Risk
… uncertainty about the future payoff
of an investment measured over some
time horizon and relative to a
benchmark.
Measuring Risk requires:
List of all possible outcomes
Chance of each one occurring.
Measuring RiskCase 1
An Investment can rise or fall in value. Assume that
an asset purchased for $1000 is equally likely to fall
to $700 or rise to $1400
Variance of Payoff  Standard
Deviation = Risk
Variance of payoff
= Expected squared deviation of return from
its expected value
=½($1400-$1050)2 + ½($700-$1050)2
= ½ ($350)2 + ½ ($350)2 = 122,500 $2
Standard Deviation of Payoff
= SQRT(Variance)
= (122,500 $2 )1/2 = $350
Measuring Risk: A second investment
with same expected payoff but broader
probability distribution
Variance of Payoff  Standard
Deviation = Risk
Variance of payoff
= Expected squared deviation of return from
its expected value
= .1($100-$1050)2 + .4($700-$1050)2
+ .4($1400-$1050)2 + .1($2000-$1050)2
= 278,500 $2
Standard Deviation of Payoff
= SQRT(Variance)
= (278,500 $2 )1/2 = $528
A risk-free asset is an investment
whose future value of known with
certainty, and whose return is the riskfree rate of return.
A risk-averse investor will always
prefer an investment with a certain
return to one with the same expected
return but some risk.
– The riskier an investment, the higher the
compensation that investors require for
holding it
 the higher the risk premium.
Sources of Risk
Idiosyncratic – Unique Risk
Systematic – Economy-wide Risk
Reducing Risk through
Diversification
Hedging Risk
Reduce overall risk by making two
investments with opposing risks.
– When one does poorly, the other does
well, and vice versa.
– While the payoff from each investment
is volatile, together their payoffs are
stable.
Reducing Risk through Diversification
Compare three strategies for investing
$100
1.
Invest $100 in GE
2.
Invest $100 in Texaco
3.
Invest half in each company
$50 in GE and $50 in Texaco
Reducing Risk through Diversification
To eliminate risk, find investments whose
payoffs are negatively correlated:
One does better than expected, the other does worse
To spread risk, find investments whose
payoffs are completely unrelated.
But perfectly negative correlation and even
complete lack of correlation in payoffs is
rarely possible  systematic risk
Diversification can still reduce risk (if not
eliminate risk)
Reducing Risk Through Diversification:
Positively Correlated Payoffs
Consider three investment strategies:
(1) GE only,
(2) Microsoft only, and
(3) half in GE and half in Microsoft.
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, the analysis is
more complicated.
– There are four possible outcomes, two for each
stock
Variance of Payoff  Standard
Deviation = Risk
Variance of payoff
= Expected squared deviation of return from
its expected value
= ¼ ($120-$110)2 + ½ ($110-$110)2
+ ¼ ($100-$110)2
= 50 $2
Standard Deviation of Payoff
= SQRT(Variance)
= (50 $2 )1/2 = $ 7.07