Portfolio Risk and Return Calculation Methods: Finance Assignment

This assignment provides solutions to calculate portfolio risk and return, covering scenarios with both risky and risk-free assets. The first solution explains the calculation of expected return and risk for a portfolio containing multiple stocks, detailing the use of weighted averages, standard deviation, and variance, including the role of the correlation coefficient. The second solution addresses the inclusion of a risk-free asset in the portfolio, highlighting that the expected return calculation remains consistent, but the risk calculation simplifies due to the zero-risk nature of the risk-free asset. The assignment uses formulas to illustrate the calculations, referencing key financial concepts and providing a practical guide for understanding portfolio management and investment analysis. References to relevant finance textbooks are also included.

Solution 1: If an investor decides to buy more than one stock than there is need to maintain the
portfolio and in portfolio there is different method to calculate the risk and return. Portfolio
refers to the group of two or more stock having different risk and returns. When the investor
buys more than one share than while calculating the combined risk and return of both the stocks
in the portfolio there is need to consider the return and risk poses by both stocks. In order to
calculate the expected return (Return) of portfolio there is need to add the weighted average of
each of the investor’s securities (Stocks) returns (Palepu, K. 2007). So to calculate the expected
return of the portfolio following mathematical equation is needed to solve:
Expected Return of the portfolio: (Percentage of weight of stock 1)*(Return of the Stock 1) +
(Percentage of weight of stock 2)*(Return of the Stock 2)
Above equation calculates expected return of portfolio for two stocks, in case of expected return
of n number of stocks than above equation be defined in similar manner as below:
Expected Return of the portfolio: (Percentage of weight of stock 1)*(Return of the Stock 1) +
(Percentage of weight of stock 2)*(Return of the Stock 2) +………..+ (Percentage of weight of
stock n)*(Return of the Stock n)
Risk of the portfolio is determined through establishing the relation between the stocks in the
portfolio and having calculation for weighted average risks of all the stocks in the portfolio. Risk
of the portfolio is calculated as the standard deviation of combined stocks in portfolio. Standard
deviation is the square root of the variance of the portfolio. Variance of the portfolio is the
weighted average of the individual stock in portfolio. As variance is dispersion of returns of each
stock from their average returns of that stock. So while determining the variance of portfolio
there is needed to establish the relation between the stocks and this relationship is referred to as
correlation coefficient. Following equation will provide the variance of the portfolio:
Portfolio Variance = “w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cov(RA, RB)”
Where: wA and wB are portfolio weights,
σ2 (RA) and σ2 (RB) are variances and
Cov (RA, RB) is the covariance also know as correlation coefficient
Standard deviation (Risk) of portfolio is calculated by making the square root of above equation
(Stickney, 2009).
Solution 2: The return of the risk free stock is calculated as the way it is calculated for the risky
stocks. In case of portfolio that contains one or more risky stocks and one risk free asset than in
that case expected return of that portfolio is calculated in the similar way as it calculated in
above question. So, it can be said that there is no difference in calculating the expected return
whether stock is risky or not.

The risk of any risk free stock is zero due non presence of any risk in such stocks so it
can be said that there is need to frame the equation of risk calculation in case of portfolio which
contain the risk free stock. So the standard deviation (risk) of the portfolio that contains one risk
free asset and other is risky asset is given as: (Percentage of weight of stock 1)*(Return of the
Stock 1). Stock 1 refers to risky asset and there is no need to make any calculation for risk free
asset as risk is zero (Stickney, 2009). The given equation will be formulated as given below to
calculate the risk of the portfolio containing one risky stock and other one risk free stock:
= w2A*σ2A
Where A is the stock that is risky in nature

References
Palepu, K. et al. 2007. Business Analysis and Valuation: Text and Cases. Cengage Learning
EMEA.
Stickney, C.P. et al. 2009. Financial Accounting: An Introduction to Concepts, Methods and
Uses. Cengage Learning.