FIN $420$: Fall $2023$ Problem Set $1$ Name $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Section $1\mathrm{.}1$

$1.$ Classify the following assets as either Real Assets or Financial Assets:

a$.$ Residential House: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

b$.$ Corporate Bond: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

c$.$ Lease Agreement: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

d$.$ Professional Certification: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

e$.$ Trademarks: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

f$.$ $$20$ Gold Coin: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($Real$/$Financial$)$

$2.$ A company aims to allocate its surplus funds for short$-$term needs later in the year. Evaluate the following statements regarding the chosen investment and determine if the statements are True or False.

a$.$ It possesses high liquidity: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ It entails high risk: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$.$ The yield is substantial: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

d$.$ The maturity period is brief: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$3.$ Your company plans to invest $$2\mathrm{.}5$ million in a $6-$month Treasury Bill. The quoted yield is $1\mathrm{.}75\%.$

a$.$ Calculate the amount to be paid per Treasury Bill:

$4.$ Identify the appropriate term for the following scenarios:

a$.$ A deposit in a Canadian bank denominated in US Dollars: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ A Euro$-$denominated bond issued by a Japanese bank: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$.$ A Brazilian Real$-$denominated bond issued by a Spanish bank: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

d$.$ A Swiss Franc$-$denominated certificate of deposit in a French bank: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$5.$ You are considering an investment in either a Corporate Bond or a Municipal Bond. The Corporate Bond offers a yield of $4\mathrm{.}8\%,$ while the Municipal Bond offers a yield of $3\mathrm{.}2\%.$ Your marginal tax rate is $28\%.$

a$.$ Which bond is the more favorable option?

b$.$ What marginal tax rate would make you indifferent between the two bonds?

$6.$ You invest $$25,000$ in Stock B at a price of $$50$ per share, contributing $$15,000$ and borrowing $$10,000$ through a broker's call loan. If the price of Stock B drops to $$40$ per share, and the maintenance margin is $45\%$:

a$.$ Calculate your initial margin:

b$.$ Determine your new margin:

c$.$ How much must you deposit to restore your initial margin?

Section $1\mathrm{.}2$

$1.$ You purchase a stock for $$60.4$ years later, you sell it for $$78.$ What is the:

a$.$ HPR

b$.$ EAR

$2.$ A stock has a Beta of $0\mathrm{.}85$ and a standard deviation of $19\%.$ The risk$-$free rate is $3\mathrm{.}8\%,$ the expected return on the market is $9\mathrm{.}6\%.$ What is the:

a$.$ Expected return of the stock?

b$.$ Sharpe ratio of the stock?

$3.$ You examine the following metrics on a collection of stocks

A B C D

E$[$ret$]6\%7\%9\%5\%$

stdev $28\%23\%32\%27\%$

skew $0\mathrm{.}2-0\mathrm{.}1-0\mathrm{.}30\mathrm{.}0$

kurt $5\mathrm{.}27\mathrm{.}88\mathrm{.}54\mathrm{.}6$

a$.$ If you$$re a mean$-$variance optimizer, which stock is the best$/$worst stock to own if the risk$-$free rate is $2\mathrm{.}8\%?$ Justify with one measure.

b$.$ If you$$re concerned about large negative down$-$moves, which stock is the safest$/$riskiest stock to own? Justify with $2$ measures.

c$.$ Assume Stock$$s C and D have a correlation of $0\mathrm{.}30.$ If you invest $30\%$ in C and $70\%$ in D$,$ what is the standard deviation of the two$-$stock portfolio?

$4.$ You invest $$250,000$ in Stock A$.$ Looking at its historical returns, you observe the mean monthly return is $1\mathrm{.}8\%$ and the monthly standard deviation is $12\mathrm{.}7\%$

a$.$ What is the Value at Risk $($at $5$th percentile$)$ of your investment in Stock A$?($Answer in investment dollars$)$

Section $1\mathrm{.}3$

$1.$ You invest $77\%$ of your fund in a risky portfolio and $23\%$ in a risk$-$free asset. The risky portfolio has an expected return of $13\%$ and a standard deviation of $28\%.$ The risk$-$free rate is $3\%.$

a$.$ Calculate the E$[$ret$]$ of the complete portfolio

b$.$ Calculate the standard deviation of the complete portfolio

c$.$ Calculate the Sharpe ratio of the complete portfolio

$2.$ From the question above, you measure your risk aversion metric $($A$)$ as equal to the market average of $1\mathrm{.}9.$

a$.$ Calculate the optimal weight of your allocation to the risky portfolio

b$.$ Calculate the E$[$ret$]$ of the complete portfolio with the optimal weight

c$.$ Calculate the E$[$SD$]$ of the complete portfolio with the optimal weight

d$.$ Calculate the Sharpe ratio of the complete portfolio with the optimal weight

$3.$ If you expect volatility on the risky portfolio from above to increase from a standard deviation of $28\%$ to a standard deviation of $36\%,$ how will this affect the weight you hold on your risky portfolio?

$4.$ A client comes in holding $80\%$ on the risky portfolio. The expected return on the market is $16\%,$ the risk$-$free rate is $2\%,$ and the standard deviation on the risky portfolio is $28\%.$ What is the clients risk$-$aversion measure?

Section $1\mathrm{.}4$

$1.$ Stock X has a Beta of $0\mathrm{.}88.$ The risk$-$free rate is $4\mathrm{.}8\%$ and the expected return of the market is $9\mathrm{.}1\%.$

a$.$ What is the E$[$ret$]$ of Stock X from the CAPM model?

$2.$ Stock A has a market beta of $1\mathrm{.}4,$ a size beta of