Introduction to Finance: Risk and Return

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Introduction to FinanceRisk and Return
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Invest?

• Investment A yields a return of about 12 per
  year on average (?????12).
• Investment B yields a return of about 8 per
  year on average.
• Investment C yields a return of about 5 per
  year on average.
• Which investment would you choose? Why?

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Defining Return

• For example, purchase Take-chan stock yesterday
  at 1000 yen per share.
• Today, you sell the shares at the market price
  1100 yen. In other words, the stock priced
  increased by 100 yen over one day.
• What is your percentage gain?
• (1100-1000)/1000 100/10000.1
• Return is 10 (one day).

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Return (???)(Pt-Pt-1)/Pt-1
Pt-1
Pt
Yesterday (t-1)
Today (t)
Pstock price (??)
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Risk?

• What is risk?
• Much of finance is about risk.
• Buying and selling risk in the market.
• What is the correct price for holding (buying or
  selling) risk?
• How much risk should be bought or sold?

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Measuring Risk

• Be able to distinguish between risk which is
  rewarded and not rewarded.
• Measure should be applicable to as many assets as
  possible. Standardized to facilitate comparison
  across assets.
• Need a measure of risk which can be compared
  across assets/projects. Thus a standardized
  measure.

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Cont.

• Need a measure which can be translated into
  expected return (opportunity cost of
  capital/equity).
• required return riskfree rate premium

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Relative Dispersion of Returns

• One measure of risk is the relative dispersion of
  returns.
• How many returns are above average?
• How many returns are below average?
• Notice we are creating a measure relative to the
  average.

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Calculate Historical Annual Returns (?????)
return
return
P94
P95
P96
P97
P98
P99
P00
P01
01
00
98
97
96
95
94
99
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Plot Historical Returns (Histogram)
Number of Observations (return)
4
Return
0
Positive returns
Negative returns
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One way of characterizing the distribution of
returns in the future.
Small probability of very low (very
negative) returns (Recession).
Low probability of very high returns (Boom).
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Distribution (??)
Frequency
Dispersion, Variability is depicted by the
spread in the distribution.
Return
Expected Return (?????)
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Variance (??)

• One statistical measure (???) of this spread is
  variance (??).
• This measures variability relative to the mean or
  average (???).
• The square root of the variance is called the
  standard deviation (????).

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Variance (??)
Frequency
Take Difference And Square
Return
expected Return (?????)
Ret1
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Sample Variance (Historical Data)

• Take the difference between the observed return
  and the average return.
• Square each of the above differences.
• Square each difference to avoid positive and
  negative differences from canceling.
• Add all the squared differences.

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Cont.

• Take the average of the squared differences. In
  other words, divide the sum of the squared
  differences by the number of observations less
  one (degrees of freedom,???).
• Thus, the variance is an average as well.

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Year 01 00 99 98 97 96 95 Return 10 -5 5 -6
-10 0 6
Average or Mean Return0
Variance ? Standard Deviation ?
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• A larger variance (standard deviation) means
  there is a greater spread or variability.
• Thus a larger variance would mean greater risk.
• A smaller variance would mean relatively less
  risk.

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Same Average (expected) Return but
Different Variances
Return
(?????)
Return
(?????)
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Which would you choose?

• Stock with standard deviation of 15 (average
  return 5)
• Stock with standard deviation of 20 (average
  return 5)

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Our original question?

• Investment A yields a return of about 12 per
  year on average. Standard Deviation 18.
• Investment B yields a return of about 8 per
  year on average. Standard Deviation 6.
• Investment C yields a return of about 5 per
  year on average. Standard Deviation 1.
• P. 91 text

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Measuring Risk as Standard Deviation
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Examples Risk-Return

• P. 92 Text (Look at Graph)
• P. 102 Text (Table 5-3)
• We can plot each security (stock) in risk-return
  space.

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Plotting Risky Assets
Expected Return (?????)
stock 1
ret 1
ret 2
Risk( ???) standard deviation (????)
stock 2
std dev 2
std dev 1
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Expected Return
Risk standard deviation