Question

The stock of BurgerHouse 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                                        $2.00                            $50

Good economy                            1.5                                46                                

Normal economy                         1.00                              43

Recession                                   .50                                34

1) Calculate the expected holding-period return and standard deviation of the holding period return. All four scenarios are equally likely.

2) Calculate the expected return and standard deviation of a portfolio invested 60% in ABC and 40% in Treasury bills. The return on bills is 3%.

Answer 1

HPR = Stock Price ((End of period value - original value)+Income) / original value) * 100

HPR(boom)= ((50-50)+2)/50 = 4%

HPR(Good)= ((46-50)+1.50)/50 = -5%

HPR(Normal)= ((43-50)+1)/50 = -12%

HPR(Recession)= ((34-50)+.50)/50 = -31%

Calculation of Expected Return: (Weight of Boom * Return from Boom) + (Weight of Good * Return from Good) +(Weight of Normal * Return from Normal) +(Weight of Recession * Return from Recession)

Since all four scenarios are equally likely the weight of all will be 1/4

Expected return : (1/4 x 4%) + (1/4 x -5%) + (1/4 x -12%) + (1/4 x -31%) = -11%

Calculation of Standard deviation:

Variance: [Weight of Boom * (Return from Boom – total expected return)2] + [Weight of Good *(Return from Good – total expected return)2] + [Weight of Normal * (Return from Normal – total expected return)2] + [Weight of Recession * (Return from Recession – total expected return)2]

= 1/4(4 – (-11)) 2+ 1/4(-5 – (-11)) 2+ 1/4(-12 – (-11)) 2 + 1/4(-31 – (-11)) 2

= 109.25

Standard Deviation will be Square Root of Variance = 10.45%

b. Expected Return of business venture -11%

Return on Treasury Bill 3%

Weight of business venture ABC W1 = .60

Weight of Treasury Bill W2 = .40

Expected Return of portfolio = (.60 * -11) + (.40 * 3) = 5.40%

Standard deviation of portfolio = Weight of ABC in portfolio * Standard deviation of ABC = (.60*10.45) =6.27%