Portfolio Management

Question 3) Portfolio 3:A 50−50 Portfolio (50% in S&P500 and 50% in S&P500S&P500 Environmental & Socially Responsible Index)

Answer) The performance of portfolio can not only be measured by the returns of the portfolio. It has to incorporate the risk factor also as when investing in a portfolio, an investor takes some risk. The performance here is calculated by Sharpe ratio. For a portfolio, this measure risk adjusted return. The numerator associates with the excess return for investing in a riskier portfolio and the denominator shows the volatility of the portfolio. Therefore, the Sharpe ratio is also called the ”reward-to-variability” ratio. The formula for the Sharpe ratio is given as:

Where rp is the return on portfolio and rf is the risk free rate and σp is the standard deviation on the portfolio.

The standard deviation of the portfolio can be calculated as:

Weights of the components of portfolio are given as Wa and Wb and R(Ka.Kb) denotes the correlation coefficient of the portfolio components.

Since we have to compare the performance of portfolio before Covid 19(before 15 Jan 2020 and after Covid 19(after 15 Jan 2020). So we calculate the average return on portfolio before Covid -19 and after Covid-19 and similarly we calculate the standard deviations and risk free rate of return for the same period. After calculating the market premium for these periods and dividing by standard deviations of the same period, we get the Sharpe ratios. It is observed that the value of Sharpe ratio for period before Covid is higher than after pandemic. This means that even the return from the portfolio at both the times were not very different but the optimal portfolio was the one with higher risk adjusted returns which is before Covid 19 in this case.

The calculations are shown in excel file.


Before 15 Jan 2020

After 15 Jan 2020

Risk Premium on portfolio



Standard deviation of portfolio



Sharpe Ratio



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