The mechanics of computing the means and deviations were presented in an earlier chapter.
E[RT] = 0.196 / 12 = 0.016333
E[RM] = 0.236 / 12 = 0.019667
E (RT -E[RT) (RM-E[RM]) = 0.03871141
E (RM-E[RM])2 = 0.03394667
= 0.03871141 / 0.03394667
= 1.14036
b. The beta of the average stock is 1. Travis' beta is higher. This indicates that Travis stock is riskier than the average stock.
E (RB) = 0.1 x 8 + 0.3 x 8 + 0.4 x 10 + 0.2 x 10 = 9.2%
E (RM) = 0.1 x 5 + 0.3 x 10 + 0.4 x 15 + 0.2 x 20 = 13.5%
State {RS- E (RS)} {RM - E(RM)} Pr {RB - E(RB)} {RM - E(RM)} Pr
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STATE 1 : (0.03 - 0.137) (0.05 - 0.135)x 0.1 (0.08 - 0.092) (0.05 - 0.135) x 0.1
STATE 2 : (0.08 - 0.137) (0.10 - 0.135) x 0.3 (0.08 - 0.092) (0.10 - 0.135) x 0.3
STATE 3 : (0.20 - 0.137) (0.15 - 0.135) x 0.4 (0.10 - 0.092) (0.15 - 0.135) x 0.4
STATE 4 : (0.15 - 0.137) (0.20 - 0.135) x 0.2 (0.10 - 0.092) (0.20 - 0.135) x 0.2
Sum 0.002056 0.00038
= Cov (RS,RM) = Cov (RB,RM)
M2 = 0.1 (0.05 - 0.135)2 + 0.3 (0.10 - 0.135)2
+ 0.4 (0.15-0.135)2 + 0.2 (0.20 - 0.135)2
= 0.002025
a. Beta of debt = Cov (RB, RM) / M2 = 0.00038/0.002025
= 0.188
b. Beta of stock = Cov (RS, RM)M2 = 0.002055/0.002025
= 1.015
c. B/S = 0.5
Thus, B/ (S&B) = 1/3 = 0.3333
S/ (S&B) = 2/3 = 0.6667
Beta of asset = 0.188 x 0.3333 + 1.015 x 0.6667
= 0.739
= 7 + 1.29 (13-7)
= 14.74%
b. B/ (S+B) = S / (S+B) = 0.5
WACC = 0.5 x 7 x 0.65 + 0.5 x 14.74
= 9.645%
Weak Form: Prices reflect all information contained in historical data.
Semi-strong form: In addition to historical data, prices reflect all publicly available
information.
Strong form: Prices reflect all information, public or private.
b. True: Market efficiency exists when prices reflect all available information. To be weak form efficient, the market must incorporate all historical data into prices. Under the semi-strong form of the hypothesis, the market incorporates all publicly available information in addition to the historical data. In a strong form efficient market, prices reflect all publicly and privately available information.
c. False: Market efficiency implies that market participants are rational. Rational people will immediately act upon new information and they will bid prices up or down to reflect that information.
d. False: Since in efficient markets prices reflect all available information, prices will fluctuate whenever new information becomes available.
e. True: Without competition among investors, information could not be readily transmitted. Without quick transmissions of information, prices would not reflect the information immediately and markets would not be efficient.