A fund manager $($FM$)$ is constructing a portfolio of two asset classes, a stock and a

corporate bond. The return on the stock is $12\%,$ and its standard deviation of return

is $17\%,$ while for the bond is $5\%$ and its standard deviation is $12\%.$ The correlation

between their returns is $0\mathrm{.}2.$

$1\mathrm{.}1$ If the FM requires a portfolio return of $9\mathrm{.}2\%,$ what should the proportions of each

asset class be$?($present your calculations$)$

$(5$ marks$)$

$1\mathrm{.}2$ What is the standard deviation of return of the above portfolio? $($present your

calculations$)$

$(5$ marks$)$

$1\mathrm{.}3$ Interpret the standard deviation of return of the portfolio in relation to the

weighted average of the risk of those two assets $($present your calculations$).$

$(5$ marks$)$

$1\mathrm{.}4$ Present, on a graph, the relationship between risk and return of the portfolio in

$1\mathrm{.}1.$ Identify the point $($P$)$ which would represent the portfolio.

$(5$ marks$)$

$1\mathrm{.}5$ Discuss the diversification benefits from the combination of those two assets.

Relate to your graph.

$(5$ marks$)$

$1\mathrm{.}6$ What is the utility of an investor at point P $($the portfolio in $1\mathrm{.}1)$ with a risk

aversion coefficient of $3?$

$(5$ marks$)$

$1\mathrm{.}7$ Gold is owned by many rational investors as part of an extended portfolio. Why?

$(5$ marks$)$

Q$1$ Total: $35$ marks

Question $2$: Leveraged Portfolios

$2\mathrm{.}1$ Anna Smith creates her first portfolio and invests in two assets, T$-$bills and an

index fund that closely tracks the FTSE$100$ index. The return on the T$-$bills is

$4\%.$ The expected return on the index fund is $18\%$ and the standard deviation is

$20\%.$

$($a$)$ Draw the Capital Market Line $($CML$)$ and mark the point where the

investment in the index fund is $65\%.$

$(3$ marks$)$

$($b$)$ Determine the risk and return at that point $(65\%).$

$(6$ marks$)$

$2\mathrm{.}2$ Anna, after having a successful year of managing her investment, decides to

create a leveraged portfolio. She accepts the higher risk of such portfolio

because she believes that the market will generate attractive returns in the next

few years. Anna approaches her broker to borrow money against securities she

holds in her portfolio. The brokers rate for lending to clients is $6$ percent. The

risk$-$ free $($T$-$bill$)$ rate is $4\%.$ Assuming that she can achieve the same return of

$18\%$ on the index fund with a standard deviation of $20\%,$ she borrows $25\%$ of

her initial investment and invests all in the index fund.

$($a$)$ Plot the new leverage $($borrowing$)$ portfolio on a graph.

$(3$ marks$)$

$($b$)$ Calculate the expected risk and return on Annas new investment.

$(6$ marks$)$

$2\mathrm{.}3$

$($a$)$ Compare, and briefly, discuss the risk and return for the two portfolios in $2\mathrm{.}1$

and $2\mathrm{.}2.$

$(3$ marks$)$

$($b$)$ What is the slope $($on the graph$)$ of the $1$st unleveraged portfolio and the slope

$($on the graph$)$ of the $2$nd leveraged portfolio? Discuss your results.

$(6$ marks$)$