Part I

Question $1$: Portfolio of Two Assets

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