practice problem $3$

Asset Return beta St dev

A $0\mathrm{.}1$

B $20\mathrm{.}4$

Market $0\mathrm{.}10\mathrm{.}2$

Risk free $0\mathrm{.}04$

$1)$ Find the beta of A $-->$

$2)$ Find the return of B$-->$

$3)$ Find the beta of market

$4)$ Find the beta of risk free security

$5)$ Find the st dev of risk free security

$6)$ If the correlation between the market and security A is $\mathrm{.}75$ what is the st dev of A

beta $($A$)=\backslash$sigma A$*\backslash$sigma m$*\backslash$rho $($A$,$m$)/\backslash$sigma m$^2$

$7)$ what is the correlation of B and market

beta $($B$)=\backslash$sigma B$*\backslash$sigma m$*\backslash$rho $($B$,$m$)/\backslash$sigma m$^2$

$8)$ if the correlation between A and B is $0\mathrm{.}5$ what is the covariance between A and B

$9)$ what is the st dev of the portfolio with $50\%$ of the money is risk free security and rest in A

what is the return of that portfolio

$10)$ what are the Xa and Xb which will lead to minimum variance portfolio of just A and B ignore earlier correlation number and assume corr$($A$,$ B$)=-1$

minimum variance will be $0$ or y axis

$11)$ you want to make the most efficient portfolio $($ remember the CML capital market line$)$

you want the portfolio return to be $20\%$

you have $100$ dollars $,$ which security you will use and what will be your allocation of money to each security

$2)$ beta $($A$)=\backslash$sigma $($a$,$m$)/\backslash$sigma m$^2$

covariance of return of $($A$,$m$)/$ Variance of m

where a is the security whose equities beta is calculated and m is the market

$3)$ beta $($A$)\backslash$sigma A$*\backslash$if the correlation between A and $B$ is $0\mathrm{.}5$ what is the covariance between A and Bsigma m$*\backslash$rho $($A$,$m$)/\backslash$sigma m$^2$

beta of equity of security A

$4)$ capm formula also known as capital asset pricing model

E$($ra$)=$ rf $+$ betaA$($rm$-$rf$)$