Portfolio Performance Measurement

To calculate the performance of a fund manager, first step is to calculate the portfolio return. There are various methods which can be used by the fund managers, two main methods are:-  

• Money Weighted Return – This is also known as internal rate of return. This is the return which will make the net present value of the investment as zero. An assumption is made that the portfolio will generate the same return over the period. Since there are many cash inflow and outflow in a portfolio this method is calculation intensive and various numerical methods are used to calculate the return. This method is preferred when the portfolio manager has the control over the portfolio cash inflow and outflow as it considers the amount of money invested. 
• Time Weighted Return – In this method, the holding period of an investment is divided whenever there is a significant cash inflow or outflow in portfolio. Then geometric mean return of all the periods is calculated, this return is the time weighted return of the portfolio. This is the preferred method when the portfolio manager does not control the portfolio cash inflow and outflow. The best approach for calculation is to calculation the daily holding period return.
  

There are modified approaches to both of the above methods. These are listed below:-

• Simple Dietz method – This method is the first order approximation of the internal rate of return. Here an assumption is made that the cash inflow in the portfolio is done at the middle of the period in consideration
  
• Modified Dietz method – A modification of the simple Dietz method where daily weighting is considered
  
• Linked Modified Dietz – This is a hybrid of money weighted and time weighted return. The return is calculated for a sliced time period using IRR and then the geometric mean return of each periodic return is calculated
  

The next step after the performance measurement is to compare the portfolio or composite return to the benchmark return. There are various measures to find out if the portfolio manager has created value or not, the basis of comparison is the level of risk taken in the portfolio compared to the benchmark. These are also known as risk adjusted performance measures, following are the main measures:-

• Sharpe Ratio: This measure was   developed by Prof. William Sharpe. This is the ratio of portfolio’s excess return with respect to risk free rate to the standard deviation of the portfolio. Here the assumption is that the portfolio returns are normally distributed. The higher the Sharpe ratio, the better is the portfolio performance.
  
• Modified Sharpe Ratio: When the portfolio is composed of assets whose returns are non-normal, Sharpe ratio does not yield good result, to incorporate the skenewss of such cases modified Sharpe ratio is employed. Modified Sharpe ratio is the ratio of excess portfolio return to the modified VaR of the portfolio.
  
• Treynor Ratio:  This ratio measures the excess portfolio return over risk free rate to that of the portfolio Beta. Essentially this ratio is finding the excess return per unit of market risk taken by the portfolio manager. The higher the ratio, the better is the performance.
  
• Sortino Ratio: If a portfolio return is more than the expected return, it is not seen as risk, but when the return is less than the required return we are exposed to the risk. So, the risk can be viewed as one sided risk, or the downside risk. Sortino ratio, measure portfolio performance on this basis, this ratio is the ratio of excess return over the minimum acceptable return to the downside risk of the portfolio. Downside risk is calculated from the semi variance of the returns which are below the minimum acceptable return. Like Sharpe and Treynor ratio, the higher the Sortino ratio, the better it is.
  
• Information Ratio: Information ratio is the ratio of active return (excess portfolio return over the benchmark) to the tracking error (standard deviation of the active return). This ratio helps in identifying how much extra return the portfolio manager has generated in comparison to the relevant benchmark.

Apart from these there are other measures which will be discussed in the next article.