Risk and return

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• Risk and return
• (chapter 8)

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Investment returns
The rate of return on an investment can be
calculated as follows (Amount received
Amount invested) Return ___________________
_____
Amount invested For example, if 1,000 is
invested and 1,100 is returned after one year,
the rate of return for this investment is
(1,100 - 1,000) / 1,000 10.
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What is investment risk?

• Investment risk is related to the probability of
  earning a low or negative actual return.
• The greater the chance of lower than expected or
  negative returns, the riskier the investment.

Firm X
Firm Y
Rate of Return ()
15
100
0
-70
Expected Rate of Return
Firm X (red) has a lower distribution of returns
than firm Y (purple) though both have the same
average return. We say that firm Xs returns are
less variable/volatile (greater standard
deviation ?) and thus X is a less risky
investment than Y
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Selected Realized Returns, 1926 2004

• Average Standard
• Return Deviation
• Small-company stocks 17.5 33.1
• Large-company stocks 12.4 20.3
• L-T corporate bonds 6.2 8.6
• L-T government bonds 5.8 9.3
• U.S. Treasury bills 3.8 3.1

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Return Calculating the expected return for each
alternative
Outcome Prob. of outcome Return in
1(recession) .1 -15 2 (normal
growth) .6 15 3 (boom) .3 25 r expected
rate of return (.1)(-15) (.6)(15)
(.3)(25)15
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Risk Calculating the standard deviation for each
alternative
Standard deviation (s) measures total, or
stand-alone, risk. Greater the s, greater the
risk. Why?
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Investor attitude towards risk

• Risk aversion assumes investors dislike risk
  and require higher rates of return to encourage
  them to hold riskier securities.
• Risk premium the difference between the return
  on a risky asset and less risky asset, which
  serves as compensation for investors to hold
  riskier securities
• Very often risk premium refers to the difference
  between the return on a risky asset and risk-free
  rate (ex. a treasury bond)

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Portfolio returns
The rate of return on a portfolio is a weighted
average of the rates of return of each asset
comprising the portfolio, with the portfolio
proportions as weights. rp W1r1 W2r2 W1
Proportion of funds in Security 1 W2
Proportion of funds in Security 2 r1
Expected return on Security 1 r2 Expected
return on Security 2
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Assume that you invested 3000 in Countrywide
stock and 2,000 in Yahoo stock. The expected
return of Countrywide stock is 15 and the
expected return of Yahoo is 20. What is the
portfolio expected return? Answer
W13,000/(3,0002,000)0.6 W22,000/
(3,0002,000)0.4 Expected portfolio return
0.6150.420 17
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The benefits of diversification

• Come from the correlation between asset returns
• Correlation, ? a measure of the strength of the
  linear relationship between two variables
• -1.0 lt r lt 1.0
• If r 1.0, securities 1 and 2 are perfectly
  positively correlated
• If r -1.0, 1 and 2 are perfectly negatively
  correlated
• If r 0, 1 and 2 are not correlated
• The smaller the correlation, the greater the risk
  reduction potential ? greater the benefit of
  diversification
• If r 1.0, no risk reduction is possible
• Most stocks are positively correlated with the
  market (? ? 0.65)
• Combining stocks and bonds in a portfolio
  generally lowers risk.

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Illustrating diversification effects of a stock
portfolio
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Breaking down sources of risk

• Stand-alone risk Market risk Firm-specific
  risk
• Market risk portion of a securitys stand-alone
  risk that cannot be eliminated through
  diversification. Measured by beta.
• Firm-specific risk portion of a securitys
  stand-alone risk that can be eliminated through
  proper diversification.
• If an investor chooses to hold a one-stock
  portfolio (exposed to more risk than a
  diversified investor), would the investor be
  compensated for the risk they bear?
• NO!
• Stand-alone risk is not important to a
  well-diversified investor.
• Rational, risk-averse investors are concerned
  with sp, which is based upon market risk.

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Coefficient of Variation (CV)
Shows the risk per unit of return. You want to
invest in a security with the highest expected
return per unit of risk, and thus the lowest CV

• Average Standard
• Return Deviation CV
• Small-company stocks 17.3 33.2 1.92
• Large-company stocks 12.7 20.2 1.59
• L-T corporate bonds 6.1 8.6 1.41

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Capital Asset Pricing Model (CAPM)

• Model based upon concept that a stocks required
  rate of return is equal to the risk-free rate of
  return plus a risk premium that reflects the
  riskiness of the stock after diversification.
• Primary conclusion The relevant riskiness of a
  stock is its contribution to the riskiness of a
  well-diversified portfolio
• Beta measures a stocks market risk
• Indicates how risky a stock is if the stock is
  held in a well-diversified portfolio
• Beta is calculated using regression analysis

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The Security Market Line (SML)Calculating
required rates of return

• SML ki kRF ßi (kM kRF)
• SML is the empirical part of CAPM
• Assume kRF 8 , kM 15 and companys BETA (ßi
  ) is 1.2
• The market (or equity) risk premium is RPM kM
  kRF
• 15 8 7.
• ki 8 1.2x(15 - 8) 16.4

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Comments on beta

• If beta 1.0, the security is just as risky as
  the average stock (the market)
• If beta gt 1.0, the security is riskier than
  average (the market)
• If beta lt 1.0, the security is less risky than
  average (the market)
• Beta is greater than zero
• CAPM/SML concepts are based upon expectations,
  but betas are calculated using historical data.
  A companys historical data may not reflect
  investors expectations about future riskiness.

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Learning objectives

• Know how to calculate a rate of return
  historical rates of return 1926-2001
• Discuss the investment risk know that our risk
  measure will be the standard deviation of returns
  (no calculations are necessary)
• Know how to calculate expected return, standard
  deviation and coefficient of variation given
  probabilities of each outcome
• Know what is risk aversion and risk premium
• Know how to calculate the portfolio return
• Discuss the diversification effects of a
  portfolio the role of correlation and its two
  signs and the benefits of diversification
• Know the two sources of risk market and firm
  specific
• Briefly discuss what is CAPM and beta
• Know how to calculate required return using SML
• Recommended problems ST-1, Questions
  8-4,8-7,8-8, problems 8-1, 8-3,8-4