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How are you doing?

Posted on October 8, 2007 by Richard Beddard
Filed Under Investing |

Most investors grossly overestimate their abilities, which is one of the reasons they do so badly. Although the maths can be complicated, the individual investor can, and should, measure his performance.

No, seriously. How are you doing? Or, more specifically, how are your shares doing?

If you can tell me, you’re in the minority according to an academic paper summarised on the CXO Blog. Investors overestimate their returns by an average of 11.5% a year. It may not sound much, but compounded they could be making a gazillion dollar error. Many of us don’t even know whether we’re earning a positive or negative return.

The title of the paper, says it all:

Why Inexperienced Investors Do Not Learn: They Don’t Know Their Past Portfolio Performance

Sadly, the authors of the study disabused the motley collection of 215 online investors it had surveyed. They did worse than a benchmark index, the German DAX. It’s this kind of research that gives private investors a bad name, and perhaps we deserve it. After all, you’d expect a money manager to be able to measure his performance and if you’re managing your own money, you are a money manager.

Steve Le Compte at CXO says:

In summary, individual investors/traders should be diligent and honest in assessing personal past performance if they want to learn from experience.

The trouble is calculating performance, as opposed to chasing it, is boring. It’s also a tricky mathematical problem, at least for those, like me, whose investment careers rest on not having to do much more mathematical than dividing the price of a share by its earnings, or working out simple percentage changes from one year to another.

What’s more we have online portfolios with brokers, or financial websites like the Interactive Investor mothership. Most, though, measure the simple return of current shareholdings, which conveniently allows investors to forget about the horrendous trades they made in the past and takes no account of the time that money has been in the market.

The ideal method of measuring performance would be:

  1. accurate,
  2. quick and easy to calculate, and…
  3. suitable for comparison with indices, benchmarks and other people’s portfolios.

I, like many investors I’ve seen on the web use the XIRR spreadsheet function to calculate Internal Rate of Return, principally because it fulfills criteria 2 (it’s easy). Provide a spreadsheet with a list of dates cash moved into, or out of, a portfolio and the sums involved, and XIRR spits out a return. Here’s an example:

An investor opens a brokerage account with £5,000. A couple of days later he cashes in some funds managed by his financial adviser and adds the money (£10,000) to his account. Six months later he decides he likes the idea of managing his own money and transfers another £20,000 into his account. Meanwhile he’s investing the money in, say, shares or funds.

After one year, his account is worth £37,821. That’s a simple return of just over 8% for the year. But is 8% a fair reflection of his performance? After all a large chunk of money, was only invested for about half the time. If we type a list of the dates and transactions into a Google Spreadsheet (or Excel) and use XIRR, the annualised return is closer to 11%.

This is the function:

XIRR(range of values, range of dates, estimated return)

And here’s the spreadsheet (the convention is to treat money you pay into investments as negative cash flow, and money you take out as positive. XIRR uses trial and error to arrive at the final rate of return so you need to give it a starting point).*1

Of course, if our investor cashed in his investments on his first anniversary, he’d only have made 8%, but he can take heart from the fact that he may be a better investor than that. Time will tell. The longer the period, the more accurate and revealing performance measurement should be. I used XIRR to calculate my performance from the peak of the last bull market to arrive at an annualised return of 17% over seven years, but what I’m really interested to see is what my annualised return is from March 2000 to the peak of this bull market, a full cycle.

Sadly, I can only commend XIRR as a quick and dirty method, because I don’t know to what it extent it fulfills criteria 1 and 3. It’s vastly better than guesswork, apparently the predominant method of performance measurement used by private investors, but movements of cash into, and out of, a portfolio influence the return. That means it’s not strictly comparable to benchmarks like the FTSE-All Share.

Take my 17% annualised return. It’s partly because I threw money at the stock market in 2003, right at the beginning of the bull market we’ve experienced since. Was it skill? Or luck? I don’t even know. It was a coincidence that I had spare cash to invest, but I consciously chose to invest it. Luck, or skill, my portfolio is more valuable, and it’s return is higher, because I had more money invested when the market was rising, than when it was falling.

