Question

The stock of XYZ 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	$58
Normal economy	1.40	52
Recession	0.70	43

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.)

b. Calculate the expected return and standard deviation of a portfolio invested half in XYZ stock and half in Treasury bills. The return on bills is 3%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

A B C D E F G in Expected Return 7.33% 2.27% -4.20% 5.40% Variance 0.92% 0.01% 1.08% 1 2 Selling Price of stock $50 3 State of the economy Probability Dividend Stock Price Return 5 Boom 0.333 $3.0 $58 22.0% 6 Normal economy 0.333 $1.4 $52 6.8% 7 Recession 0.333 $0.7 $43 -12.6% 8 Expected Holding Period Return of XYZ Stock 9 Variance 10 Standard Deviation of Holding Period Return of XYZ Stock 11 Weighted 12 Portfolios Investment Return Return 13 XYZ Stock 50% 5.40% 2.70% 14 Treasury Bill 50% 3.00% 1.50% 15 Expected Return of portfolio 4.20% 16 Standard Deviation of portfolio 7.08% 2.01% 14.16% 17

a. Expected Holding Period Return of XYZ Stock = 5.40%

Standard Deviation of Holding Period Return of XYZ Stock = 14.16%

Note:

1. Return of the stock = ((Price at the end of year 1 - Price at the beginning of year 1) + Dividend received during the year) / Price at the beginning of year 1

2. Expected Return is the return of the stock multiplied with the probability of state of economy

3. Standard Deviation is the square-root of variance and variance is the squared deviation of the returns from the expected return adjusted for probability of state of economy

b. Expected Return of portfolio = 4.20%

Standard Deviation of portfolio = 7.08%

Note:

1. Return of portfolio = (Return of stock * Investment propotion in stock) + (Return of treasury bill* Investment propotion in treasury bill)

2. Standard deviation of portflio:

There is no risk in investing in treasury bills and hence standard deviation of treasury bill is zero. Thus, the only standard deviation will be that of XYZ Stock. Since 50% is invested in XYZ stock, standard deviation of portfolio will be 50% of standard deviation of XYZ Stock.

Workings:

B c. D E F G A 1 2 Selling Price of stock 50 3 58 43 4 State of the economy Probability Dividend Stock Price 5 Boom =1/3 3 6 Normal economy =1/3 1.4 52 7 Recession =1/3 0.7 8 Expected Holding Period Return of XYZ Stock 9 Variance 10 Standard Deviation of Holding Period Return of XYZ Stock 11 Return Expected Return Variance =((D5-$B$2)+C5)/$B$2 =E5*B5 =(E5-$F$8)^2*B5 =((D6-$B$2) +C6)/$B$2=E6*B6 =(E6-$F$8)^2*B6 =((D7-$B$2) +C7)/$B$2 =E7*B7 =(E7-$F$8)^2*B7 =SUM(F5:F7) I-SUM(G5:67) =SQRT(G9) 12 Portfolios Investment Return Weighted Return 13 XYZ Stock 0.5 =F8 =B13*C13 14 Treasury Bill 0.5 0.03 =B14*C14 15 Expected Return of portfolio =SUM(D13:014) 16 Standard Deviation of portfolio =G10*B13 17