##### Posted by Jason M. Kueser | January 14, 2016

### When is “Rate of Return” not the “Real” Rate of Return?

Investors need to be careful when they review and rely on performance reports provided by their stockbroker or financial advisor. I recently reviewed a performance report that was provided to an investor by a major warehouse brokerage firm. This report actually showed that the investor had lost money, but showed a positive cumulative rate of return!

How could this be? The method used to calculate the rate of return on the performance report was Time Weighted.

There are a variety of ways to calculate return on investments – or on a portfolio of investments.

Many investors rely on their broker/financial advisor to provide them with information related to the performance of their investments. Rather than calculate their rate of return on their own, investors often look at performance reports they receive from their broker/financial advisor. Without knowing which methodology is used to calculate the rate of return shown on the performance report, the investor is really in the dark as to the actual performance of their investments.

Ultimately, when investors are looking at rate of return, they are generally looking for information about how much they have earned on their investments. This includes income received from the security, as well as any capital gains. For most investors, they are looking for a percentage that reflects the profit (income and gains) on an investment over a period of time. For most investments, greater return is calculated on annualized basis, which reflects the average rate of return on the investment (or portfolio of investments) each year the investment(s) was/were owned.

A simple way of calculating rate of return is, as follows: If you invest $100,000 in a portfolio of investments and that portfolio grows to $110,000 after one year, you have a return of 10%. That would also be the annualized rate of return because the period one year. When you calculate annualized rates of return for periods that are longer than one year, it can get a bit complicated, but there are calculators (or an Excel spreadsheet) that you can use that will provide annualized rate of return calculations for multi-year periods.

The method described above is a simple – and accurate – way to calculate rate of return on an investment or portfolio of investments. To be honest, most, if not all, of the individual investors I have had talked to about rates of return are looking for this information.

However, there are other methods of calculating rate of return that are used by investment “professionals,” including Dollar Weighted Rate of Return, and Time Weighted Rate of Return.

An accepted definition of Dollar Weighted Rate of Return (also known as internal rate of return or Money Weighted Rate of Return) is

“the discount rate on which the NPV = 0 or the present value of inflows = present value of outflows.” (*See* Investopedia.com). An accepted definition of Time Weighted Rate of Return is “the compounded growth rate of one dollar over the period being measured.” (*See* Investopedia.com).

It should be understood that both of these methods for calculating rate of return are generally used by money managers (i.e., mutual fund managers, private equity managers, etc.). Time Weighted Rate of Return is generally considered a “better” measure of the performance of an investment manager who does not have control over the timing of cash flows (such as a mutual fund manager). In fact, money management firms must use time weighted returns to meet Global Investment Performance Standards, which are set by the CFA Institute (the CFA Institute is an organization that offers credentials to individuals in the investment management industry). On the other hand, Dollar Weighted Rate of Return is generally considered a “better” measure of the performance of an investment manager who has control over the timing of cash flows (such as a private equity fund manager). As you can see, these methods are more appropriate for measuring the performance of an investment manager that manages a portfolio for multiple clients, with different and varying cash flow needs.

Unfortunately, the securities industry has taken something that is appropriate in one situation and tried to apply it in a different situation.

As noted above, I was recently reviewing a performance report provided to an individual client by a large, wirehouse firm. The report provided annual cash flow and account balance information and then provided, on a separate page, an analysis of Time Weighted Rate of Return.

The dangers of providing performance information to individual clients using Time Weighted Rate of Return stuck out significantly. This performance report showed that, over the period from 2010 through 2015, the investor had made $91,000 of contributions into their account, took no withdrawals from the account, and had and ending balance of approximately $86,000 in their account. Simple math would tell you the investor suffered a loss of approximately $5,000 (or approximately 5.5%) on their investment.* However, * the report actually showed that the investor had a cumulative rate of return of 44.12%. * You are reading this correctly. A major wirehouse represented to a client that had lost $5,000 that they had a positive rate of return of more than 40%!

This appears to be due to the fact that the account was profitable from 2010 through 2014, there was a $60,000 deposit into the account in 2015, and the account suffered a loss of almost $17,000 during 2015. Because the losses in 2015 occurred over a relatively short time period (related to the five-year total period), those losses, while sizable, were not weighted as much as the gains that occurred from 2010 through 2014.

This example shows several things. First, when looking at performance reports, it is important to understand the methodology used to calculate rate of return. Second, investors need to understand how rate of return can be skewed using different methodologies. Third, it is important to use common sense in evaluating the performance of your investments.

*The performance report itself actually showed the investor had depreciation of approximate $12,000, which represented the $5000 loss on the investment, as well as the loss of approximately $7000 of interest and dividends earned in the portfolio during the five-year period.