Stock X has an expected return of 8% and Stock Z has an expected return of 12%.
ID: 2650100 • Letter: S
Question
Stock X has an expected return of 8% and Stock Z has an expected return of 12%. The standard deviation of the expected return is 10% for both stocks. Assume that these are the only two stocks available in a hypothetical world.
A) If the correlation between the returns of the two stocks is +1:
-What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?
-Does this portfolio offer any benefits of diversification (if the correlation is +1)? How do you know?
-Will any investor include Stock X in his or her portfolio? Explain why or why not.
B) If the correlation between the returns of the two stocks is +0.3:
-What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?
-Does this portfolio offer any benefits of diversification (if the correlation is +0.3)? How do you know?
-Will any investor include Stock X in his or her portfolio (if the correlation is +0.3)? Explain why or why not.
C) Can diversification offer benefits to investors if the correlation between stocks is positive?
Explanation / Answer
Working formula
1. Portfolio return = Weightage of Stock X * Return of Stock X + Weightage of Stock Z * Return of Stock Z
2. Portfolion standard deviation = sqrt[(Weightage of Stock X)2 * (Standard deviation of Stock X)2 + (Weightage of Stock Z)2 * (Standard deviation of Stock Z)2 + 2 * CovarianceXZ * (Weightage of Stock X) * (Standard deviation of Stock X) * (Weightage of Stock Z) * (Standard deviation of Stock Z)
3. CovarianceXZ = CorrelationXZ * Standard deviation of Stock X * Standard deviation of Stock Z
(A) Portfolio return = 0.5 * 8% + 0.5 * 12%
= 10%
CovarianceXZ = 1 * 0.1 * 0.1
= 0.01
Portfolion standard deviation = sqrt[(0.5)2 * (0.1)2 + (0.5)2 * (0.1)2 + 2 * 0.01 * 0.5 * 0.1 * 0.5 * 0.1]
= 0.0711 or 7.11%
Yes, the portfolio offers diversification as can be seen from the fact that portfolio standard deviation is lower than the individual standard deviation which reflects reduction in volatility of return.
Inclusion of Stock X is based on risk appetite of the investor. An investor with high risk appetite would not include Stock X for higher return for higher volatility. However, a risk averse investor would invest in Stock X as it offers lower volatility and lower return.
(B) Portfolio return = 0.5 * 8% + 0.5 * 12%
= 10%
CovarianceXZ = 0.3 * 0.1 * 0.1
= 0.003
Portfolion standard deviation = sqrt[(0.5)2 * (0.1)2 + (0.5)2 * (0.1)2 + 2 * 0.003 * 0.5 * 0.1 * 0.5 * 0.1]
= 0.0708 or 7.08%
Yes, the portfolio offers diversification as can be seen from the fact that portfolio standard deviation is lower than the individual standard deviation which reflects reduction in volatility of return.
Inclusion of Stock X is based on risk appetite of the investor. An investor with high risk appetite would not include Stock X for higher return for higher volatility. However, a risk averse investor would invest in Stock X as it offers lower volatility and lower return.
(C) Yes as can be seen in the above examples.
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