Question

8-3a Expected Portfolio Returns Calculate the expected return of the portfolio based on the following individual investments and its percentage of the total portfolio. Expected Return Weight -5.4% 10% 3% 23% 3.9% 20% 10% 0% 50% 20% B. 8-3b Portfolio Risk Based on the expected portfolio retums below, te expected return for the portfolio is 5.8% (you can check this). Calculate the standard deviation of the following portfolio: Expected Return Probability 10% 1% 8-3e Beta-Part 1 Returns on technology stocks tend to be greater than the market average while the opposite is true for utility stocks. Do you expect a tech stock's beta to be greater than, about the same or less than the market beta? Same question for the utility stock 8-3c Beta --Part 2 A stock has a beta of 1.5. If the market sees an average return of 10%, what is expected return of the stock? 1.5 x 10%-15 8-3e Beta -- Part 3 Calculate the value of a stock's beta given the following: Risk-free rate: Expected return for the market: 7%

Answer 1

Question 8-3a

Expected return from the portfolio = Sum of the investment weighted return of the individual securities in the portfolio

= W_A x R_A + W_B x R_B + ......+ W_E x R_E

where W_A = investment weight of the investment A in the portfolio and so on....and

R_A = expected return of the investment A in the portfolio and so on.....

Hence, Expected return from the portfolio = 20% x (-5.4%) + 10% x 10% + 0% x 3% + 50% x 23% + 20% x 3.9% = 12.20%

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Question 8-3b

Let's first calculate the variance under the given situation

Variance = Sum of probability weighted square of the deviation of the expected return of a scenario from the expected return of the portfolio, over the three scenarios

= P₁ x (R₁ - R_e)² + P₂ x (R₂ - R_e)² + P₃ x (R₃ - R_e)²​​​​​​​

where P₁ = probability of occurrence of scenario 1 and so on...

R₁ = expected return in scenario 1 and so on...

and R_e = Expected return of the portfolio = 5.80%

Please see the table now:

Scenario	Expected Return	Probability	Deviation from expected return on portfolio	Deviation squared	Probability x deviation squared
	Ri	Pi	Ri - Re	(Ri - Re)^2	Pi x (Ri - Re)^2
1	10%	40%	4.2%	0.0017640	0.0007056
2	5%	30%	-0.8%	0.0000640	0.0000192
3	1%	30%	-4.8%	0.0023040	0.0006912
Total					0.001416

Hence, Variance = $\sigma$² = 0.001416

Hence, standard deviation = $\sigma$ =  $\sqrt{0.001416}$ = 0.03763 = 3.76%

Question 8.3(c) - part 1

Risk return profile of a security go hand in hand. Technically, in order to avoid arbitrage, a stock with higher return should also have higher risk associated with it. Hence it should have higher beta as beta is an indicator of the risk profile of the stock.

As the returns on technology stocks > market average

Hence, the risk associated with technology stocks > riskiness of the market portfolio

Hence, beta of technology stock > Market beta.

As the returns on utility stocks < market average

Hence, the risk associated with utility stocks < riskiness of the market portfolio

Hence, beta of the utility stock < Market beta.

Question 8.3(c) - part 2

The solution is available in the picture of the question uploaded by you.

Question 8.3(c) - Part 3

The question is incomplete