Question

Corporate Finance

(15 points) Suppose the risk-free rate is 6.3% and the market portfolio has an expected rate of return of 14.8%. The market portfolio has a variance of 0.0121. Portfolio Z has a correlation coefficient with the market of 0.45 and a variance of 0.0169. According to CAPM, what is the expected rate of return on portfolio Z? 4.

Answer 1

For the above question,

• Risk free rate ( r_{​​​​​​ f} ) = 6.3%
• Expected rate of return E(rm) = 14.8%
• Variance ( $\sigma$²_m )= 0.0121
• Portfolio Z correlation coefficient ( $\rho$_z,m)= 0.45
• Portfolio Z variance = 0.0169

We know, $\rho$​​​ _​​​​​​​​_z,m = Cov (Rz, Rm) / (0.02)(0.57)   $\therefore$ Cov (Rz, Rm) = 0.03192

Also, $\beta$_z = Cov (R_{​​​​​​ z ,} R _m ) / $\sigma$²_{m = 0.03192 / 0.0121 (Had Put the value) = 2.6380}

Thus, Expected rate of return on portfolio Z :-

= 6.3% + 2.6380*( 14.8% - 6.3% ) = 2.87%  

[ Note : Expected rate of return = Risk free rate + beta*(market return rate - risk free rate) ]

  

_​​​