Measures of Return

Measures of Return

In portfolio management, the measures of return are used to evaluate the performance of an investment portfolio over a specific period. There are various measures of return that portfolio managers use to assess the profitability of the portfolio. The three commonly used measures of return are the total return, the average annual return, and the compound annual growth rate (CAGR).

The total return is the overall gain or loss of the portfolio over a particular period, including any interest or dividends earned during that period. It is expressed as a percentage and is calculated by dividing the final portfolio value by the initial portfolio value and subtracting 1. The total return is a straightforward measure of the portfolio’s performance and considers all sources of return.

The average annual return is the average percentage return earned by the portfolio each year. It is calculated by dividing the total return by the number of years the investment was held. This measure of return is useful in comparing the performance of different investments over the same period, especially when the investments have different holding periods.

The compound annual growth rate (CAGR) is the rate at which an investment has grown annually over a specific period. It takes into account the compounding effect of the investment, which means that returns from previous years are reinvested in the portfolio. The CAGR is a useful measure of return to evaluate long-term investments, such as retirement accounts, and assess the growth of the portfolio over time.

There are three methods that are widely used for calculating the realized rate of return on a portfolio. They are detailed in the flowing section.

Money-Weighted Rate of Return (MWROR)

Money-weighted rate of return (MWR) measures the return of a portfolio in a way that the return is sensitive to changes in the money invested. MWROR measures the return from a client’s perspective where he or she does have control over the (external) cash flows. It does not allow a comparison across peer groups but allows a comparison against a benchmark (adjusted for cash flows). MWROR is best measured by the internal rate of return (IRR).

This method is used when one is trying to measure the performance experienced by an investor. It is a way to measure the return of a portfolio over a specified time period. The return is influenced by the time of decisions to deposit or withdraw funds from the portfolio, as well as the decisions made by the portfolio manager. MWROR takes into consideration not only the amount of the cash flow but also the timing of the cash flow.

Calculation involves the compound growth rate in the value of all funds invested over the evaluation period. It is nothing but the internal rate of return (IRR).

MVt = MVt-1(1+Rt)m + CF1(1+Rt)m-L(1) + … + CFn(1+Rt)m-L(n)

Where:

m = number of time units in the sub-period (e.g., 90 days)

L(i) = number of time units from the beginning of the evaluation period (e.g., a cash flow on the 5th day)

Example:

Year	Market Value	Cash Flow
2009	1000	–
2010	1100	100
2011	1200	150
2012	1300	80
2013	1500	–

Using the above mentioned formula:

1000(1+R) 4 + 100(1+R) 3 + 150(1+R) 2 + 80(1+R) = 1500

Time-Weighted Rate of Return (TWROR)

Time weighted return provides a method to calculate the performance solely attributed to the portfolio manager’s actions. TWROR eliminates the impact of the timing of cash flows and leaves only the effects of the market and the portfolio manager’s actions.

To calculate TWROR, the performance period is broken into sub-periods. The returns of the sub-periods are calculated and then geometrically linked to derive the TWROR for the performance period. Compounding of growth rate over the evaluation period of one invested is done. Interim external cash flows result in sub-periods that begin with each cash flow, and TWROR is linked with the sub-periods together.

rTWR = [(1+rt, 1) × (1+rt, 2) × … × (1+rt, n)] -1

Where, t is the evaluation period, 1…n are the sub-periods.

Example:

During a year there are 3 sub-periods, with returns equal to 1%, 8% and -3%. The time weighted return for the year is.

(1+.01) X (1+.08) X (1-.03) – 1 = 0.058 = 5.8%