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:

[(boom $2.00 dividend $58 stock price),(normal economy $2 dividend and $54 stock price) (recession $0.50 dividend and $39.5 stock price)]

Calculate the expected holding period return and standard deviation of the holding period return, the boom and normal economy states are 40% likely to happen.

calculate the expected return and standard deviation of a portfolio invested half in business adventures and half is treasury bill. The return on bill is 5%

Answer 1

Boom:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($58.00 + $2.00 - $50.00) / $50.00
Expected Return = 0.20

Normal:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($54.00 + $2.00 - $50.00) / $50.00
Expected Return = 0.12

Recession:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($39.50 + $0.50 - $50.00) / $50.00
Expected Return = -0.20

Answer a.

Probability of Boom = 0.40
Probability of Normal = 0.40
Probability of Recession = 0.20

Expected Holding Return = 0.40 * 0.20 + 0.40 * 0.12 + 0.20 * (-0.20)
Expected Holding Return = 0.088 or 8.80%

Variance = 0.40 * (0.20 - 0.088)^2 + 0.40 * (0.12 - 0.088)^2 + 0.20 * (-0.20 - 0.088)^2
Variance = 0.022016

Standard Deviation = (0.022016)^(1/2)
Standard Deviation = 0.1484 or 14.84%

Answer b.

Weight of Stock = 0.50
Weight of Treasury Bill = 0.50

Expected Return of Portfolio = Weight of Stock * Expected Return of Stock + Weight of Treasury Bill * Expected Return of Treasury Bill
Expected Return of Portfolio = 0.50 * 0.0880 + 0.50 * 0.0500
Expected Return of Portfolio = 0.0690 or 6.90%

Standard Deviation of Portfolio = Weight of Stock * Standard Deviation of Stock
Standard Deviation of Portfolio = 0.50 * 14.84%
Standard Deviation of Portfolio = 7.42%