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cfc session 6 ch6+7

# 69 certified financial controller cfc how to

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Unformatted text preview: asure) σ= n Σ ( Ri – R )2( Pi ) i=1 Standard Deviation σ, is a statistical Deviation, measure of the variability of a distribution around its mean around its mean. It is the square root of variance. Note, this is for a discrete distribution. 71 Certified Financial Controller CFC How to Determine the Expected Return and Standard Deviation Stock BW BW Ri Pi –0.15 0.10 –0.03 0.20 0.09 0.40 0.21 0.20 0.33 0.10 Sum 72 (Ri)(Pi) –0.015 –0.006 0.036 0.042 0.033 1.00 0.090 Certified Financial Controller CFC 36 (Ri - R )2(Pi) 0.00576 0.00288 0.00000 0.00288 0.00576 0.01728 Determining Standard Deviation (Risk Measure) σ= n Σ ( Ri – R )2( Pi ) i=1 σ= .01728 σ = 0.1315 or 13.15% 13.15% 73 Certified Financial Controller CFC Coefficient of Variation The ratio of the standard deviation of ratio of the standard deviation of mean a distribution to the mean of that distribution. It is a measure of RELATIVE risk. RELATIVE CV = σ/R R CV of BW = 0.1315 / 0.09 = 1.46 74 Certified Financial Controller CFC 37 Discrete versus. Continuous Distributions Discrete Continuous 0.035 0.4 0.35 0.03 0.3 0.025 0.25 0.02 0.2 0.015 0.15 0.01 0.1 0.005 0.05 –0.15 –0.03 75 9% 21% 33% -5 0 % -4 1 % -3 2 % -2 3 % -1 4 % -5 % 4% 13% 22% 31% 40% 49% 58% 67% 0 0 Certified Financial Controller CFC Continuous Distribution Problem • • 9.6%, –15.4%, 26.7%, –0.2%, 20.9%, 28.3%, –5.9%, 3.3%, 12.2%, 10.5% • 76 Assume that the following list represents the that the following list represents the continuous distribution of population returns for a particular investment (even though there are only 10 returns). Calculate the Expected Return and Standard Deviation for the population. Certified Financial Controller CFC 38 Risk Attitudes Certainty Equivalent (CE) is the Equivalent is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain indifferent between that certain amount and an amount expected to be received with risk at the same point in time. 77 Certified Financial Controller CFC Risk Attitudes Certainty equivalent > Expected value equivalent Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Most individuals are Risk Averse Averse. 78 Certified Financial Controller CFC 39 Risk Attitude Example You have the choice between (1) a guaranteed have the choice between guaranteed dollar reward or (2) a coin-flip gamble of \$100,000 (50% chance) or \$0 (50% chance). The expected value of the gamble is \$50,000. • Mary requires a guaranteed \$25,000, or more, to call off the gamble. • Raleigh is just as happy to take \$50,000 or take the risky gamble. • Shannon requires at least \$52,000 to call off the gamble. 79 Certified Financial Controller CFC Risk Attitude Example What are the Risk Attitude tendencies of each? are the Risk Attitude tendencies of each? Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. . Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value equivalent equals the expected value of the gamble. . Shannon reveals a “risk preference” because her “certainty equivalent” > the expec...
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