Question 1

An investor buys shares for £10 and sells them after two years for £15. At the end of each of the two years the dividends paid are 10p and 20p respectively. What is the rate of return?

Accepted Answer

The total gain includes the increase in share price from £10 to £15, plus dividends of 10p and 20p. The total gain is £5 + £0.10 + £0.20 = £5.30. The rate of return is (gain/investment) * 100 = (£5.30/£10) * 100 = 53%. Over two years, this is approximately 26.5% per year, but since none of the options exactly match this, the closest option is 24%.

Question 2

What are the possible values of covariance?

Accepted Answer

Covariance measures the joint variability of two random variables. It can take any value from negative infinity to positive infinity, depending on whether the variables tend to move in the same direction (positive covariance) or in opposite directions (negative covariance).

Question 3

What can you conclude if the standard deviation of returns from Project X is smaller than the standard deviation of returns from Project Y?

Accepted Answer

A smaller standard deviation indicates less variability in the returns from Project X, which means that it is easier to estimate the expected returns from Project X.

Question 4

What is R, when calculated using the formula R = Σ Ripi ?
I=1

Accepted Answer

R, when calculated using the formula R = Σ Ripi, represents the expected return.

Question 5

What is R, as calculated by the formula R = D1 + P1 - P0 , when P0 is the purchase price, P1 the   0
Security's
Value at the end of the one- year holding period, and D1 the dividend paid during the period?

Accepted Answer

R, as calculated by the formula R = D1 + P1 - P0, represents the one-year holding period return.

Question 6

Two constituents of a portfolio show perfectly positive correlation. What is the correlation coefficient?

Accepted Answer

When two constituents of a portfolio show perfectly positive correlation, it means that they move in the same direction and their correlation coefficient is +1.

Question 7

What is the return if a share is bought for £8, a dividend is paid of 80p, and the share is sold for £9.20 after one year?

Accepted Answer

The answer of What is the return if a share...

Question 8

A two- asset portfolio is made up of 60 per cent of funds with expected return 13 per cent, and 40 per cent of funds with expected return 15 per cent. What is the total return expected from the portfolio?

Accepted Answer

The expected return of the portfolio is calculated by taking the weighted average of the expected returns of the individual assets. Therefore, the calculation is (0.60 * 13%) + (0.40 * 15%) = 7.8% + 6% = 13.8%.

Question 9

What is represented by Rp in the formula Rp = aRA + (1 - a) RB ?

Accepted Answer

Rp represents the expected return of a portfolio, calculated as a weighted average of the expected returns of assets A and B, with weights a and (1-a) respectively.

Question 10

An investor decides to invest in shares in two companies, rather than in just one. The expected returns of each company are RA and RB (where RB > RA). Which statement best describes RP, the expected return from the portfolio?

Accepted Answer

The expected return of a portfolio is a weighted average of the expected returns of the individual investments, where the weights are determined by the proportion of the investment in each company. Assuming equal investment in both companies, the expected return of the portfolio RP can be calculated as: RP = (RA + RB) / 2 Since RB > RA, this implies that (RA + RB) / 2 > RA and (RA + RB) / 2 < RB. Therefore, RA < RP < RB Hence, the correct answer is D.

Question 11

What is the standard deviation of the return of the following project?

Accepted Answer

The answer of What is the standard deviation of the...

Question 12

Which three of the following statements are correct?

Accepted Answer

A) This statement is correct because an efficient portfolio maximizes return for a given level of risk, meaning that there is no other portfolio with the same or lower risk level that has a higher return.
B) This statement is incorrect because portfolio standard deviation is actually less than the weighted average risk of the individual investments due to diversification. 
C) This statement is correct because both covariance and the correlation coefficient measure the relationship between the returns of two investments. 
D) This statement is correct because the extent of statistical interdependence between investments affects the risk reduction from diversification. The less correlated the returns, the greater the potential risk reduction from diversification.

Question 13

What is X in the formula X = n
Σ [(RA - RA )(RB - RB) pi ] ?
I=1

Accepted Answer

X is the covariance between variables A and B.

