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Risk

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.

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Risk

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  1. 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.

  2. 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

  3. 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

  4. Measuring Risk: A second investment with same expected payoff but broader probability distribution

  5. 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

  6. 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 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.

  7. Sources of Risk Idiosyncratic – Unique Risk Systematic – Economy-wide Risk

  8. 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.

  9. Reducing Risk through Diversification

  10. 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

  11. 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)

  12. Reducing Risk Through Diversification:Positively Correlated Payoffs

  13. 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

  14. 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

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