# Money and Banking

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Money & Banking ­ MGT411
VU
Lesson 12
EVALUATING RISK
Sources of Risk
Idiosyncratic
Systematic
Reducing Risk through Diversification
Hedging Risk
Bond and Bond Pricing
How to Evaluate Risk
Lets go back to our previous example where \$1,000 yields either \$1,400 and \$700 with equal
probability
If we think about this investment in terms of gains and losses, this investment offers an equal
chance of gaining \$400 or loosing \$300
Should you take the risk?
Table: Evaluating the Risk of a \$1,000 investment
A. The Gain
Payoff
Probability
+ \$400
½
\$0
½
B. The Loss
Payoff
Probabilities
\$0
½
- \$300
½
Deciding if a risk is worth taking
List all the possible outcomes or payoffs
Assign a probability to each possible payoff
Divide the payoffs into gains and losses
Ask how much you would be willing to pay to receive the gain
Ask how much you would be willing to pay to avoid the loss
If you are willing to pay more to receive the gain than to avoid the loss, you should take the risk
Sources of Risk
Risk is everywhere. It comes in many forms and from almost every imaginable place
Regardless of the source, risks can be classified as either idiosyncratic or systematic
Idiosyncratic, or unique, risks affect only a small number of people.
Systematic risks affect everyone.
In the context of the entire economy,
Higher oil prices would be an idiosyncratic risk and
Changes in general economic conditions would be systematic risk.
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Money & Banking ­ MGT411
VU
ABC's
ABC's
Share
Share
Idiosyncratic Risk
ABC's share of
existing market
shrinks
Systematic Risk
ABC's
Share
Total Automobile market
Reducing Risk through Diversification
Risk can be reduced through diversification, the principle of holding more than one risk at a
time.
Holding several different investments reduces the overall risk that an investor bears
A combination of risky investments is often less risky than any one individual investment
There are two ways to diversify your investments:
You can hedge risks or
You can spread them among the many investments
Hedging Risk
Hedging is the strategy of reducing 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.
Table: Payoffs on Two Separate Investments of \$100
Payoff from Owning Only
Possibility
ABC Electric
XYZ Oil
Probability
Oil price rises
\$100
\$120
1/2
Oil price falls
\$120
\$100
1/2
Let's compare three strategies for investing \$100, given the relationships shown in the table:
Invest \$100 in ABC Electric
Invest \$100 in XYZ Oil
Invest half in each company ­ \$50 in ABC and \$50 in XYZ
Table: Results of Possible Investment Strategies:
Hedging Risk, Initial Investment = \$100
Investment Strategy
Expected Payoff
Standard Deviation
ABC Only
\$110
\$10
XYZ Only
\$110
\$10
½ and ½
\$110
\$0
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Money & Banking ­ MGT411
VU
Investments don't always move predictably in opposite directions, so you can't always reduce
risk through hedging
You can lower risk by simply spreading it around and finding investments whose payoffs are
completely unrelated
The more independent sources of risk you hold the lower your overall risk
Adding more and more independent sources of risk reduces the standard deviation until it
becomes negligible.
Consider three investment strategies:
a. ABC Electric only,
b. EFG Soft only, and
c. Half in ABC and half in EFG
The expected payoff on each of these strategies is the same: \$110.
For the first two strategies, \$100 in either company, the standard deviation is still 10, just as it
was before.
But for the third strategy, \$50 in ABC and \$50 in EFG, the analysis is more complicated.
There are four possible outcomes, two for each stock
Table: Payoffs from Investing \$50 in each of two Stocks
Initial Investment = \$100
Possibilities
ABC
EFG Soft
Total Payoff
Probability
#1
\$60
\$60
\$120
¼
#2
\$60
\$50
\$110
¼
#3
\$50
\$60
\$110
¼
#4
\$50
\$50
\$100
¼
Table: Results of Possible Investment Strategies:
Initial Investment = \$100
Investment Strategy
Expected Payoff
Standard Deviation
ABC
\$110
\$10
EFG Soft
\$110
\$10
½ and ½
\$110
\$7.1
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