Chapter 4, Part-I - Practice quizzes
These are multiple choice questions that should be used to practice your level of mastery of the material.
They are sample exercises and should not be interpreted as a complete set of exercises that can be created for this chapter material.
Please note that doing the required readings is essential.
If you are promised a nominal return of 14%, on a one year investment, and you expect the rate of inflation to be 17%, what real rate do you expect to earn?
É-lhe prometida uma rendibilidade nominal de 14%, para um investimento de um ano, e você espera que a taxa de inflação seja de 17%, qual a rendibilidade real esperada?
✓-2.56%
✗-3.0%
✗11.97%
✗14.0%
Consider the relation between nominal and real rates.
(1+r_n) = (1+r_r) \times (1+i)
(1+14\%) = (1+r_r) \times (1+17\%)
r_r=-2.56\%
A Treasury bill pays a 1% rate of return. A risk averse investor __________ invest in a risky portfolio that pays 13% with a probability of 35% or 3% with a probability of 65% because __________.
Os Bilhetes do Tesouro proporcionam uma rendibilidade de 1%. Uma investidora avessa ao risco __________ investir numa carteira com risco que proporciona 13% com a probabilidade de 35% ou 3% com a probabilidade de 65% uma vez que __________.
✗would not; because the risk premium is positive / irá; recebe um prémio de risco positivo
✗would not; because she is not rewarded any positive risk premium / não irá ; não recebe um prémio de risco positivo
✓might; she is rewarded a risk premium / poderá; recebe um prémio de risco
✗cannot be determined / não é possível determina
Consider the expected return of the risky asset.
Let’s call ‘i’ the risky asset.
The expected return is: E[r_i] = 13\% \times 35\% + 3\% \times 65\% = 6.5\%
The asset risk premium is: E[r_i]-r_f = 6.5\%-1\%=5.5\%
The investor might consider to invest in such risky asset, but we cannot be sure that she will.
Consider a treasury bill with a rate of return of 1% and the risky securities in the table below. The investor wants to combine the risk-free asset with one of the securities mentioned above. The security the investor would choose as part of his portfolio would be __________.
Considere que os Bilhetes do Tesouro proporcionam uma rendibilidade de 1% e a informação da tabela abaixo sobre activos com risco. O investidor quer combinar o activo isento de risco com um dos activos com risco acima mencionados. O activo com risco que irá escolher para fazer parte da sua carteira será o __________.
| Asset / Activo | E[r] | Variance / Variância |
|---|---|---|
| A | 0.165 | 0.133 |
| B | 0.219 | 0.035 |
| C | 0.184 | 0.04 |
| D | 0.211 | 0.125 |
✗A
✓B
✗C
✗D
Make sure to take into account the risk and reward dimensions.
Calculate the reward-to-variability ratio for each asset:
A \frac{(.165 - 0.01)}{.133^{0.5}} = 0.42502
B \frac{(.219 - 0.01)}{.035^{0.5}} = 1.11715
C \frac{(.184 - 0.01)}{.04^{0.5}} = 0.87
D \frac{(.211 - 0.01)}{.125^{0.5}} = 0.56851
An investor invests 43% of his wealth in a risky asset with an expected rate of return of 21.9% and a variance of 9.2% and the remainder in a treasury bill that pays 1%. Her portfolio’s expected rate of return and standard deviation are __________ and __________ respectively.
Uma investidora investe 43% da sua riqueza num activo com risco com uma rendibilidade esperada de 21.9% e uma variância de 9.2%, e o restante em bilhetes do tesouro com uma rendibilidade de 1%. Essa carteira terá uma rendibilidade esperada de __________ e um desvio padrão de __________.
✗11.45%; 13.04%
✗9.99%; 3.96%
✗9.99%; 9.42%
✓9.99%; 13.04%
E[r_p] = 0.43\times 0.219 + (1-0.43)\times 0.01 \\ = 0.09987
\sigma_{p} = 0.43\times \sqrt{0.092} \\ = 0.13042546
You have $135370 available to invest. The risk-free rate is 4%, and the borrowing rate is 6%. The return on the risky portfolio is 8.2%. If you wish to earn a 12.2% return by combining these two assets in a portfolio, you should __________.
Você dispõe $135370 para investir. A taxa isenta de risco é de 4%, e pode pedir emprestado à taxa de 6%. A rendibilidade esperada do activo com risco é de 8.2%. Se quiser obter uma rendibilidade esperada de 12.2% pela combinação desses dois activos deverá __________.
✗invest $128924 in the risk free asset / investir $128924 no activo isento de risco
✗borrow $128924 / pedir emprestado $128924
✗invest $246127 in the risk free asset / investir $246127 no activo isento de risco
✓borrow $246127 / pedir emprestado $246127
Be careful! The borrowing rate is different from the risk-free rate.
E[r_p] = y\times 0.082 + (1-y)\times 0.06 \\ 0.122 = y\times 0.082 + (1-y)\times 0.06 \\ y= 2.81818
Amount invested in the risk-free asset = (1-y) \times 135370 = -246127.
This means that you should borrow: $246 127
The return on the risky portfolio is 16.5%. The risk-free rate as well as the investor’s borrowing rate is 2%. The standard deviation of return on the risky portfolio is 27.3%. If you want to combine the two assets in a portfolio with the a standard deviation of 31.3%, the expected return on this portfolio will be __________.
A rendibilidade do activo com risco é de 16.5%. A taxa isenta de risco e dos empréstimos é de 2%. O desvio padrão da carteira com risco é de 27.3%. Se quiser combinar estes dois activos numa carteira com um desvio padrão de 31.3%, a rendibilidade dessa carteira será __________.
✓18.625%
✗18.75%
✗18.92%
✗19.21%
First calculate the weights of a portfolio with a standard deviation of 31.3% and then calculate the expected return of such portfolio.
\sigma^2_p = y^2 \times \sigma_c^2 \\ 0.313^2 = y^2 \times 0.273^2\\ y=1.14652
Now we can calculate the expected return of such investment:
E[r_p] = y\times E[r_c] + (1-y)\times r_f \\ E[r_p] = 1.14652\times 0.165 + (1-1.14652)\times 0.02 \\ E[r_p] = 0.18625
Financial Investments, Chapter 4, Part-I - Practice quizzes