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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 l.jpg
Chapter 5. Measuring Risk

  • Defining and measuring

  • Risk aversion & implications

  • Diversification


What is risk l.jpg
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


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Measuring risk l.jpg
Measuring risk

  • Elements

    • Distribution/probability

    • Expected value

    • Variance & standard deviation


Probability l.jpg
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 l.jpg
Example: coin flip

  • Possible outcomes?

    • 2: heads, tails

  • Likelihood?

    • 50% or .5 heads; 50% or .5 tails

    • .5+.5 =1


Expected value l.jpg
Expected value

  • i.e. mean

  • Need probability distribution

  • Center of distribution


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EV

= sum of (outcome)(prob of outcome)

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


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For a financial asset

  • Outcomes = possible payoffs

  • Or

  • Possible returns on original investment


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Example: two investments

  • Initial investment: $1000


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

= $1100 or 10% return

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


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

= $1100 or 10% return

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

= 10%


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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 l.jpg
Investment 1

  • (500 -1100)2(.2) +

    (1000-1100)2(.4) +

    (1500-1100)2(.4)

    = 116,000 dollars2 = variance

  • Standard deviation = $341


Investment 2 l.jpg
Investment 2

  • (800 -1100)2(.25) +

    (1000-1100)2(.35) +

    (1375-1100)2(.4)

    = 56,250 dollars2 = variance

  • Standard deviation = $237


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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


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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


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Risk premium

  • = higher EV given to compensate the buyer of a risky asset

    • Subprime mortgage rate vs. conforming mortgage rate


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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


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  • Systematic risk

    • aka. Market risk

    • cannot be eliminated through diversification

    • due to factors affecting all assets

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


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Diversification

  • Risk is unavoidable, but can be minimized

  • Multiple assets, with different risks

    • Combined, portfolio has smaller fluctuations

  • Accomplished through

    • Hedging

    • Risk spreading


Hedging l.jpg
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


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Spreading risk

  • Portfolio of assets with low correlation

    • Minimize idiosyncratic risk

    • Pooling risk to minimize is key to insurance


Example l.jpg
example

  • choose stocks from NYSE listings

  • go from 1 stock to 20 stocks

    • reduce risk by 40-50%


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s

idiosyncratic

risk

total

risk

systematic

risk

# assets