Question $3$

Is the portfolio of risky assets currently chosen by the college$$s fund manager an efficient portfolio? If not, please explain and calculate the investment proportions $($in the five risky assets selected by the fund$)$ required to construct an efficient risky portfolio, which would deliver the same expected return as the current choice of the risky portfolio $($for this part, assume the fund undertakes no risk$-$free investment$).$

From the graph below, we can see the grey spot $($representing the current portfolio$)$ is located on the right side of the efficient frontier. It means that we can earn the same return while lowering the SD of the portfolio, i$.$e$.$ moving the grey spot to the left side. By using solver, we find out the efficient portfolio with same return. Please refer to the portfolio with $8\mathrm{.}94\%$ of return

Question $4$

For the rest of the project, you can invest in the risk$-$free asset. Assume that the risk$-$free rate going forward equals the average T$-$bills rate in the sample. What is the level of this risk$-$free rate?

The level of this risk$-$free rate is $1\mathrm{.}22\%.$

More detailed calculations and performance statistics can be found in Figure $3.$

Question $5$

Calculate the investment proportions required to achieve the optimal $($tangency$)$ risky portfolio, given the possibility of investing in risk$-$free T$-$bills $($use Excel$$s solver module$).$ What is the expected return and standard deviation of the tangency portfolio?

The investment proportions required to achieve the optimal $($tangency$)$ risky portfolio:

SMLSTK

MEDSTK

LRGSTK

VBMFX

REITs

Weights

$-12\mathrm{.}99\%$

$24\mathrm{.}75\%$

$8\mathrm{.}92\%$

$87\mathrm{.}41\%$

$-8\mathrm{.}10\%$

The expected return and standard deviation of the tangency portfolio:

Portfolio return

$5\mathrm{.}45\%$

Portfolio standard deviation

$3\mathrm{.}43\%$

More detailed calculations and performance statistics can be found in Figure $4.$

Question $6$

Continue to assume that you can invest in the risk$-$free asset. Calculate the investment proportions required to construct an efficient portfolio with an expected return equal to the existing portfolio$$s expected return $($note: this portfolio should include the risk$-$free asset$).$ Also, calculate the expected standard deviation of returns on this portfolio.

According to Figure $5,$ the investment proportions required to construct an efficient

portfolio with an expected return equal to the existing portfolio$$s expected return

$(8\mathrm{.}94\%)$ should be:

SMLSTK

MEDSTK

LRGSTK

VBMFX

REITs

TBILL

Weights

$34\mathrm{.}98\%$

$-47\mathrm{.}74\%$

$39\mathrm{.}89\%$

$70\mathrm{.}61\%$

$37\mathrm{.}96\%$

$-35\mathrm{.}70\%$

The inclusion of T$-$bills targeting at the same return led to a higher expected

standard deviation of $12\mathrm{.}35\%$ compared with the previous portfolio.

Question $7$

Continue to assume that you can invest in the risk$-$free asset. Suggest an efficient portfolio allocation to achieve the college's objective of a 'floor' expected rate of return of $0\mathrm{.}8\%$ per month. What is the standard deviation of the portfolio?