The marginal expected shortfall (MES) is a measure of the expected loss that would result from adding a particular investment to a portfolio. It is calculated as the expected loss of the portfolio if the investment is included, minus the expected loss of the portfolio if the investment is not included.
To calculate the MES, you will need the following information:
- The expected return and standard deviation of the portfolio without the investment.
- The expected return and standard deviation of the portfolio with the investment.
- The expected return of the investment.
Once you have this information, you can use the following formula to calculate the MES:
MES = (E[Rp] – E[Rp+i]) – (StDev[Rp] – StDev[Rp+i])
Where:
- E[Rp] is the expected return of the portfolio without the investment.
- E[Rp+i] is the expected return of the portfolio with the investment.
- StDev[Rp] is the standard deviation of the portfolio without the investment.
- StDev[Rp+i] is the standard deviation of the portfolio with the investment.
It is important to note that the MES is a statistical measure and may not accurately predict the actual performance of an investment. It is also important to consider other factors, such as the risks and potential rewards of the investment, before making any investment decisions.