The stock of Business Adventures sells for $50 a share. Its likely dividend payo

Question

The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

  

Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

Explanation / Answer

                                             = (1/3*(24%^2 + 9.2%^2 + (-10.4%)^2) - 7.60%^2 )^ 0.5

                                = 0.017150.5 = 13.10%

b) Expected Return = 0.5 * 4% + 0.5 * 7.60% = 5.80%

Treasury bills are risk free, so their standard deviation will be zero.

Standard Deviation of the portfolio =

                                                       = 0.5 * 14.09% = 7.045%

Solution : We use dividend discount model to find out the price first. Price = (Dividend +Price at the end )/(1 + Required Return) For Boom, 50 = (2 + 60)/(1 + Ke) Ke = (62/50) -1 = 1.24 -1 = 24% For Normal, 50 = (1.6 + 53)/(1 + Ke) Ke = (54.6/50) -1 = 1.092 -1 = 9.2% For Recession, 50 = (0.8 + 44)/(1 + Ke) Ke = (44.8/50) -1 = 0.896 -1 = -10.4% [a] a) Expected Return = 1/3 * 24% + 1/3 * 9.2% + 1/3 *(-10.4%) = 7.6% Standard Deviation =( x2p 2) ^ 1/2

                                             = (1/3*(24%^2 + 9.2%^2 + (-10.4%)^2) - 7.60%^2 )^ 0.5

= (256.267 - 57.76 ) ^ 0.5 = (198.507)^ 0.5

                                = 0.017150.5 = 13.10%

= 14.09% approx [b]

b) Expected Return = 0.5 * 4% + 0.5 * 7.60% = 5.80%

Treasury bills are risk free, so their standard deviation will be zero.

Standard Deviation of the portfolio =

Weight of Business Adventure * Standard Deviation of Business Adventures

                                                       = 0.5 * 14.09% = 7.045%

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