With professional money managers it’s more clear-cut. They don’t decide when cash is paid into their funds, their clients do, so to measure their skill as fund managers they strip out the effect of cash flows. That means valuing a portfolio every time cash is paid in or out, or maths that makes me feel quite queasy. With the help of a friendly, and more mathematical blogger*2, I hope to publish a spreadsheet that calculates ‘time-weighted’ performance along these lines.

If you’d like to have a go yourself, I asked Fisher Investments how the industry measures performance. They very kindly explained:

In general, portfolio performance can be measured by the change in overall market value from one period to the next. Without any external cash flows, an individual can solve for the period return by using the following equation:

Rp = (End Market Value – Begin Market Value) / Begin Market Value

However, when external cash flows are introduced, an individual has to determine a method of incorporating the change in market value from the external transfer in order to prevent misrepresenting performance. Two common methods of calculating performance with external cash flows are dollar-weighted and time-weighted returns.

Dollar-weighted performance measures the compound growth rate of all funds (beginning market value and subsequent cash flows) over a defined period. This type of return is also called the money-weighted or internal rate of return. The actual calculation shown as follows:

MV1 = MV0(1+R)CD + CF1(1+R)CD – D(1) + CF2(1+R)CD – D(2) + …+ CFn(1+R)CD – D(n)

Where:

MV1 = End market value
MV0 = Begin market value
CFN = Nth Cash flow
CD = calendar days in period
D(n) = number of days from begin of period

R is the rate of return that will solve the dollar-weighted return formula listed above. As the actual calculation is an iterative trial and error process to determine the correct R, software is often required to efficiency calculate the number. Note that R is expressed as the return per unit of time in the period. In the example above, R solving the equation is a daily return. The cumulative return is found by calculating RCD.

The main criticism of dollar-weighted performance comes from the propensity to be sensitive to the size and timing of external cash flows. For example, when a large cash addition occurs before a substantial up period, the dollar-weighted return will be positively affected. Conversely, when a large cash flow occurs before a negative market period, performance will suffer. Since portfolio managers often do not have discretion over the timing and size of client cash flows, dollar-weighted performance is not a preferred method of performance calculation for investment managers. The CFA Institute’s Global Investment Performance Standards does not allow dollar-weighted performance for this same reason.

Time-weighted performance is the second common method of calculating portfolio returns, and is the preferred method for portraying performance from the perspective of the investment manager. Ideally, portfolios are valued on each day a cash flow occurs in order to most accurately calculate time-weighted performance. The actual calculation is as follows:

Rp = (End Market Value – Begin Market Value – Cash Flow) / Begin Market Value

The formula above assumes external flows occur at the end of the period, and can be manipulated to incorporate begin of day cash flows:

Rp = (End Market Value – (Begin Market Value + Cash Flow)) / (Begin Market Value + Cash Flow)

Note that an individual will end up with multiple sub-period returns when calculating performance when each cash flow occurs. All sub-period returns can be linked together in the following fashion:

Rp,total = (1 + Rp,1) * (1 + Rp,2) * … * (1 + Rp,n) – 1

The linking formula above calculates the cumulative effect of all sub-period returns. One is added to each return to link returns on a constant value, which is then subtracted from the product to attain the actual return.

Time-weighted returns remove the effect of external cash flows, and are therefore favored for attributing performance for an investment manager. The return reflects the growth rate of a constant value, as opposed to some average dollar amount as calculated by the money-weighted return.

However, time-weighted returns are not without issues. Data constraints, such as daily pricing needs and portfolio accounting reconciliation make valuing portfolios at each external cash flow beyond the capabilities of many investment managers. An accurate method of estimating true time-weighted performance was developed by Peter Dietz, and is used throughout the investment industry. It is regarded as an efficient compromise between measuring portfolio performance and data constraints. The Modified Dietz calculation is shown below:

Rp = (End Market Value – Begin Market Value – Net CF) / (Begin Market Value + ∑ (CFN * WN))

Where:

Net CF = Sum of all external cash flows during the period
CFN = Nth Cash flow
WN = Ratio of days invested [(CD-DN) / CD]
DN = Date of Nth cash flow

The Modified Dietz calculation attempts to remove the influence of cash flows from portfolio performance by adjusting the beginning market value by a weighted sum of all cash flows within the period. Note that if all cash flows occur on the last day of the period, the weighting sum in the denominator of the equation will equal zero and the Modified Dietz calculation will mirror the standard time-weighted return calculation.

