# Chapter 5 - PowerPoint PPT Presentation

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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

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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?

• Defining Risk

• Measuring Risk

• Sources of Risk

• Reducing Risk

### 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

• 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

• Time horizon: Longer is usually more risky

• Benchmark: Measured relative to risk-free.

### Measuring Risk

• List of all possible outcomes

• List the probability of each occurring

### Measuring Risk

Example: Single Coin Toss

Lists all possibilities, one of them must occur.

Probabilities sum to one.

### 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

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

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 2

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

### 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

A risk-free asset is

an investment whose future value is known with certainty

and

whose return is the risk-free rate of return.

### 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

• 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 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

### 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 & 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

• 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

Leverage raises the expected value and the standard deviation.

### 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

• 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

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

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

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

2. Systematic or Economy-wide Risk:Affects everyone

### Idiosyncratic and Systematic Risk

• Idiosyncratic: GM loses market share to another auto makers

• Systematic: The entire auto market shrinks

### Reducing Risk through Diversification

• Hedging Risk:Make investments with offsetting payoff patterns

• Spreading Risk:Make investments with independent payoff patterns.

### 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:Hedging

Compare:

1. Invest \$100 in GE

2. Invest \$100 in Texaco

3. Invest ½ in each:

\$50 in GE

+ \$50 in Texaco

### Reducing Risk:Hedging

Hedging has eliminated the risk entirely.

• You can’t always hedge

• The alternative is to spread risk around

• Find investments whose payoffs are unrelated

Consider three investment strategies:

1. GE only,

2. Microsoft only, and

3. ½ in GE + ½ in Microsoft.

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.

End of Chapter