Consider the following information about Stocks I and II: Rate of Return If Stat

Question

Consider the following information about Stocks I and II: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock I Stock II Recession .26 .03 .34 Normal .56 .20 .14 Irrational exuberance .18 .09 .54 The market risk premium is 5 percent, and the risk-free rate is 3 percent. (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16. Enter your return answers as a percent. ) The standard deviation on Stock I's return is percent, and the Stock I beta is . The standard deviation on Stock II's return is percent, and the Stock II beta is . Therefore, based on the stock's systematic risk/beta, Stock (Click to select)III is "riskier".

Explanation / Answer

ANSWER IS

The normal return of Stock One (I) is:

E(RStock1) = .26 (.03) + .56 (.20) + .18 (.09)

E(RStock1) = 0.136 or 13.60%

We utilize the CAPM for locate the beta of Stock One (2).......

0.136 = .03 +eta1 (.05)

eta1 = 2.12

Figuring of difference for Stock one.....

sigma^{2}_{Stock_{1}}= .26 (.03 - 0.136)2 + .56 (.20 - 0.136)2 + .18 (.09 - 0.136)2

sigma^{2}_{Stock_{1}}= 0.0056

Figuring of Standard Deviation for Stock one.....

sigma_{Stock1} = sqrt{sigma^{2}_{Stock_{1}}} = sqrt{0.0056} = 0.07483 or 7.48%

The normal return of Stock Two (2) is:

E(RStock2) = .26 (- .34) + .56 (.14) + .18 (.54)

E(RStock2) = 0.0872 or 8.72%

We utilize the CAPM for locate the beta of Stock Two (2).......

0.0872= .03 +eta2 (.05)

eta2 = 1.144

Figuring of difference for Stock two.....

sigma^{2}_{Stock_{2}}= .26 (- .34 - 0.144)2 + .56 (.14 - 0.144)2 + .18 (.54 - 0.144)2

sigma^{2}_{Stock_{2}}= 0.08914

Figuring of Standard Deviation for Stock Two.....

sigma_{Stock2} = sqrt{sigma^{2}_{Stock_{2}}} = sqrt{0.08914} = 0.29856 or 29.85%

Stock Two is more aggregate danger, since its has low systemetic risck since the beta is much low than stock one. In this way, the stock one has more precise hazard and stock two has more aggregate danger and unsystemetic hazard.

Yet, unsystemetic hazard expanded, Stock one is mor hazardous in light of the fact that more unpredictability in it's arrival. Thus, stock one will have a more prominent expected retun and higher danger premium.

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