In summary, complications arise when external cash flows occur within a period in which an individual is attempting to measure performance. Using a dollar-weighted calculation will illustrate a return incorporating the timing and size of cash flows, and may be useful for an individual client who desires a measure of performance that includes these effects. However, for the portfolio manager, returns must be time-weighted to accurately measure portfolio performance of a constant portfolio value, without influence of client directed cash flows.

Let me know how you get on :-)

Footnotes:

  1. For XIRR to work in Excel, you need to install an add-in. Here are Microsoft’s instructions.
  2. Graeme, of course. He prefers time-weighting, and is quite critical of IRR methods.
  3. Thanks also to Le Fras Strydom, who works at the Interactive Investor mothership and bore the brunt of a number of queries, as I put this post together.

Comments

12 Responses to “How are you doing?”

  1. Malcolm on October 9th, 2007 4:20 pm

    You need to monitor but the above is way too complicated - most will have given up half way through the article.
    It’s much simpler if you convert everything into unit prices (like having your own unit trust).
    So if you start off with £5000 you call this 5000 units at £1. If this rises to say £6000 then you have 5000 units at £1.20. At this point if you decide to add another £20000 to your portfolio then this is another 16,667 shares (20000/1.20) making a total holding of 21,667 shares. If the total value of your portfolio then rises to (say) £30000 then this is equivalent to £1.385 per share (30000/21667). The increase in the unit value from £1 to £1.385 reflects the success of your investment over the period (ie. 38.5% profit in this case). You do the same in reverse when you take money out. So if you now withdrew £12,000 to buy a new car you are effectively selling 8664 shares (£12000/1.385). You are therefore left holding 13003 shares at £1.385 (value £18000). And so you go on.

    Cheers,
    Malcolm

  2. Richard Beddard on October 9th, 2007 6:08 pm

    Hi Malcolm,

    Thanks for your reply. This sounds like the Unit Value System used by investment clubs. I used to be in an investment club and we had many discussions about whether the rise and fall in the unit value of our club was a good indicator of our performance. In the end I concluded it wasn’t.

    This article explains why. It’s by the makers of software that helps investment clubs run their accounts. But I think the same problem could occur to individuals using the UVS.

    That said, the distortions would be less, if you had suffered less extreme movements in your portfolio than in their example.

    Incidentally another reason I found the UVS tiresome was the requirement to revalue your portfolio every time people paid money into the club (a bit like the time weighted approach in my blog). With IRR you only need to value it at the beginning and the end of the period you are measuring, accepting of course that brings about its own distortions, as I described.

    I don’t think there is a really easy answer to measuring performance!

  3. Robin Soole on October 9th, 2007 11:00 pm

    Hi Richard,

    I did give up halfway through the Fisher explanation I am afraid. However, scanning it briefly I think I am using some ‘time weighted’ style of return calculation. I use a computer program to do the following.

    Every time I add some cash, I discount it to time zero so that it does not impact on the current return. I provide an example to make this clearer.

    Suppose I have £1000 at time zero.
    At some point in the future my return is 10% so my total value is now £1100.
    I decide to add £200 on this day which brings my total value to £1300. However my starting value should not be increased by £200.
    The £200 can be discounted to time zero so that my total return remains at 10%.
    This is easy to do. The new starting value is calculated to be £1181.82 (=1300/1.1)
    Now, if the investment goes up another 10% bringing it to £1430 then the total return is correctly calculated to be 21% from the starting value.

    I actually use a slightly more complex system than this where I maintain two balances, a cash balance and a total stock valuation. This way, if I decide to hold cash for a while then this decision is accurately reflected in my returns.

  4. Richard Beddard on October 10th, 2007 11:24 am

    Hi Robin,

    Looks like you have it sussed. I think it partly comes down to how much effort you’re prepared to put in. I’m going to have a stab at time-weighting once Graeme has shared his method. It will be interesting to see how different the result is to the IRR calculation, and how much more onerous it is to do (I say that, not because it is onerous, but because IRR could hardly be less onerous).

