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.

Answer 1

1) For finding which stock is more attractive, we'll calculate the Risk-Reward.

RISK REWARD = EXPECTED RETURN / STANDARD DEVIATION

Bull Inc.=  10/30 = 0.33

Bear Inc.= 6/20 = 0.3

Bull Inc. is more attractive since it gives more risk to reward.
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2) The correlation between the stock returns is -0.50 means that stocks are forming negative correlation which means when one stock moves , the other will move in the opposite direction. Negative correlations between two stocks may exist for many reason like opposite sensitivities to changes in interest rates.To protect themselves against volatility for the overall portfolio Investors would include some negatively correlated assets. This means that there is an inverse relationship between two variables when one variable decreases, the other increases. So in this question also, Bull inc and Bear inc is having negative relation .

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3) Weight of Stock B is 60% i.e. 0.6

Total investement= 800000

Stock B= 800000 * 60%
= 480000

Now, weight of stock A is :

Stock A = 800000 - 480000
= 320000

Stock A=( 320000/ 800000 ) * 100
= 40% i.e 0.4

Standard Deviation of A = 30% i.e 0.3
Standard Deviation of B = 20% i.e 0.2
Weight of A 40% i.e 0.4
Weight of B 60% i.e 0.6
Correlation = (-0.50)

by putting above values to the equation we get,

Portfolio Risk=  

=

= 0.12

Return of Stock A is 10% i.e 0.1
Return of Stock B is 6% i.e 0.06
Weight of Stock A is 0.4
Weight of Stock B is 0.6

now, putting above values in the equation we get,

Expected Return =  R_A * W_A +  R_B *  W_B

= 0.1 * 0.4 + 0.06 * 0.6
= 0.04 + 0.036
= 0.076 or 7.6%

Expected Return is 7.6%

The benefits of portfolio diversification are:

1. Minimization the risk of loss – If we diversify int two investments and one investment performs very badly for a specific period, but may be other investement proves fruitful over that same period, thus it will reduce the potential losses of your investment portfolio from concentrating all your money under one type of head.

2. Preservation of Capital – Diversification can help protect your savings by not putting all egss in one basket and putting it in different baskets. It means that investors can save the money if one investment turn out to be loss . So he can take the benefits from the other investment and thus preserve the capital of investors.

3. It generates more return – It can happen sometimes investments don’t always give benefits as expected, but by diversifying the investments you're having the benefits and having returns if other investment doesn't give benefits expected but another one gives significant returns.