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Single versus Multi-Period Returns

By Mary A. Lauritano; CFA, MBA

The total return on a financial asset over a single time period is broken down into the income return (dividend or interest) plus the capital change or the change in the market price of the asset (negative or positive). This rate of return is called the holding period return.

Holding period return = Change in asset price (+ or –) plus cash received / Beginning value            

Example:

An investment was purchased by a physician at the beginning of the time period for $150,000. The investor received $20,000 of income from the investment during the period, and the investment was worth $175,000 at the end of the period. The holding period return was:

Holding period return = ($175,000 – $150,000) + $20,000 / $150,000 = 30%                        

Measuring one-period rates of return becomes more difficult when investments are considered over a period of time.

The average return can be computed over a multi-period time span using three methods: dollar-weighted (internal) rate of return, time-weighted (geometric) rate of return, and time-weighted (average method) rate of return.

Each method has its particular use and interpretation.

Dollar-weighted rate of return

The dollar-weighted rate of return measures the performance of the manager and the timing of the external cash flows initiated by the client.

From the physician investor’s viewpoint, this is the best measure of the overall performance of the portfolio because it includes the timing of when funds were added or subtracted. The primary drawback of this measure is that it mixes the timing of the client’s cash flow with the portfolio manager’s performance.

Time-weighted rates of return

Geometric mean vs. arithmetic mean

Put simply, the geometric mean is the compound rate of return and the arithmetic mean is the average rate of return. Geometric returns never exceed arithmetic returns. Geometric return measures past performance; it is the constant rate of return needed in each year to match actual performance over a time period.

Arithmetic return is an unbiased estimate of expected return, assuming the past is equal to the future. Therefore, arithmetic return is a better indicator of future performance.

When it is necessary to measure only that portion of performance due to the investor/manager, the time-weighted (geometric), or annual compound, rate of return is the best measure of the actual historical performance of the manager, because it indicates the annual average return for each dollar given to the account manager.

Assessment

The performance standards of the Association for Investment Management and Research (AIMR), now CMA Institute, require managers to use this geometric method when they report performance.

The time-weighted (arithmetic method) rate of return is the return that occurred in a “typical year” for the account manager. It is the simple arithmetic average of the period-to-period returns produced by the manager, excluding the effects of external cash flows.

The geometric mean return indicates the rate at which wealth grows; the arithmetic mean return indicates the annual average return from investing. The geometric mean is preferred to the arithmetic mean because investors want to know the rate at which wealth grows over time.

Conclusion

What are your thoughts on the above, and how do you determine asset return? Please comment.

Related Information Sources:

Practice Management: http://www.springerpub.com/prod.aspx?prod_id=23759

Financial Planning: http://www.jbpub.com/catalog/0763745790

Risk Management: http://www.jbpub.com/catalog/9780763733421

Healthcare Organizations: www.HealthcareFinancials.com

Administrative Terms: www.HealthDictionarySeries.com

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Filed under: Portfolio Management |