Assume that you manage a risky portfolio with an expected return of $15\%$ and a standard deviation of $25\%.$ The T$-$bill rate is $4\%.$ You estimate that a passive portfolio invested to mimic the S $8$ P $500$ stock index provides an expected rate of retum of $12\%$ with a standard deviation of $21\%$

Calculate the Sharpe ratio for the passive portfolio and risky portfolio.

$\backslash$table$[[,$Passive Portfolio,Risky Portfolio$],[$Sharpe Ratio,,$]]$

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FIN $311$: Investments $|$ Summer $2024$

$7.$ Assuming the management and transaction costs are the same, which portfolio from question $4$ provides the best risk adjusted return? Explain your answer.

$8.$ Consider the following two portfolios covariance and correlation. Explain which one presents higher risk. Refer to the specific variables in your explanations.

$\backslash$table$[[,$Portfolio $1,$Portfolio $2],[$Covariance$,-74\mathrm{.}8,30\mathrm{.}08],[$Correlation coefficient,$-0\mathrm{.}49,0\mathrm{.}20]]$