# Money and Banking

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Money & Banking ­ MGT411
VU
Lesson 11
MEASURING RISK
Measuring Risk
Variance and Standard Deviation
Value at Risk (VAR)
Measuring Risk
Most of us have an intuitive sense for risk and its measurement;
The wider the range of outcomes the greater the risk
A financial instrument with no risk at all is a risk-free investment or a risk-free asset;
Its future value is known with certainty and
Its return is the risk-free rate of return
If the risk-free return is 5 percent, a \$1000 risk-free investment will pay \$1050, its expected
value, with certainty.
If there is a chance that the payoff will be either more or less than \$1050, the investment is
risky.
We can measure risk by measuring the spread among an investment's possible outcomes. There
are two measures that can be used:
Variance and Standard Deviation
Value at Risk (VAR)
Measure of riskiness of worst case
Variance
The variance is defined as the probability weighted average of the squared deviations of the
possible outcomes from their expected value
To calculate the variance of an investment, following steps are involved:
Compute expected value
Subtract expected value from each possible payoff
Square each result
Multiply by its probability
Compute the expected value:
(\$1400 x ½) + (\$700 x ½) = \$1050.
Subtract this from each of the possible payoffs:
\$1400-\$1050= \$350
\$700-\$1050= ­\$350
Square each of the results:
\$3502  = 122,500(dollars)2 and
(­\$350)2 = 122,500(dollars)2
Multiply each result times its probability and adds up the results:
½ [122,500(dollars)2] + ½ [122,500(dollars)2]
= 122,500(dollars)2
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Money & Banking ­ MGT411
VU
More compactly;
Variance = ½(\$1400-\$1050)2 + ½(\$700-\$1050)2
= 122,500(dollars)2
Standard Deviation
The standard deviation is the square root of the variance, or:
Standard Deviation (case 1) =\$350
Standard Deviation (case 2) =\$528
The greater the standard deviation, the higher the risk
It more useful because it is measured in the same units as the payoffs (that is, dollars and not
squared dollars)
The standard deviation can then also be converted into a percentage of the initial investment,
providing a baseline against which we can measure the risk of alternative investments
Given a choice between two investments with the same expected payoff, most people would
choose the one with the lower standard deviation because it would have less risk
Value at Risk
Sometimes we are less concerned with the spread of possible outcomes than we are with the
value of the worst outcome.
To assess this sort of risk we use a concept called "value at risk."
Value at risk measures risk at the maximum potential loss
Risk Aversion
Most people don't like risk and will pay to avoid it; most of us are risk averse
A risk-averse investor will always prefer an investment with a certain return to one with the
same expected return, but any amount of uncertainty.
Buying insurance is paying someone to take our risks, so if someone wants us to take on risk we
must be paid to do so
The riskier an investment ­ the higher the compensation that investors require for holding it ­
Riskier investments must have higher expected returns
There is a trade-off between risk and expected return;
You can't get a high return without taking considerable risk.
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Money & Banking ­ MGT411
VU
Figure: The Trade-off between Risk and Expected Return
Higher Risk=Higher Expected Return
The higher the risk, the higher
the expected return. The risk