. If you have $30,000 invested in each of two stocks and $20,000 invested in each...

. If you have $30,000 invested in each of two stocks and $20,000 invested in each of another three stocks and the betas on the stocks above are 0.8, 1.1, 1.0, 1.2 and 1.4, respectively, what is the beta of your portfolio, and what is the required return on the portfolio if the risk-free rate is 4.6% and the return on the market portfolio is 10.4%? What are the risk premiums for the market and for your portfolio?

Solutions

Expert Solution

Beta of portfolio is weighted average beta of each of the stocks

Stock	Amount invested	Weights of stock		Beta	Weighted average
1	$30,000	25.00%	30000/120000	0.80	0.20
2	$30,000	25.00%	30000/120000	1.10	0.28
3	$20,000	16.67%	20000/120000	1.00	0.17
4	$20,000	16.67%	20000/120000	1.20	0.20
5	$20,000	16.67%	20000/120000	1.40	0.23
	$120,000				1.075

Thus, beta of the portfolio is 1.075

In order to calculate required return on the portfolio the required return for each stock will have to be calculated as required return on portfolio is weighted average stock return.

Formula to calculate required return for each stock using CAPM model
Required return = Risk free rate + Beta*(Market return - Risk free rate)

Calculation of required return for each stock		Required return	Weights of stock	Weighted average
Stock 1	0.046 + (0.80*(0.104-0.046))	9.24%	25.00%	2.31%
Stock 2	0.046 + (1.10*(0.104-0.046))	10.98%	25.00%	2.75%
Stock 3	0.046 + (1*(0.104-0.046))	10.40%	16.67%	1.73%
Stock 4	0.046 + (1.20*(0.104-0.046))	11.56%	16.67%	1.93%
Stock 5	0.046 + (1.40*(0.104-0.046))	12.72%	16.67%	2.12%
				10.84%
Thus, the required return on portfolio is 10.84%

Calculation of risk premium for market and portfolio
Risk premium = Return of portfolio - Return of market
Risk premium	10.84-10.4
Risk premium	0.43%

Thus, risk premium for market and your portfolio is 0.43%.

jeff jeffy answered 7 months ago

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