Chapter 5. Measuring Risk

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# Chapter 5. Measuring Risk - PowerPoint PPT Presentation

Chapter 5. Measuring Risk. Defining and measuring Risk aversion &amp; 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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Presentation Transcript
Chapter 5. Measuring Risk
• Defining and measuring
• Risk aversion & implications
• Diversification
What is risk?
• In financial markets:
• Uncertainty about receiving promised cash flows
• Relative to other assets
• Over a certain time horizon
Risk affects value
• So quantification is important!
• Examples: FICO score, beta
Measuring risk
• Elements
• Distribution/probability
• Expected value
• Variance & standard deviation
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
• Possible outcomes?
• Likelihood?
• 50% or .5 heads; 50% or .5 tails
• .5+.5 =1
Expected value
• i.e. mean
• Need probability distribution
• Center of distribution
EV

= sum of (outcome)(prob of outcome)

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

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

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

= \$1100 or 10% return

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

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

= \$1100 or 10% return

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

= 10%

Same EV—should we be indifferent?
• Differ
• How likely each payoff is
• Need another measure!
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
• (500 -1100)2(.2) +

(1000-1100)2(.4) +

(1500-1100)2(.4)

= 116,000 dollars2 = variance

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

(1000-1100)2(.35) +

(1375-1100)2(.4)

= 56,250 dollars2 = variance

• Standard deviation = \$237
Lower std. dev
• Small range of likely outcomes
• Less risk
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
• 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
• = higher EV given to compensate the buyer of a risky asset
• Subprime mortgage rate vs. conforming mortgage rate
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

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

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

Diversification
• Risk is unavoidable, but can be minimized
• Multiple assets, with different risks
• Combined, portfolio has smaller fluctuations
• Accomplished through
• 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
• Portfolio of assets with low correlation
• Minimize idiosyncratic risk
• Pooling risk to minimize is key to insurance
example
• choose stocks from NYSE listings
• go from 1 stock to 20 stocks
• reduce risk by 40-50%

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