Question

Question 1u The last A-year returns of the stocok of a given company have been the following of a given com pany have been the following Year Return -4 10% 16,40% 33, 10% 19,90% Estimate the standard deviation of a portfolio that allocates 30% of the wealth to b invested to this stock and the rest to the risk free asset. (Round your answer to two decim al digits).

hi guys how do i solve this

Answer 1

Standard deviation is a measure of risk. Higher the standard deviation- higher the risk and vice versa. It measure the deviation of return with mean return or expected return.

In order to calculate standard deviation of a portfolio we must have following information -

• Standard deviation of individual Assets
• Weights of Assets
• correlation coefficient between assets

Thus, Firstly we calculate the standard deviation of stock. please refer below spreadsheet for calculation.

Standard deviation of a Risk free assets is always zero as it has fixed income and doesn't fluctuate.

Correlation between Risky assets and Risk free assets is always zero.

Standard deviation of a Portfolio having two assets can be calculated with following formula -

$\sigma _{p} = \sqrt{W_{1}^{2}*\sigma _{1}^{2}+W_{2}^{2}*\sigma _{2}^{2}+2*W_{1}*W_{2}*\sigma _{1}*\sigma _{2}*\rho _{12}}$

Where,

W = weights

$\sigma$ = standard deviation

$\rho$ = correlation coefficient.

Standard deviation of a portfolio having a risk and a risk-free assets can be calculated as below -

$\sigma _{p} = \sqrt{W_{1}^{2}*\sigma _{1}^{2}$

This because - standard deviation of risk free assets is zero and correlation with risk assets also zero.

Formula reference -

Thus, Portfolio standard deviation is 3.55%