Variance and Standard Deviation Variance and standard deviation still measure the volatility of returns Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations o2-∑p,(R-E(R2 i=l 5
5 Variance and Standard Deviation n Variance and standard deviation still measure the volatility of returns n Using unequal probabilities for the entire range of possibilities n Weighted average of squared deviations n i pi Ri E R 1 2 2 σ ( ( ))
Example:Variance and Standard Deviation Consider the previous example.What are the variance and standard deviation for each stock? State Probability C T Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ?? 0.02 0.01 Stock C 62=.3(.15-.099)2+.5(.1-.099)2+.2(.02-.099)2=.002029 0=.045 Stock T 2=.3(.25-.177)2+.5(.2-.177)2+.2(.01-.177)2=.007441 6=.0863 6
6 Example: Variance and Standard Deviation n Consider the previous example. What are the variance and standard deviation for each stock? n Stock C 2 = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .002029 = .045 n Stock T 2 = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2 = .007441 = .0863 State Probability C T Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01
Another Example Consider the following information: State Probability Ret.on ABC,Inc ▣ Boom .25 .15 o Normal .50 .08 Slowdown .15 .04 Recession .10 -.03 What is the expected return? ■Vhat is the variance? What is the standard deviation?
7 Another Example n Consider the following information: q State Probability Ret. on ABC, Inc q Boom .25 .15 q Normal .50 .08 q Slowdown .15 .04 q Recession .10 -.03 n What is the expected return? n What is the variance? n What is the standard deviation?
Portfolios A portfolio is a collection of assets An asset's risk and return are important to how the stock affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation,just as with individual assets 8
8 Portfolios n A portfolio is a collection of assets n An asset’s risk and return are important to how the stock affects the risk and return of the portfolio n The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Example:Portfolio Weights ■ Suppose you have $15,000 to invest and you have purchased securities in the following amounts.What are your portfolio weights in each security? 口$2,000 of DCLK DCLK:2/15=.133 ▣$3,000ofKO K0:3/15=.2 0 $4,000 of INTC lNTC:4/15=.267 $6,000 of KEl KE:6/15=.4 9
9 Example: Portfolio Weights n Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? q $2,000 of DCLK q $3,000 of KO q $4,000 of INTC q $6,000 of KEI •DCLK: 2/15 = .133 •KO: 3/15 = .2 •INTC: 4/15 = .267 •KEI: 6/15 = .4