Measuring Return

Let’s continue our discussion of Modern Portfolio Theory. Last week I suggested that portfolio construction involves carefully selecting securities based on their risk and return characteristics.

I probably should have mentioned that return can be calculated in various ways. The simplest is the mean or average. To calculate this return we simply add up all the returns and divide by the total numbers of return in the data set. If we had annual returns from 2000-2004 of -9.1%, -11.9%, -22.1%, 28.7% and 10.9%, the average return would be -0.70%. This was the actual return of the Standard & Poor’s 500 index.

When evaluating investment advisors, fund managers or portfolio managers, there is a different measure that gives us better insight into performance. Time-weighted return eliminates the distortions caused by the inflows and outflows of money over time. This is also called the geometric mean. It is calculated using holding period returns (HPR) for each investment period (e.g. a year) and linking them together.

The formula for holding period return is (ending value - beginning value + dividends/interest +/- other cash flow) divided by the beginning value.

To calculate time-weighted returns we add 1 to each of these HPRs, multiply these values against each other then subtract 1 from that result.

Here’s the formula

= [(1 + HPR1)*(1 + HPR2)*(1 + HPR3) ... *(1 + HPRN)] - 1.

If the investment period is greater than 1 year, then we need to annualize the return for the HPRs we calculated. The formula for this is (1 + compounded rate)1/Y – 1 where Y is the total time of years.

Yet another way to measure performance is money-weighted return. This involves calculating the internal rate of return. We calculate the return that will cause the inflows and outflows to be equal. For investment outflows include the purchase price, reinvested dividends or interest and contributions. Inflows include the proceeds from the sale of the investment, dividends or interest received and withdrawals. Calculating money-weighted return requires using Microsoft Excel or a financial calculator. We use the money weighted return instead of holding period return for investment periods that are greater than 1 year.

Source for formulas: Investopedia