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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

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
- Investment: broadly defined
- 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
- 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)

- 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

Risk Premium

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

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

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.

Reducing Risk:Spreading

- You can’t always hedge
- The alternative is to spread risk around
- Find investments whose payoffs are unrelated

Reducing Risk:Spreading

Consider three investment strategies:

1. GE only,

2. Microsoft only, and

3. ½ in GE + ½ in Microsoft.

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.

End of Chapter

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