Chapter 5. Measuring Risk

1. Chapter 5. Measuring Risk • Defining and measuring • Risk aversion & implications • Diversification

2. 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

3. Risk affects value • So quantification is important! • Examples: FICO score, beta

4. Measuring risk • Elements • Distribution/probability • Expected value • Variance & standard deviation

5. 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

6. Example: coin flip • Possible outcomes? • 2: heads, tails • Likelihood? • 50% or .5 heads; 50% or .5 tails • .5+.5 =1

7. Expected value • i.e. mean • Need probability distribution • Center of distribution

8. EV = sum of (outcome)(prob of outcome) Or if n outcomes, X1, X2, . . .,Xn

9. For a financial asset • Outcomes = possible payoffs • Or • Possible returns on original investment

10. Example: two investments • Initial investment: $1000

11. EV = $500(.2) + $1000(.4) + $1500(.4) = $1100 or 10% return = -50%(.2) + 0%(.4) + 50%(.4) = 10%

12. EV = $800(.25) + $1000(.35) + $1375(.4) = $1100 or 10% return = -20%(.25) + 0%(.35) + 37.5%(.4) = 10%

13. Same EV—should we be indifferent? • Differ • in spread of payoffs • How likely each payoff is • Need another measure!

14. 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

15. Investment 1 • (500 -1100)2(.2) + (1000-1100)2(.4) + (1500-1100)2(.4) = 116,000 dollars2 = variance • Standard deviation = $341

16. Investment 2 • (800 -1100)2(.25) + (1000-1100)2(.35) + (1375-1100)2(.4) = 56,250 dollars2 = variance • Standard deviation = $237

17. Lower std. dev • Small range of likely outcomes • Less risk

18. 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

19. 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

20. Risk premium • = higher EV given to compensate the buyer of a risky asset • Subprime mortgage rate vs. conforming mortgage rate

21. 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

22. Systematic risk • aka. Market risk • cannot be eliminated through diversification • due to factors affecting all assets -- energy prices, interest rates, inflation, business cycles

23. Diversification • Risk is unavoidable, but can be minimized • Multiple assets, with different risks • Combined, portfolio has smaller fluctuations • Accomplished through • Hedging • Risk spreading

24. 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

25. Spreading risk • Portfolio of assets with low correlation • Minimize idiosyncratic risk • Pooling risk to minimize is key to insurance

26. example • choose stocks from NYSE listings • go from 1 stock to 20 stocks • reduce risk by 40-50%

27. s idiosyncratic risk total risk systematic risk # assets