Question

Suppose you observe the following situation:

State of the economy	Probability of state of economy	Share ABC rate of return if state occurs	Share XYZ rate of return if state occurs
Recession	0.20	-15%	25%
Normal	0.50	10%	20%
Boom	0.30	50%	10%

Suppose you have $30,000 in total. If you invest $15,000 in Share ABC and the remainder in Share XYZ, what will the expected return on your portfolio be?

	a.	The expected return in your portfolio is 17.5%.
	b.	The expected return in your portfolio is 20%.
	c.	The expected return in your portfolio is 1.35%.
	d.	The expected return in your portfolio is 12%.

Answer 1

Solution:-

                        Expected return of ABC shares=Rr×Pr+ Rn×Pn+ Rb×Pn

                                                                                                =(-15%)×0.20+10%×0.50+50%×0.30

                                                                        =17%

                where, Rr=return in recession

                        Pr =Probability of recession and so on

           

Expected return of XYZ shares=Rr×Pr+ Rn×Pn+ Rb×Pn

                                                                                                =(25%)×0.20+20%×0.50+10%×0.30

                                                                        =18%

The expected return of the portfolio=(Expected return of ABC×weight of ABC                       in portfolio)+( Expected return of XYZ×weight of XYZ in portfolio)

=17%×0.50+18%×0.50

=17.50%

Hence the expected return of portfolio is 17.50% ie option "a"