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# Chapter 5. Measuring Risk - PowerPoint PPT Presentation

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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Presentation Transcript

• Defining and measuring

• Risk aversion & implications

• Diversification

• In financial markets:

• Uncertainty about receiving promised cash flows

• Relative to other assets

• Over a certain time horizon

• Elements

• Distribution/probability

• Expected value

• Variance & standard deviation

• 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

• Possible outcomes?

• Likelihood?

• 50% or .5 heads; 50% or .5 tails

• .5+.5 =1

• i.e. mean

• Need probability distribution

• Center of distribution

= sum of (outcome)(prob of outcome)

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

• Outcomes = possible payoffs

• Or

• Possible returns on original investment

• Initial investment: \$1000

= \$1100 or 10% return

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

= \$1100 or 10% return

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

= 10%

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

• (500 -1100)2(.2) +

(1000-1100)2(.4) +

(1500-1100)2(.4)

= 116,000 dollars2 = variance

• Standard deviation = \$341

• (800 -1100)2(.25) +

(1000-1100)2(.35) +

(1375-1100)2(.4)

= 56,250 dollars2 = variance

• Standard deviation = \$237

• 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

• 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

• 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

• Risk is unavoidable, but can be minimized

• Multiple assets, with different risks

• Combined, portfolio has smaller fluctuations

• Accomplished through

• 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

• choose stocks from NYSE listings

• go from 1 stock to 20 stocks

• reduce risk by 40-50%

idiosyncratic

risk

total

risk

systematic

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# assets