Ask Colin

How do you plot an equity curve of a portfolio?

This is an issue that is more complicated than it appears on the surface.


Assume that you start the year with a certain quantum of investment capital. It will be either invested in shares or held in cash as a reserve. You value the portfolio at the closing market price on June 30 and add the cash reserve. That is your starting capital for the year.


Now assume that during the year you do not take any capital out of the investment portfolio and neither do you add new capital to the portfolio.


In this situation it is easy. You value your shares again at the closing price each day, week or month (whatever is your preference). Weekly or monthly would be fine. Daily is probably a lot of work for little reward.


If you are using the Insight Trader Portfolio Manager, it will update your portfolio each day and, providing your record keeping is up to date, that will give you your total equity (shares at market value plus cash reserve). If you want to go back to an earlier starting point or to calculate points in between, just change the current date in Portfolio Manager and it will value the portfolio at those dates.


If you do not use Portfolio Manager, you will need to generate the same equity numbers using your own records. Going backwards is difficult unless your software allows you to reference to past dates as Portfolio Manager does.


You manually enter these data into an Insight Trader file that you might title Equity Curve. This is one number per week or per month and is not a big task. If you have a lot of past data you want to input, it is possible to create a data file and use Datacapt to input it.


That is all easy enough. However, the real world does not always respect the assumptions. You might want to add capital to the portfolio. This is fine for Portfolio Manager, but the Equity Curve will jump at that point reflecting the addition. You might want to take capital out of the portfolio – say to pay tax. That is also fine in Portfolio Manager, but will cause the Equity Curve to fall sharply reflecting the withdrawal.


Assuming again that these changes are only occasional, this probably presents little problem. You will know why it jumped or dropped. However, you may be adding or subtracting capital frequently. A good example is the receipt of dividends. I regard dividends as part of the total return, so it is not a problem, but it can be in some circumstances. Somewhat worse would be if you were in a retirement phase and took regular amounts out for living expenses. This would have nothing to do with investment results and would be a problem. You could deal with it though by taking out living expenses at the start of the year and keeping that money separate to the portfolio. Then again, that may not suit you.


There are other things that may create problems, which may or may not affect you.


An equity curve on its own is not a big problem. Where it can get difficult is that you need to compare it to something. I use my target return and the All Ordinaries Accumulation Index. If you have additions and withdrawals in your equity curve, which you recognise, that is fine, but they will not be reflected in the other two curves, so comparison is difficult.


It is possible to create two theoretical portfolios in Portfolio Manager – one for your target return and one for the Accumulation Index. If you put the same capital into each at the start of the year and do the same additions and subtractions through the year, you will have three curves that can be compared. However, there are some tricky underlying assumptions here.


The alternative to plotting the dollar value of the portfolio is to plot the rate of return. This is not an easy subject. It is dependent on the starting point and the method of calculating return. I use a quick-and-dirty method that suits my objective. I don’t plot the curve, but I look at the data every day. My target return is to average 12.5%pa over all market cycles. This is the long term return of the All Ordinaries Accumulation index. So, what I need to do is to try to match or beat the index most of the time. If I am ahead of the index through the year, I am ahead of my objective.


I calculate my return as a percentage of the starting capital for the year. I do not annualise it. I just calculate that growth percentage through the year for the portfolio and for the index and compare the two numbers. The only time it is a true annualised return is at the end of the year.


The issue for me is that I sometimes take capital out or put more capital into the portfolio. I deal with this by calculating my growth number on a time weighted average capital (this is described in one of my past Newsletters). This is also a quick-and-dirty method during the year, but it serves my purpose and is conceptually acceptable, though not perfect at the end of the year.


So, what I look at each day is that my portfolio has grown x% since the start of the year and the index has grown y%. If x% is greater than y%, I am on target. The only other concern is if the difference between x% and y% starts to narrow. In that case I need to consider whether I have a problem. This is where plotting it on a chart might help many people. They can see visually what I am visualising in my head.


Note that I do not annualise the two growth percentages, but this could be done if you wish. It is not conceptually easy to do in all situations and can be a very complex calculation.


Another issue I have not touched upon is whether you allow for exit costs in valuing your portfolio (I do and so does Portfolio Manager). Yet another issue is whether you value the stocks you hold at market value or at the stop-loss level for each stock. This has some merit, because you are more likely to realise the stop-loss price than the current price. Then again, it you are a long term buy-and-hold investor, the stop-loss level may or may not be relevant - some investors never sell any stock they have bought.


I am sure this is a far longer answer than you expected. However, while it is a simple concept, it has many methodological and conceptual wrinkles that may be more or less relevant depending on your situation.


I can also tell you that it is on a long list of projects to implement this in Insight Trader Portfolio Manager. However, there it is a very big problem, because it needs to deal with all possible situations. My own situation is relatively simple in comparison.