I manage three main accounts. All three are primarily equity accounts; two are US based and the third is an Australian retirement account known as a Self Managed Super Fund, SMSF.  Before we get to the returns, let’s detour for a minute to how to calculate investment returns. Every couple years I need to relearn the differences between the alternative methods for calculating returns, so maybe just maybe, if I write it all down I’ll remember.

There are four methods for calculating returns and while their names often change their faces remain the same.

Total return is the easiest though least useful method. It is simply the end balance divided by the start balance minus one. For example if you start with $100,000 and end with $200,000, your return is 200,000/100,000-1 =1 or 100%. If your portfolio has no external cash flows, dividends and the like don’t count, and you only want to calculate your returns for one year then that simple formula is all you need. Total return is also a good measure for individual positions.

CAGR or compound annual growth rate is the total return expressed as an annual return. For individual investments or portfolios without cash flows CAGR is the best measure. I’ll use the same figures from above and simply add some dates.

• Let’s keep things simple and say the investment was over two years. The formula is =(end balance/start balance) ^ (1/2) -1 . In Excel that will look like =(C4/C3)^(1/2)-1. The ^ means CAGR. The (1/2) is annal return for a two year period. Here is a spreadsheet with some examples for you to work through. The result is a 41% CAGR or annual return.
• Things aren’t always as simple as two year periods. If it was three years the (1/2) would become (1/3) and so on. But what about part years? I find it easiest to switch the CAGR from years to days. Let’s say we want to calculate the returns for an investment we bought on the 2nd March 2007 and sold on 6 November 2009. The formula for this is =(end balance/start balance) ^(365/(end date-start date))-1 . In Excel it will look like =(C4/C3)^(365/(I8-G8))-1.
• The ^ can also be replaced using POWER, e.g =(C4/C3)^(1/2)-1 can also be calculated as =POWER((C4/C3),(1/2))-1. Some example calculators using Power are included in the spreadsheet.

Internal Rate of Return and Time Weighted Return. If your portfolio has cash flows, i.e. you deposit or withdraw money, then you need to use either internal rate of return, IRR, or time weighted return, TWR, also called TWRR time weighted rate of return and TWIRR time weighted internal rate of return. The difference between the two is that TWR ignores the timing of the cash flows while IRR accounts for the timing of the cash flows. Rather than explaining each in depth, I’ve created a example for each in this spreadsheet. In summary, to calculate IRR use the XIRR function in Excel, while TWR calculates returns from one cash flow to the next and sums those ignoring the cash flows.

Which of the two should you use? That question never seems to get old. If you’re a fund manager or reading the returns of a fund manager then you’re most likely using TWR. That’s because fund managers don’t have control over the cash flows, so they shouldn’t receive any benefit or penalty for the cash flows.

Individual investors should use the method they deem most appropriate. The important question is, do you have control of the cash flows. If the answer is no then use TWR, if yes then IRR is the best choice. If you are attempting to calculate your past performance then there is another important question. Do you know the account balances at the date of the cash flows? If not then you have to use IRR as TWR requires balances at the time of cash flows.

In the past I’ve used IRR as it’s easier and I have control of the cash flow in most of my accounts. However, now that Joe Vannucci at The Motley Fool has reeducated me on TWR, I realise that going forward I should use TWR for our retirement account. The reason is I do not have primary control over the cash flows in that account. Most of the new funds are deposited automatically each month by my partner’s employer. For our US accounts I have total control over the cash flows and so use IRR.

My 2008 and 2009 Performance

US Based Accounts

I compare my performance to SPY, QQQQ and those two combined, i.e. something I could actually invest in that reflects my portfolio. All figures are adjusted year end close.

I have two primary US accounts. In 2007 a Motley Fool poster said he wondered if individual investors could select their best future performers from amoung their investments. That was in a conversation about concentrated vs diversified. I took his question as a challenge.

I was just about to change my broker, so decided to see if I could select my best companies. My portfolio had become bloated, i.e. diversified and I wanted to return to my concentrated ways. I left my top picks with one broker and transferred the rest.

The concentrated or high conviction account as I call it has been hitting new highs so I thought it would be my best US performer for 2009. I was surprised to find it was my worst performer and under-performed the market.

I continue on my path to return to my concentrated ways. My combined US accounts have a APY, annual percentage yield of 0.2% since 2008 and return of 0.4% as my diversified account is larger. That’s not much, but I’ll take it as the SPY and QQQQ have CAGRs of -10.8% and -5.1% respectively over that time frame.

Australian SMSF Account

For our Australian investments I use the S&P/ASX 200 Fund (STW) for comparison purposes. Sadly adjusted historical data for STW is getting more difficult to come by and my current source has now disappeared. (Anyone know a good source or have their own spreadsheet?) Getting accurate data for the Australian fiscal year of July to June is easy, but it seems calendar year data is more difficult to come by.

My spreadsheet which I used prior to swapping our SMSF accounting over to GnuCash last year was also based around fiscal year reporting. Not to be deterred I’ve cobbled together the data. Consequently there could be up to half a percent error in my data. Though as you can see that wouldn’t change the picture in the slightest.

I do not expect my out performance will continue at such pace, though I will certainly do my best to try to continue thrashing the indices. I hope your returns have been even better.

If the above contains too many numbers, ‘yeah babe I’m thinking of you’, here’s a pretty picture.

Related posts:

1. Fusion Investment Portfolio Update – July 2009
2. Leucadia Q4 2009
3. Fusion Investment Portfolio Update – August 2009
4. Fusion Investment Fund Update
5. Cost of Ownership
6. Self Managed Super Fund Performance