Question

You decide to invest your money in a stock portfolio consisting of 60% TATA motors and 40% in Flipkart. Using the data in the following table, you find that TATA has an annual standard

deviation of 0.363 and Flipkart 0.34. The correlation coefficient between the returns of both stocks is 0.34.
a. Calculate the variance and standard deviation of this portfolio.
b. Calculate the relative contribution of each stock to this portfolio’s variance.
c. Calculate the β of each stock relative to this two-stock portfolio. Check your results!
d. Now calculate portfolio risk (standard deviation) and return using some different values for the weights and plot the results in risk-return space. Using the given table.
e. The graph you plotted under (d) gives you a good idea what the minimum variance portfolio looks like, but can you calculate the properties exactly? What weights give the portfolio its minimum variance? What is this portfolio’s standard deviation and return?
f. How would the graph under (d) look if TATA and Flipkart were perfectly positively correlated?

Answer 1

The variance and standard deviation of the portfolio can be calculated by considering the weights, standard deviations, and correlation coefficient of each stock. The relative contribution of each stock to the portfolio's variance can be determined by calculating the squared weight multiplied by the squared standard deviation of each stock. The β of each stock can be calculated by dividing the product of the standard deviation and correlation coefficient by the standard deviation of the portfolio.

Step-by-step explanation:

a. Calculate the variance and standard deviation of this portfolio.

To calculate the variance and standard deviation of the portfolio, we need to consider the weights and standard deviations of each stock, as well as the correlation coefficient:

Variance = (Weight of TATA)2 x (Standard deviation of TATA)2 + (Weight of Flipkart)2 x (Standard deviation of Flipkart)2 + 2 x (Weight of TATA) x (Weight of Flipkart) x (Standard deviation of TATA) x (Standard deviation of Flipkart) x (Correlation coefficient)

Standard deviation = Square root of variance

b. Calculate the relative contribution of each stock to this portfolio’s variance.

TATA's relative contribution to variance = ((Weight of TATA)2 x (Standard deviation of TATA)2) / Variance

Flipkart's relative contribution to variance = ((Weight of Flipkart)2 x (Standard deviation of Flipkart)2) / Variance

c. Calculate the β of each stock relative to this two-stock portfolio.

β of TATA = (Standard deviation of TATA x correlation coefficient) / Standard deviation of portfolio

β of Flipkart = (Standard deviation of Flipkart x correlation coefficient) / Standard deviation of portfolio

d. The portfolio risk (standard deviation) and return depend on the weights assigned to each stock, so different values will produce different results. To plot the results in risk-return space, you need to assign different weight combinations to TATA and Flipkart and calculate the resulting portfolio risk (standard deviation) and return. Enter the values into the appropriate formulas to calculate these results.

e. To calculate the properties of the minimum variance portfolio, you need to find the weights that minimize the portfolio's variance. By solving the optimization problem, you can determine the weights that give the minimum variance. Plug these weights into the appropriate formulas to calculate the portfolio's standard deviation and return.

f. If TATA and Flipkart were perfectly positively correlated, the graph in risk-return space would appear as a diagonal line, indicating that as the risk (standard deviation) increases, the return also increases.