Various Facets of Rates of Return

This Web page presents the rates of return on investment for the Mobius investment club since its creation in October 1997. As one can easily establish, there is a large number of rates of return that can be calculated. It is essential to understand that one cannot put forward rates of return without explaining the context and meaning of these rates. Hence, we have tried hard to put some rigour and methodology in calculating all the rates of return in the club - as well as validating them. Below, we discuss some of these rates.

Calculating rates of return can also be complex and may require the full set of raw data from the club (all transactions, in/out cash flows and monthly valuation). In many cases, most of this data should be available from the treasurer (validated by auditors) that computes the monthly accounts and club Unit Value. However, there are ways to derive rates of return by making some assumptions and approximations. In the tables below, we show how to obtain the accurate rate of returns as well as approximate if for some reason either the full data is not available or it would be too long to derive them.

If you have any question or comment, please do not hesitate to email Mourad Kara

MWR: Money Weighted Rate of Return

An accurate way of measuring the return on investment is to use the Money Weighted Rate of Return (also known as the Internal Rate of Return or IRR). This metric takes into account the value of earlier payments, cash flows as well as periods of payments.

The table below shows the MWR for the Mobius club in terms of annualised rate of returns. We have calculated the annual MWR for every complete year (up to 31st of December) and also the annual return since the club’s creation (from 01/10/1997) up to the 31st of December of a given year.

Year For one year only Since club creation
1998 -4.54% -5.82%
1999 14.00% 7.21%
2000 -7.94% 0.40%
2001 -20.02% -7.39%
2002 0.08% -4.83%
2003 19.98% 2.25%
2004 3.18% 2.47%
2005 9.33% 3.71%
2006 7.25% 4.33%
All rates are annualised. AER - Annual Equivalent Rate

All very well, but what all these rates mean? - Easiest done with an example. Let's take the year 1999 where the MWR for one year is 14.00%. Suppose that there is a bank offering a fixed interest rate savings account at 14.00% annual rate. Also, suppose the club took the total funds (Net Asset Value) available at 01/01/1999 and invested in that savings account from 01/01/1999 and subsequently invested using the same pattern of in/out cashflows as executed in the club. Then this account would have produced the same cumulative return as the club's NAV (net asset value) at 31/12/1999. In other words, the club has returned to its members the equivalent of 14% on their regular investments.

Now let's look at another example and another year, say 2003 and now we look at the third column "Since club creation" which reads a rate of 2.25%. Assume that a fixed interest rate savings account advertises a 2.25% annual rate. If the club invested in this savings account between 01/10/1997 and 31/12/2003 using the same sequence and amounts of monthly (in/out) cashflow transactions, then this account would have generated the same cumulative return as the club's NAV at 31/12/2003.

A few important points to note here:

  1. It is essential to note that the MWR is only valid for the set of in/out monthly cashflows executed. This means if the club had used a different set of in/out monthly cashflows, then the MWR could be very different.
  2. It is misleading to use the MWR to compare one club's MWR to another. For this purpose, there are better measures (see the TWR below).
  3. The MWR is the rate of return that matters to investors because it tells you how much you got back from the money you put in (on a monthly basis).
  4. One can compare the MWR to the best rates of interest in force at the time of investment to decide whether it was better just to leave the money in a savings account (taking into account inflation too).
  5. The rate of returns are valid for the members' funds as a collective investment. One can also further break down the MWR for individual members, in particular if members pay in different monthly subscriptions and have joined the club at different periods.

TWR: Time Weighted Rate of Return

When (private) investors invest in mutual funds such as Unit Trusts, investment trusts or OEIC, two sets of metrics can be used to evaluate the performance.

  1. The first one is of interest to the investor and is measured in terms of MWR as seen above, i.e. what is the cumulative total return on the payments made over several periods of time?
  2. The second set of metrics tracks the performance of a fund (against an appropriate index or benchmark). The second set in effect measures how well the professional fund managers have done with the investors’ money. It compares the performance of the fund managers and their associated portfolios with other similar funds (competitors) and/or an underlying benchmark.

The TWR belongs to the second category. Often funds and Unit trusts fund managers advertise their funds stating performance over a number of periods such as the past 5 years, 3 years, 1 year and 3 month. These performance can either be relative to a nominal amount such as £100 or can be an actual return rate (in %). These rates are calculated using the TWR. TWR represents the return an investor would have achieved with a single deposit left to accumulate and compound over some period of time.

The table below depicts the TWR for the Mobius club. As with the MWR, there are two columns, one depicts the TWR for a single given year, and the other covers the whole period, from the club creation (01/10/97) to the end of a given year (31st of December).

Year For one year only Since club creation
1998 -5.22% -8.83%
1999 13.46% 0.48%
2000 -8.12% -2.27%
2001 -22.14% -7.36%
2002 1.10% -5.81%
2003 19.33% -2.17%
2004 2.95% -1.48%
2005 9.48% -0.21%
2006 7.36% 0.05%
All rates are annualised. AER - Annual Equivalent Rate

Let's talk through the table above and take as an example the year 2004 with the column "for one year only", the rate is 2.95%. This is the annual return rate that an investor would have received if he invested in the Mobius club a single amount on the 01/01/2004 and reviewed his return on the 31/12/2004. Note that this return is not sensitive to any cash flow transaction.

Likewise, if we take year 2003 and the third column, then an investor putting a single contribution on the 01/10/1997 in the Mobius club would have incurred a loss equivalent to -2.17% per annum on the 31/12/2003.

Note that the TWR is a hypothetical rate measures the return of a portfolio in a way that return is not sensitive to changes in the money invested in the portfolio (multiple in/out cashflow transactions). TWR measures the return from a portfolio manager's point of view and allows comparison against a benchmark and across peer groups.

For any investment club, investors and managers are the same (they are the members), and members pay in monthly contributions and TWR assumes a single deposit at the beginning of the period. So the TWR serves only the purpose of comparing the performance of one club's portfolio to another over a specific period.

This is the first release of our effort towards defining and explaining different ways of interpreting return rates. By December 2009, our aim is to provide the formulas and steps used (in a tutorial fashion) to compute these rates as well as ways to validate that these are correct.