Question

The stock of Business Adventures sells for $35 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	$1.20	$45
Normal economy	1.20	38
Recession	.60	26

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.)

Expected return	%
Standard deviation	%

b.	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.)

Expected return	%
Standard deviation	%

Answer 1

We will have to calculate the holding period return under each of the state of economy and than calculate the expected holding period return of the stock
Formula to calculate holding period return
Holding period return = ([End price - Beginning price] + Dividend)/Beginning price
Calculation of holding period return under each of the state economy
Boom = (45-35+1.20)/35		32.00%
Normal = (38-35+1.20)/35		12.00%
Recession = (26-35+0.60)/35		-24.00%
Since each of the state is equally likely the expected holding period return for stock is
Expected holding period return = (1/3)*(0.32) + (1/3)*(0.12)+(1/3)*(-0.24)
		6.67%
The expected holding period return is 6.67%
Calculation of standard deviation of the stock
State of economy (A)	Probability (B)	Return (C )	Deviation of return from expected return (D) (C - 0.067)	Square of deviation (D^2)	Probability*Square of deviation
Boom	0.333333333	0.32	0.2533	0.06418	0.021393
Normal	0.333333333	0.12	0.0533	0.00284	0.000948
Recession	0.333333333	-0.24	-0.3067	0.09404	0.031348
				Variance	0.053689
				Standard deviation = Square root of variance	23.17%
The Standard deviation of the stock is 23.17%
b)
Calculation of expected return of portfolio where equal amount is invested in the stock and treasury bills
Expected return = (0.50*0.067) + (0.50*0.04)
	5.33%
The expected return of the portfolio would be 5.33%
Treasury bills are risk free and therefore standard deviation is 0
Standard deviation of portfolio = 0.50*0.2317
	11.59%
The standard deviation of portfolio would be 11.59%