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Chapter 5

Chapter 5. Understanding Risk. Understanding Risk: The Big Questions. What is risk? How can we measure risk? What happens when the quantity of risk changes?. Understanding Risk: Roadmap. Defining Risk Measuring Risk The Risk-Return Tradeoff Sources of Risk Reducing Risk.

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Chapter 5

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  1. Chapter 5 Understanding Risk

  2. Understanding Risk:The Big Questions • What is risk? • How can we measure risk? • What happens when the quantity of risk changes?

  3. Understanding Risk:Roadmap • Defining Risk • Measuring Risk • The Risk-Return Tradeoff • Sources of Risk • Reducing Risk

  4. Risk: Definition Risk is a measure of uncertainty about the future payoff of an investment, measured over some time horizon and relative to a benchmark.

  5. Risk: Elements of the Definition • Measure: uncertainties that are not quantifiable can’t be priced • Uncertainty about the future: future is one of a series of possible outcomes • Payoff: list the possible payoffs • Investment: broadly defined • Time horizon: Longer is usually more risky • Benchmark: Measured relative to risk-free.

  6. Measuring Risk • List of all possible outcomes • List the probability of each occurring

  7. Measuring Risk Example: Single Coin Toss Lists all possibilities, one of them must occur. Probabilities sum to one.

  8. Measuring Risk:Case 1 $1000 Investment • Rise in value to $1400 • Fall in value to $700 Two possibilities are equally likely

  9. Measuring Risk:Expected Value Expected Value = ½ ($700) + ½ ($1400) = $1050

  10. Are you saving enough for retirement? • Retirement planners can help figure out • Be careful • Investments with high returns are risky • Risk means you can end up with less than the expected return

  11. Measuring Risk:Case 2 What if $1000 Investment • Rise in value to $2000 • Rise in value to $1400 • Fall in value to $700 • Fall in value to $100

  12. Measuring Risk:Case 2 Expected Value = 0.1x($100) + 0.4x($700) + 0.4x($1400) +0.1x($2000) = $1050

  13. Measuring Risk:Comparing Cases 1 & 2 • Expected value is the same: $1050, or 5% on a $100 investment • Is the risk the same? • Case 2 seems to have more risk • Why?

  14. Measuring Risk:Defining a Risk-Free Asset A risk-free asset is an investment whose future value is known with certainty and whose return is the risk-free rate of return.

  15. Measuring Risk:Comparing Cases 1 & 2 • Consider a risk-free investment $1000 yields $1050 with certainty. • Compare Case 1 and the risk-free investment • As the spread of the potential payoffs rises, the risk rises.

  16. Measuring Risk:Variance & Standard Deviation • Variance: Average of squared deviation of the outcomes from the expected value, weighted by the probabilities. • Standard Deviation: Square root of the variance(Same units as the payoff)

  17. Measuring Risk:Case 1 1. Compute the expected value: ($1400 x ½) + ($700 x ½) = $1050. 2. Subtract this from each of the possible payoffs: $1400 – $1050= $350 $700 – $1050= –$350 3. Square each of the results: $3502= 122,500(dollars)2 and (–$350)2=122,500(dollars)2 4. Multiply each result times its probability and add up the results: ½ [122,500(dollars)2] + ½ [122,500(dollars)2] =122,500(dollars)2 5. Standard deviation = = =$350

  18. Measuring Risk:Case 2

  19. Measuring Risk:Comparing Cases 1 & 2 Case 1: Standard Deviation =$350 Case 2: Standard Deviation =$528 The greater the standard deviation, the higher the risk.

  20. Measuring Risk: Comparing Cases 1 & 2 Case 2 has a higher standard deviation because it has a bigger spread

  21. Car insurance is especially expensive for young drivers • You have to have liability insurance • What about collision • See if you should get a high deductible

  22. Leverage: Borrowing to finance part of an investment • Invest • $1000 or your own + $1000 borrowed • Expected return doubles • Standard Deviation doubles

  23. Leverage raises the expected value and the standard deviation.

  24. Measuring Risk:Value-at-Risk (VaR) • Sometimes we are less concerned with spread than with the worst possible outcome • Example: We don’t want a bank to fail • VaR: The worst possible loss over a specific horizon at a given probability

  25. Lotteries are very risky investments • Why do people play? • The loss of $1 is inconsequential compared with the chance to win millions

  26. Risk Aversion • A risk-averse investor: prefers an investment with a certain return to one with the same expected return, but any amount of uncertainty • A risk-averse person requires compensation to assume a risk • A risk-averse person pays to avoid risk

  27. Risk Premium The riskier an investment – the higher the compensation that investors require for holding it – the higher the risk premium.

  28. Risk-Return Tradeoff More risk  Bigger risk premium  Higher expected returnRisk Requires Compensation

  29. How much risk should you tolerate? • Take a risk quiz (pg. 117): • What would you do if a month after you invest the value drops 20%? • As you get older, your risk tolerance will probably fall

  30. Sources of Risk 1. Idiosyncratic or Unique: Affects a specific a person or business. 2. Systematic or Economy-wide Risk:Affects everyone

  31. Idiosyncratic and Systematic Risk • Idiosyncratic: GM loses market share to another auto makers • Systematic: The entire auto market shrinks

  32. Reducing Risk through Diversification • Hedging Risk:Make investments with offsetting payoff patterns • Spreading Risk:Make investments with independent payoff patterns.

  33. Reducing Risk:Hedging Reduce overall risk by making two investments with opposing risks. • When one does poorly, the other does well, and vice versa • So while the payoff from each investment is volatile, together their payoffs are stable

  34. Reducing Risk:Hedging Compare: 1. Invest $100 in GE 2. Invest $100 in Texaco 3. Invest ½ in each: $50 in GE + $50 in Texaco

  35. Reducing Risk:Hedging Hedging has eliminated the risk entirely.

  36. Reducing Risk:Spreading • You can’t always hedge • The alternative is to spread risk around • Find investments whose payoffs are unrelated

  37. Reducing Risk:Spreading Consider three investment strategies: 1. GE only, 2. Microsoft only, and 3. ½ in GE + ½ in Microsoft.

  38. Reducing Risk:Spreading

  39. Reducing Risk:Spreading The more independent sources of risk in your portfolio, the lower the overall risk

  40. Diversification is especially important for you retirement savings • Many Enron employees investment their retirement savings in Enron stock • If the company you work for goes bankrupt, you will lose your job. Don’t lose your savings, too. Diversify.

  41. Chapter 5 End of Chapter

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