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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

Chapter 5

Understanding Risk

understanding risk the big questions
Understanding Risk:The Big Questions
  • What is risk?
  • How can we measure risk?
  • What happens when the quantity of risk changes?
understanding risk roadmap
Understanding Risk:Roadmap
  • Defining Risk
  • Measuring Risk
  • The Risk-Return Tradeoff
  • Sources of Risk
  • Reducing Risk
risk definition
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.

risk elements of the definition
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.
measuring risk
Measuring Risk
  • List of all possible outcomes
  • List the probability of each occurring
measuring risk1
Measuring Risk

Example: Single Coin Toss

Lists all possibilities, one of them must occur.

Probabilities sum to one.

measuring risk case 1
Measuring Risk:Case 1

$1000 Investment

  • Rise in value to $1400
  • Fall in value to $700

Two possibilities are equally likely

measuring risk expected value
Measuring Risk:Expected Value

Expected Value = ½ ($700) + ½ ($1400) = $1050

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
measuring risk case 2
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
measuring risk case 21
Measuring Risk:Case 2

Expected Value = 0.1x($100) + 0.4x($700) + 0.4x($1400) +0.1x($2000) = $1050

measuring risk comparing cases 1 2
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?
measuring risk defining a risk free asset
Measuring Risk:Defining a Risk-Free Asset

A risk-free asset is

an investment whose future value is known with certainty


whose return is the risk-free rate of return.

measuring risk comparing cases 1 21
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.
measuring risk variance standard deviation
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)
measuring risk case 11
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


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

measuring risk comparing cases 1 22
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.

measuring risk comparing cases 1 23
Measuring Risk: Comparing Cases 1 & 2

Case 2 has a higher standard deviation because it has a bigger spread

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
Leverage: Borrowing to finance part of an investment
  • Invest
    • $1000 or your own + $1000 borrowed
    • Expected return doubles
    • Standard Deviation doubles
measuring risk value at risk var
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
Lotteries are very risky investments
  • Why do people play?
  • The loss of $1 is inconsequential compared with the chance to win millions
risk aversion
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
risk premium
Risk Premium

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

risk return tradeoff
Risk-Return Tradeoff

More risk  Bigger risk premium  Higher expected returnRisk Requires Compensation

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
sources of risk
Sources of Risk

1. Idiosyncratic or Unique: Affects a specific a person or business.

2. Systematic or Economy-wide Risk:Affects everyone

idiosyncratic and systematic risk
Idiosyncratic and Systematic Risk
  • Idiosyncratic: GM loses market share to another auto makers
  • Systematic: The entire auto market shrinks
reducing risk through diversification
Reducing Risk through Diversification
  • Hedging Risk:Make investments with offsetting payoff patterns
  • Spreading Risk:Make investments with independent payoff patterns.
reducing risk hedging
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
reducing risk hedging1
Reducing Risk:Hedging


1. Invest $100 in GE

2. Invest $100 in Texaco

3. Invest ½ in each:

$50 in GE

+ $50 in Texaco

reducing risk hedging2
Reducing Risk:Hedging

Hedging has eliminated the risk entirely.

reducing risk spreading
Reducing Risk:Spreading
  • You can’t always hedge
  • The alternative is to spread risk around
  • Find investments whose payoffs are unrelated
reducing risk spreading1
Reducing Risk:Spreading

Consider three investment strategies:

1. GE only,

2. Microsoft only, and

3. ½ in GE + ½ in Microsoft.

reducing risk spreading3
Reducing Risk:Spreading

The more independent sources of risk in your portfolio, the lower the overall risk

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.
chapter 51

Chapter 5

End of Chapter