RiskRisk… … 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 outcomesList of all possible outcomes

Chance of each one occurring.Chance of each one occurring.

Measuring RiskCase 1An 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 Variance of Payoff Standard Standard Deviation = Deviation = RiskRisk

Variance of payoff = Expected = Expected squared deviationsquared deviation of return from of return from

its expected value its expected value =½($1400-$1050)=½($1400-$1050)22 + ½($700-$1050) + ½($700-$1050)22

= ½ ($350)= ½ ($350)22 + ½ ($350) + ½ ($350)22 = 122,500 $ = 122,500 $22

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 Variance of Payoff Standard Standard Deviation = Deviation = RiskRisk

Variance of payoff = Expected = Expected squared deviationsquared deviation of return from of return from

its expected value its expected value = .1($100-$1050)= .1($100-$1050)22 + .4($700-$1050) + .4($700-$1050)22

+ .4($1400-$1050)+ .4($1400-$1050)22 + .1($2000-$1050) + .1($2000-$1050)22

= 278,500 $= 278,500 $22

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 risk-free rate of return.

A A risk-averse risk-averse investor will always investor will always prefer an investment with a certain prefer an investment with a certain return to one with the same return to one with the same expectedexpected return but some risk. return but some risk. – The riskier an investment, the higher the The riskier an investment, the higher the

compensation that investors require for compensation that investors require for holding it 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 To eliminate risk, find investments whose payoffs are negatively correlated: payoffs are negatively correlated: One does better than expected, the other does worseOne does better than expected, the other does worse

To spread risk, find investments whose To spread risk, find investments whose payoffs are completely unrelated.payoffs are completely unrelated.

But perfectly negative correlation and even But perfectly negative correlation and even complete lack of correlation in payoffs is lack of correlation in payoffs is rarely possible rarely possible systematic risk systematic risk

Diversification can still reduce risk (if not Diversification can still reduce risk (if not eliminate risk)eliminate risk)

Reducing Risk Through Diversification::PPositively 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 Variance of Payoff Standard Standard Deviation = Deviation = RiskRisk

Variance of payoff = Expected = Expected squared deviationsquared deviation of return from of return from

its expected value its expected value = ¼ ($120-$110)= ¼ ($120-$110)22 + ½ ($110-$110) + ½ ($110-$110)2 2

+ ¼ ($100-$110)+ ¼ ($100-$110)22 = 50 $= 50 $22

Standard Deviation of Payoff = SQRT(Variance) = (50 $2 )1/2 = $ 7.07