Question

You have gathered information about the expected returns and standard deviations of two stocks, which is given in the table below:

	Expected return	Standard deviation
Bull Inc	10.0%	30.0%
Bear Inc	6.0%	20.0%

a. Discuss which stock is more attractive and why? (hint: think about the assumptions first)

You are going to form a portfolio, which includes these two stocks. The value of your total portfolio is 800 000 and investment into stock B is 60% of the total portfolio.

b. It is estimated that the correlation between the stock returns is -0.50. Explain, what does this result mean?

c. Calculate the portfolio risk and expected return, and explain the benefits of diversification.

(Show your work, you may upload the solution file

Answer 1

a) RISK REWARD

	EXPECTED RETURN	STANDARD DEVIATION	RISK REWARD
BULL INC	10	30	10/30 = 0.33
BEAR INC	6	20	6/20 = 0.3

BULL INC IS MORE ATTRACTIVE SINCE IT GIVES MORE RISK TO REWARD

b)

they form a negative correlation of -0.5 which means if bull inc makes a profit of 1% then bear inc will have a loss of 0.5% and vice versa . such things helps in portfolio diversification

c)

EXPECTED RETURN = R1 x W1 + R2 x W2

R1 = 10

W1 = 40%

R2 = 6

W2 = 60%

EXPECTED RETURN = 10 x 0.4 + 6 x 0.6

= 4 + 3.6

= 7.6%
on a portfolio of 800,000 = 800,000 x 7.6% =60,800 return is expected

PORTFOLIO RISK = (W1² x STD DEV1² + W2² x STD DEV2² + 2 x W1 x W2 x STD DEV1 x STD DEV2 x CORRELATION BETWEEN THEM)^1/2

W1 = 0.4

W2 =0.6

STD DEV1 = 30%

STD DEV2 = 20%

CORELATION = -0.5

PORTFOLIO RISK = (0.4² x 30² + 0.6² x 20² + 2 x 0.4 x 0.6 x 30 x 20 x (-0.5))^1/2

  = (144+ 144 - 144 )^1/2

  = (144)^1/2

  = 12%

Three key advantages of diversification include:

1. Minimising risk of loss – if one investment performs poorly over a certain period, other investments may perform better over that same period, reducing the potential losses of your investment portfolio from concentrating all your capital under one type of investment.

2. Preserving capital – not all investors are in the accumulation phase of life; some who are close to retirement have goals oriented towards preservation of capital, and diversification can help protect your savings.

3. Generating returns – sometimes investments don’t always perform as expected, by diversifying you’re not merely relying upon one source for income.