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## PowerPoint Slideshow about 'Chapter 5. Measuring Risk' - cathal

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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

- 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?
- 2: heads, tails
- Likelihood?
- 50% or .5 heads; 50% or .5 tails
- .5+.5 =1

Expected value

- i.e. mean
- Need probability distribution
- Center of distribution

For a financial asset

- Outcomes = possible payoffs
- Or
- Possible returns on original investment

Example: two investments

- Initial investment: $1000

Same EV—should we be indifferent?

- Differ
- in spread of payoffs
- 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

Risk premium

- = 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
- Risk spreading

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

- 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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