1 / 27

Chapter 5. Measuring Risk

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

cathal
Télécharger la présentation

Chapter 5. Measuring Risk

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related