You have a $ 2 million portfolio consisting of $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio's new beta be after these transactions?

1/20= 5%

older stock contribution of risk= 0.9*0.05=0.045
New stock contribution of risk= 1.4*0.05=0.07
Now just simply eliminating the effect of older beta and adding the contribution of new beta
1.1-0.045+0.07=1.125

Suppose you manage a $4 million fund that consists of four stocks with the following

investments:
Stock Investment Beta
A $ 400,000 1.50
B 600,000 0.50
C 1,000,000 1.25
D 2,000,000 0.75
If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the
fund’s required rate of return?

Porfolio beta=weight of stock A* beta of stock A+ weight of stock B*beta of stock B+ weight of stock C*beta of stock C + weight of stock D*beta of stock D

=0.1*1.50+0.15*-0.5+0.25*1.25+0.5*0.75
=0.7625
Fund's required rate of return=Risk free rate+(Market return-Risk free rate)*Beta
=6+(14-6)*0.7625
=12.1%

To find the new beta of the portfolio after these transactions, we need to calculate the weighted average beta using the amounts invested in each stock.

First, let's determine the current beta of the portfolio. Since each stock has an equal investment of $100,000, the current beta is simply the average of the betas of the 20 stocks:

Current Beta = (20 * Beta of each stock) / Number of stocks
Current Beta = (20 * 1.1) / 20
Current Beta = 1.1

Next, let's calculate the impact of the proposed transactions on the portfolio's beta. We are selling $100,000 of a stock with a beta of 0.9 and buying another stock with a beta of 1.4.

The impact of selling the stock with a beta of 0.9 is:
Impact on Beta = - (Amount sold / Total Portfolio) * Beta of the stock
Impact on Beta = - (100,000 / 2,000,000) * 0.9
Impact on Beta = -0.045

The impact of buying the stock with a beta of 1.4 is:
Impact on Beta = (Amount bought / Total Portfolio) * Beta of the stock
Impact on Beta = (100,000 / 2,000,000) * 1.4
Impact on Beta = 0.07

Finally, we can find the new beta of the portfolio by adding the impact of the transactions to the current beta:
New Beta = Current Beta + Impact on Beta
New Beta = 1.1 + (-0.045) + 0.07
New Beta = 1.125

Therefore, the portfolio's new beta after these transactions would be approximately 1.125.