I$\text{'}$m currently preparing for an exam and would appreciate some help with the following questions. Could someone please provide corrections and explanations for them? Your guidance would really help me better understand these concepts. Thanks in advance!

QCM $6$

Question: Which statement is true regarding neoclassical financial theory?

A$.$ The normal distribution assumption of returns is not one of Markowitz's assumptions.

B$.$ Tobin's hypothesis concerns the homogeneous expectations of asset return$-$risk pairs.

C$.$ Tobin's super$-$efficient portfolio is not the efficient portfolio according to Markowitz.

D$.$ The CAPM is an empirical model, whereas the market model is a theoretical one.

E$.$ In neoclassical theory, the investment decisions of irrational economic agents are assumed to affect asset prices.

F$.$ All of the above statements are false.

Suggested Answer: F$.$ All the above statements are false. The provided options are either inaccurate or contradict established financial theory.

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QCM $7$

Question: Which statement is true among the following?

A$.$ The expected return of an individual stock is a negative linear function of the risk$-$free rate.

B$.$ The expected return of an individual stock with a negative beta is a negative linear function of the risk$-$free rate.

C$.$ The expected return of an individual stock is not a linear function of the risk$-$free rate.

D$.$ The expected return of an individual stock with a beta of $0\mathrm{.}5$ is a positive linear function of the risk$-$free rate.

E$.$ The expected return of an individual stock with a beta of $0\mathrm{.}5$ is a quadratic function of the risk$-$free rate.

F$.$ None of the above statements are correct.

Suggested Answer: D$.$ The expected return of an individual stock with a beta of $0\mathrm{.}5$ is a positive linear function of the risk$-$free rate. According to the CAPM, the relationship between expected return and the risk$-$free rate is linear and positive for a positive beta.

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QCM $8$

Question: Assume the conclusions of neoclassical theory are valid. You know the following about the market portfolio and an individual stock i in the market.

Covariance matrix M i

M $6,25\%0,5\%$

i $0,5\%1\%$

The risk$-$free rate of return is $2\%$;

E$($RM$)=24\%$

Stock i has an alpha coefficient of $1\%.$

What can you conclude?

A$.$ The observed market return of stock i is undervalued.

B$.$ The observed market price of stock i is overvalued.

C$.$ Stock i is not included in the market portfolio.

D$.$ The market is in equilibrium.

E$.$ The specific risk portion of i$\text{'}$s total risk is $40\%.$

F$.$ The observed market return of stock i is $4\mathrm{.}76\%.$

Suggested Answer: F

$.$ alpha$\_$i $=1\%($Alpha coefficient of stock i$)$

$$ E$($RM$)=24\%($Expected market return$)$

$$ rf $=2\%($Risk$-$free rate$)$

$$ Cov$($M$,$i$)=0\mathrm{.}5\%($Covariance between the market and stock i$)$

$$ Var$($M$)=6\mathrm{.}25\%($Variance of the market M$)$

Calculation of beta for stock i:

$\backslash$beta i$=$Cov$($M$,$i$)$Var$($M$)=0\mathrm{.}5\%6\mathrm{.}25\%=0\mathrm{.}08$

Calculation of the expected return for stock i using the CAPM model:

E$($Ri$)=$rf$+\backslash$beta i$\backslash$times $($E$($RM$)$rf$)=2\%+0\mathrm{.}08\backslash$times $(24\%2\%)=2\%+1\mathrm{.}76\%=3\mathrm{.}76$

Observed return with an alpha of $1\%$:

Observed Return$=$E$($Ri$)+$alpha I $=3\mathrm{.}76\%+1\%=4\mathrm{.}76\%$

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QCM $9$

Question: Consider the following function: Y $=-3*$ X$^2+4$ where X $>0.$

Which statement is correct?

A$.$ This function could not represent the utility function of an individual's wealth, regardless of their risk profile.

B$.$ This function could not represent the utility function of a risk$-$averse individual but could represent that of a risk$-$seeking individual.

C$.$ This function could not represent the utility function of a risk$-$averse individual but could represent that of a risk$-$neutral individual.

D$.$ This function could represent the utility function of an individual, regardless of their risk profile.

E$.$ This function could represent the utility function of a risk$-$seeking individual but not a risk$-$averse one.

F$.$ None of the above statements are correct.

Suggested Answer: B$.$ This function could not represent the utility function of a risk$-$averse individual but could represent that of a risk$-$seeking individual, as the function suggests increasing utility with increasing wealth for a risk$-$seeking person.

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QCM $10$

Question: Consider a market where only $2$ risky assets, x and y$,$ are traded. The correlation between the returns of these two assets is perfectly positive. Also, consider that the volatility of asset x is higher than that of asset y$,$ and short selling is prohibited. Which statement is true?

A$.$ The variance of returns of any portfolio formed from these two assets is a linear function of the proportion invested in asset x$.$

B$.$ The diversification effect of any portfolio formed by x and y is maximized for certain proportions of investment in each asset.

C$.$ In the $(\backslash$sigma $($Rp$)$ ; E$($Rp$))$ plane, the efficient frontier portfolios formed from x and y is a positively sloped straight line.

D$.$ In the $(\backslash$sigma $($Rp$)$