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: Dividend Stock Price Boom $3.00 $60 Normal economy 1.20 58 Recession 0.75 49 a. 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.)

Answer 1

The expected holding-period return is 14.25% and the standard deviation of the holding-period return is 23.53%.

Step-by-step explanation:

To calculate the expected holding-period return, we need to find the weighted average of the returns in each scenario, using the probabilities that each scenario will occur. Since all three scenarios are equally likely, the probability is 1/3 for each scenario.

In the boom scenario, the return is calculated as (Dividend + End-of-year price - Stock Price) / Stock Price = (3.00 + 60 - 50) / 50 = 26%.

In the normal economy scenario, the return is (1.20 + 58 - 50) / 50 = 18.4%.

In the recession scenario, the return is (0.75 + 49 - 50) / 50 = -1.5%.

To calculate the expected holding-period return, we multiply each scenario's return by its probability and sum them up: (0.33 * 26%) + (0.33 * 18.4%) + (0.33 * -1.5%) = 14.25%.

To calculate the standard deviation of the holding-period return, we need the deviation of each scenario's return from the expected return. The deviations are: Boom: 26% - 14.25% = 11.75%, Normal economy: 18.4% - 14.25% = 4.15%, Recession: -1.5% - 14.25% = -15.75%. Square each deviation and multiply by its probability: (0.33 * 11.75%²) + (0.33 * 4.15%²) + (0.33 * -15.75%²) = 55.47%. Finally, take the square root of this value to get the standard deviation: √55.47% = 23.53%.

Answer 2

Holding period return = 14.49%, Standard Deviation = 11.08 approx

Step-by-step explanation:

Eco Scenario Dividend Stock Price HPR Prob Expected HPR

Boom 3 60 26 0.33 8.58

Normal 1.2 58 18.4 0.33 6.072

Recession 0.75 49 (0.5) 0.33 (0.165)

Expected HPR 14.49%

Calculation Of Standard Deviation

(A) (B) (A) - (B)

`P_(1)`
`P_(0)`
`D_(1)` Given return Exp return d p
`p.d^(2)`

60 50 3 26 14.49 11.51 0.33 43.718

58 50 1.2 18.4 14.49 3.91 0.33 5.045

49 50 0.75 (0.5) 14.49 14.99 0.33 74.15

Total
`p.d^(2)` = 122.91

wherein, d = deviation

p = probability

Standard Deviation =
`\sqrt{Total\ p.d^(2) }` =
`√(122.91)` = 11.08

Working Note:

Holding period return =
`(P_(1)\ -\ P_(0) \ +\ D_(1) )/(P_(0) )`

Boom =
`(60\ -\ 50 \ +\ 3 )/(50 )` = 26%

Similarly, for normal =
`(58\ -\ 50 \ +\ 1.2 )/(50 )` = 18.4%

Recession =
`(49\ -\ 50 \ +\ 0.75 )/(50)` = (0.5)%

figure in bracket indicates negative return