$4.$ The following data has been provided in respect of asset A$,$ B$,$ C and market. The average return on long term government securities has been estimated at $8\%.$

Return Distribution $(\%$

$)$

State of Nature $($ Si$)$ Probability $($ Pi$)$ Return on NSE index A B C

$10\mathrm{.}25101265$

$20\mathrm{.}1510666$

$30\mathrm{.}3126126$

$40\mathrm{.}11241212$

$50\mathrm{.}2821412$

Required

Based on the data provided;

$($i$)$ Estimate the beta for asset A$,$ B and C

$($ii$)$ Estimate the required rate of return for each asset using CAPM assuming that the average return on government securities $($ Risk free rate of return$)$ is $8\%$