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 Normal economy Recession Dividend $3.00 1.40 0.70 Stock Price $58 52 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.) 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 3%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return Standard deviation

Answer 1

Ans:- (a) In this part we need to find the Expected holding period return and Standard deviation when all the three scenarios are equally likely which means Probability will be 0.33 for all cases.

519 M N O Economy Probability Price (P1) $ Price (PO) $ Dividend ($) HPR ( P1+D - PO)/PO Prob * HPR Dev(HPR-ER) Dev2 Dev^2*Prob 0.33 3 Boom Normal Recession 0.33 50 1.4 0.7 22.000% 6.800% -12.600% 7.260% 2.244% -4.158% 16.654% 6.800% -17.946% 2.774% 0.462% 3.221% 0.915% 0.153% 1.063% 0.33 43 50 Expected return 5.346% Variance 2.131% SD 14.60%

519 E F M Economy Probability Price (P1) $ Price (PO)$ Dividend ($) HPR ( P1+D - PO)/PO Prob * HPR Dev(HPR-ER) Dev^2 Dev^2* Prob 3 Boom Normal Recession 0.33 0.33 0.33 58 52 50 =(G7+17-H7)/H7 =(G8+18-H8)/H8 =(G9+19-H9)/H9 1.4 0.7 =J7*F7 =J8*F8 =39*F9 =J7-K11 =J8-K12 = 29-K11 =L7^2 =L8^2 =L9^2 =M7*F7 =M8*F8 =M9*F9 43 50 Expected return =SUM(K7:K9) Variance =SUM(N7:N9) SD =SQRT(N11)

Dev is the deviation, HPR is the Holding period return. The expected return is 5.346% and the Standard deviation is 14.60%.

(b) The expected return of a portfolio,if it is invested half in Business Adventure and half in treasury bill if returns on the bill is 4%   

= 0.5 * 5.346 + 0.5 * 3 = 4.1730%.

The standard deviation of the portfolio will be 0.5 * SD of Business Adventures i.e 0.5 * 14.60 = 7.30% because half of the portfolio is invested in treasury bill which is risk-free.

Note:- Please go through it and feel free to ask any doubt. If this