    While I think I need to know I’m adding value, which in my case means beating benchmarks (the FTSE All-Share, RPI), I’m not too worried about calculating that value to the nth degree. However, if your approach to investing is to precisely track benchmarks then you’ll put a lot more effort into comparative performance measurement i.e. time weighting.

    One way or another, you need to know how you’re doing!

  5. Alex on October 10th, 2007 2:49 pm

    Hi Richard,

    > Let me know how you get on :-)

    I’d call my system more a rough estimation.
    I usually invest for more than a year, so I prefer making my estimations on a yearly base:

    Checking the yearly Cash flow:
    - Earnings by dividends (Div)
    - Earnings by sold shares (SS)
    - Expenses by bought shares (BS)
    Cashflow of the year x:[CF(x) = Div+SS-BS]

    Estimation: All investments were made in the exact middle of the year (x), at Juli 31. Over the years statistics should roughly run to this date.
    The cashflow has to be added negativly to the Investment, because a positive CF tells that money has been taken out of the pot and the contrary.

    In the end the hypothetical rate of interests is calculated to achieve the same money virtually still holded in shares. The yearly cash flow is disconted to the half interest rate fort the actual year (Juli 31):
    (Invests at 01.01. of (x+1) = rate/2 * (-CF(x)) + rate * Invests at 0101 of (x)

    For aditionally years the „interests on interests“-effect is included:
    Invests(x+1) = rate/2 * (-CF(x)) + rate * [rate/2 * (-CF(x-1)) + rate * Invests(x-1)] etc. pp.

    The variable for the variable „rate“ can be varied by hand to find the real „interest rate“ =“Return of Investment“.
    Sounds a bit difficult, but works fine in Excel. Helps me to estimate ROI for a time of four or more years. For a shorter period the random error could rise significantly.

    For sole share investments I estimate on a daily level:
    ROI = (Earnings-Investments/Investments)^(365,25/days of holding the share).
    I’ve lost the interest pf interest-effect for dividends, but I didn’t find an easy way to include them.

    My personal ambition is a longtime annual rate over 10%, best over 15%. Actually I’m between both. ;-)

  6. Robin Soole on October 11th, 2007 9:55 am

    Hi Richard,

    Although your article concentrates on the calculation of returns, the choice of benchmark is, in many ways, more important.

    For example, although the recent equity market returns have been great, my actual returns, relative to my benchmark have actually gone down slightly. I suspect I know why this is (I am holding 10% cash for various reasons) so I am not too worried.

    As a passive investor, I try to match my benchmark as closely as possible. If I am not happy with my returns then I would construct a different benchmark. You are an active investor and will make bets against your benchmark in order to get out performance.

    In either case, the benchmark is essential.

  7. Windy on October 11th, 2007 5:59 pm

    The XIRR is the way to go for a private investor to measure returns

    re a benchmark
    1 firstly you need to decide one an index etc
    2 secondly you need to buy/sell the benchmark/index at the same time and using the same cash/ins out as the share

    Then you do an XIRR calculation on the share and the index cashflow and hey presto -you’re there!

  8. Richard Beddard on October 12th, 2007 9:39 am

    Thanks Windy, I like that idea too :-)

  9. Measuring your return (again) : Interactive Investor Blog on October 12th, 2007 4:14 pm

    […] Although I’m intrigued by this suggestion… […]

  10. Dary Mc Govern on October 12th, 2007 6:07 pm

    ‘Money Weighted Return’ metrics versus ‘Time Weighted Return’ metrics is always a good way of kicking of a debate.

    The choice of metric when trying to establish rates of return should be driven by what you wish to achieve, as discussed in the following link:

    http://timetotrade.eu/wiki/index.php/Time_Weighted_Return_versus_Money_Weighted_Return_Performance_Metrics

  11. Angela frith on October 13th, 2007 9:11 pm

    Oh dear, I feel quite inadequate. Does this mean I dont know what I am doing?

    I was frightened by an algebraic equasion at an early age, so now I just use the clever computer programme I invested in.

  12. Richard Beddard on October 14th, 2007 9:09 am

    Thanks for the link, Dary.

    Hi Angela, you’re in good company! One of the reasons I got my hands dirty is the software I use doesn’t tackle it. It charts how much profit I’ve made in money terms but won’t give me a rate of return. What do you use, might I ask?

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