all assets would
  earn the same return.
• As risk aversion increases, the risk premium (the
  slope of the line) increases.

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Impact of Risk Aversion on SML
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Impact of Risk Aversion on SML
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Impact of Stock Risk on SML

• If a stock becomes less risky (the systematic
  risk goes down), what will happen to the SML?
• Nothing! The beta of the stock changes, and the
  required return merely moves down the SML!

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Project Planning and Risk

• In taking on assets projects, the corporate
  manager should not concern herself with project
  risk, but the impact on the firms beta.
• A firms beta is only the weighted average beta
  of all project betas.

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Practical Notes on CAPM

• CAPM as a theory is forward looking (expected
  correlation in future).
• Beta estimates are based on historical data, and
  are therefore backward looking.

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CAPM and Small Business

• Owners have portfolios of assets
• One asset is ownership in business.
• Rational owners would diversify their holdings to
  optimize risk/return.
• Owners may get more than financial utility from
  ownership.
• Financial utility is all that is considered in
  CAPM.