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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

Chapter 5

  • 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

Chapter 5

  • 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

Chapter 5

  • 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: deviation.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

Chapter 5

Risk aversion
Risk Aversion deviation.

  • 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 deviation.

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 deviation.

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

Chapter 5

  • How much risk should you tolerate? deviation.

  • 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 deviation.

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 deviation.

  • Idiosyncratic: GM loses market share to another auto makers

  • Systematic: The entire auto market shrinks

Reducing risk through diversification
Reducing Risk through Diversification deviation.

  • Hedging Risk:Make investments with offsetting payoff patterns

  • Spreading Risk:Make investments with independent payoff patterns.

Reducing risk hedging
Reducing Risk: deviation.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: deviation.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: deviation.Hedging

Hedging has eliminated the risk entirely.

Reducing risk spreading
Reducing Risk: deviation.Spreading

  • You can’t always hedge

  • The alternative is to spread risk around

  • Find investments whose payoffs are unrelated

Reducing risk spreading1
Reducing Risk: deviation.Spreading

Consider three investment strategies:

1. GE only,

2. Microsoft only, and

3. ½ in GE + ½ in Microsoft.

Reducing risk spreading2
Reducing Risk: deviation.Spreading

Reducing risk spreading3
Reducing Risk: deviation.Spreading

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

Chapter 5

Chapter 51

Chapter 5 savings

End of Chapter