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Chapter 5. Measuring Risk. Defining and measuring Risk aversion & implications Diversification. What is risk?. Risk is about uncertainty In financial markets: Uncertainty about receiving promised cash flows Relative to other assets Over a certain time horizon. Risk affects value

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chapter 5 measuring risk
Chapter 5. Measuring Risk
  • Defining and measuring
  • Risk aversion & implications
  • Diversification
what is risk
What is risk?
  • Risk is about uncertainty
  • In financial markets:
    • Uncertainty about receiving promised cash flows
      • Relative to other assets
      • Over a certain time horizon
slide3
Risk affects value
    • So quantification is important!
    • Examples: FICO score, beta
measuring risk
Measuring risk
  • Elements
    • Distribution/probability
    • Expected value
    • Variance & standard deviation
probability
Probability
  • Likelihood of an event
  • Between 0 and 1
  • Probabilities of all possible outcomes must add to 1
  • Probabilities distribution
    • All outcomes and their associated probability
example coin flip
Example: coin flip
  • Possible outcomes?
    • 2: heads, tails
  • Likelihood?
    • 50% or .5 heads; 50% or .5 tails
    • .5+.5 =1
expected value
Expected value
  • i.e. mean
  • Need probability distribution
  • Center of distribution
slide8
EV

= sum of (outcome)(prob of outcome)

Or if n outcomes, X1, X2, . . .,Xn

for a financial asset
For a financial asset
  • Outcomes = possible payoffs
  • Or
  • Possible returns on original investment
example two investments
Example: two investments
  • Initial investment: $1000
slide11

EV = $500(.2) + $1000(.4) + $1500(.4)

= $1100 or 10% return

= -50%(.2) + 0%(.4) + 50%(.4) = 10%

slide12

EV = $800(.25) + $1000(.35) + $1375(.4)

= $1100 or 10% return

= -20%(.25) + 0%(.35) + 37.5%(.4)

= 10%

slide13
Same EV—should we be indifferent?
    • Differ
      • in spread of payoffs
      • How likely each payoff is
    • Need another measure!
variance 2
Variance (σ2)
  • Deviation of outcome from EV
  • Square it
  • Wt. it by probability of outcome
  • Sum up all outcomes
  • standard deviation (σ) is sq. rt. of the variance
investment 1
Investment 1
  • (500 -1100)2(.2) +

(1000-1100)2(.4) +

(1500-1100)2(.4)

= 116,000 dollars2 = variance

  • Standard deviation = $341
investment 2
Investment 2
  • (800 -1100)2(.25) +

(1000-1100)2(.35) +

(1375-1100)2(.4)

= 56,250 dollars2 = variance

  • Standard deviation = $237
slide17
Lower std. dev
    • Small range of likely outcomes
    • Less risk
alternative measures
Alternative measures
  • Skewness/kurtosis
  • Value at risk (VaR)
    • Value of the worst case scenario over a give horizon, at a given probability
    • Import in mgmt. of financial institutions
risk aversion
Risk aversion
  • We assume people are risk averse.
  • People do not like risk, ALL ELSE EQUAL
    • investment 2 preferred
  • people will take risk if the reward is there
    • i.e. higher EV
    • Risk requires compensation
risk premium
Risk premium
  • = higher EV given to compensate the buyer of a risky asset
    • Subprime mortgage rate vs. conforming mortgage rate
sources of risk
Sources of Risk
  • Idiosyncratic risk
    • aka nonsytematic risk
    • specific to a firm
    • can be eliminated through diversification
    • examples:

-- Safeway and a strike

-- Microsoft and antitrust cases

slide22
Systematic risk
    • aka. Market risk
    • cannot be eliminated through diversification
    • due to factors affecting all assets

-- energy prices, interest rates, inflation, business cycles

diversification
Diversification
  • Risk is unavoidable, but can be minimized
  • Multiple assets, with different risks
    • Combined, portfolio has smaller fluctuations
  • Accomplished through
    • Hedging
    • Risk spreading
hedging
Hedging
  • Combine investments with opposing risks
    • Negative correlation in returns
    • Combined payoff is stable
  • Derivatives markets are a hedging tool
  • Reality: a perfect hedge is hard to achieve
spreading risk
Spreading risk
  • Portfolio of assets with low correlation
    • Minimize idiosyncratic risk
    • Pooling risk to minimize is key to insurance
example
example
  • choose stocks from NYSE listings
  • go from 1 stock to 20 stocks
    • reduce risk by 40-50%
slide27

s

idiosyncratic

risk

total

risk

systematic

risk

# assets

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