Malik is a portfolio manager of a unit trust fund and expects an excess fund of RM$5$ million for the upcoming investment period. He forecasts a $70\%$ probability that the upcoming period will be an expansion phase and reserves a $30\%$ probability for a recession due to geopolitical tension. Malik is considering investing the excess funds into two companies, namely Maju Bhd and Hebat Bhd$.$ The following information is available:

Economic conditions

Maju Bhd$$s Return

Hebat Bhd$$s Return

Expansion

$25\%$

$8\%$

Recession

$5\%$

$10\%$

Additional information:

Beta for Maju Bhd and Hebat Bhd are $1\mathrm{.}5$ and $1\mathrm{.}2$ respectively.

The government T$-$Bill rate is $5$ percent.

The expected market return is $13$ percent.

Required:

a$.$

Calculate the following for Maju Bhd and Hebat Bhd shares:

i$.$

Expected return

ii$.$

Standard deviation

iii.

Covariance

iv$.$

Correlation

b$.$

If Malik intends to hold a portfolio consisting of $40\%$ shares in Maju Bhd and $60\%$ shares in Hebat Bhd$,$ calculate the expected return and the standard deviation of the portfolio.

c$.$

Assume Capital Asset Pricing Model $($CAPM$)$ holds, advise whether Malik should invest in the portfolio.

d$.$

Assuming that the portfolio is not the best investment opportunity, recommend other alternatives for Malik$$s investment $($either invest solely in Maju Bhd only or Hebat Bhd$).$

e$.$

Calculate the following if Malik plan to change the portfolio's composition by investing in an equally weighted in Maju Bhd and Hebat Bhd$.$

i$.$

Beta of the portfolio

ii$.$

Required return of the portfolio