Question 14

What term is used for the weighted average of the expected returns on the constituent investments?

Accepted Answer

The term used for the weighted average of the expected returns on the constituent investments is the portfolio expected return. This takes into account the expected returns of each individual investment within the portfolio and their respective weights. It is a key measure used to determine the overall performance and potential of a portfolio. A and B are incorrect as they refer to either the average or total expected returns, which do not take into account the weights of each investment within the portfolio. D refers to the expected return of the overall market, which is not specific to the individual portfolio.

Question 15

Which two of the following options correctly give rules for portfolio management according to mean- variance portfolio theory?

Accepted Answer

Mean-variance portfolio theory states that the portfolio standard deviation is less than the weighted average risk of the individual investments unless they are perfectly positively correlated, and that portfolio returns are a weighted average of the expected returns on the individual investments.

Question 16

Two companies operate in the same industry and tend to follow practically identical patterns of performance. Which statement describes the relationship between the returns of the two companies?

Accepted Answer

When two companies in the same industry tend to follow practically identical patterns of performance, it indicates a perfect positive correlation between them. This means that their returns move together in the same direction at the same time. Therefore, the best choice is D.

Question 17

Which one of the following approaches will increase the level of risk, provided the constituents of a portfolio are not perfectly positively correlated?

Accepted Answer

Diversification helps to reduce the risk of the portfolio by spreading it across different securities. By reducing diversification, the portfolio becomes more concentrated and therefore, increases the level of risk.

Question 18

What is the effect on outcomes if a portfolio has statistically independent shares from two companies, and the expected returns are the same for both?

Accepted Answer

Because the shares are statistically independent, their combination will result in a reduction in overall risk, as measured by the standard deviation, while the expected return remains the same. This is due to the diversification effect of combining uncorrelated assets. Therefore, the answer is D - the expected return is the same but the standard deviation is reduced.

Question 19

Which of the following statements is correct?

Accepted Answer

Option D is correct. To achieve maximum utility, select the portfolio where the highest attainable indifference curve is tangential to the efficiency frontier. This is because this point represents the optimal combination of risk and return, providing the most utility to the investor. The other options are incorrect because achieving maximum attainable utility is not always possible and selecting the portfolio with the lowest risk does not necessarily lead to maximum utility. Similarly, choosing the highest returns portfolio may not lead to the highest utility if it involves too much risk.

Question 20

A two- asset portfolio is made up of 80 per cent of Share A, for which the variance is 50%, and 20 per cent of Share B, with variance 60%. The covariance between the two shares is 25%. What is the standard deviation of the two- asset portfolio?

Accepted Answer

The standard deviation of a two-asset portfolio can be calculated using the formula for the variance of a portfolio, which is: $$ \sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\text{Cov}(A,B) $$where:- $ \sigma_p^2 $ is the variance of the portfolio,- $ w_A $ and $ w_B $ are the weights of assets A and B in the portfolio, respectively,- $ \sigma_A^2 $ and $ \sigma_B^2 $ are the variances of assets A and B, respectively,- $ \text{Cov}(A,B) $ is the covariance between assets A and B.Given:- $ w_A = 0.8 $, $ w_B = 0.2 $,- $ \sigma_A^2 = 50\% = 0.5 $, $ \sigma_B^2 = 60\% = 0.6 $,- $ \text{Cov}(A,B) = 25\% = 0.25 $.Plugging these values into the formula gives:$$ \sigma_p^2 = (0.8)^2(0.5) + (0.2)^2(0.6) + 2(0.8)(0.2)(0.25) $$$$ \sigma_p^2 = 0.32 + 0.024 + 0.08 $$$$ \sigma_p^2 = 0.424 $$The standard deviation of the portfolio, $ \sigma_p $, is the square root of the variance:$$ \sigma_p = \sqrt{0.424} \approx 0.6512 \text{ or } 65.12\% $$Therefore, the correct answer is 65.12%.

Quiz 7: Portfolio Theory