Are you a stock picker ^{[1]} who wonders whether you’re beating the market?

Or perhaps you’re a passive investor ^{[2]} keen to see how the returns from your DIY ETF portfolio ^{[3]} compares to Vanguard’s *LifeStrategy* fund?

Whatever the motivation, you’ll need to track and compare your performance versus active and index funds to know for sure.

And that means comparing your returns calculated using the same methodology that they use.

If you think you’re a great investor but really you’re lagging the market by 3% a year, it will have a disastrous impact on your wealth compared to if you’d used index funds.

That’s not to mention the many hours wasted in fruitless research and so on (unless you happen to enjoy it.)

### Many unhappy returns

Now I’ve warned before that there are good reasons not to closely track ^{[4]} your returns.

For starters, if stock picking is your hobby, then finding out you’re in the ‘D’ League – less Neil Woodford, more Woody Woodpecker – will be thoroughly depressing.

True, you might end up richer if you then give up on active investing and turn passive – although that partly depends on what hobby you replace active investing with. (Sailing boats don’t come cheap…)

But if you’ve wrapped your self-worth up in your ability to beat the market, be prepared to take an emotional beating when you discover the dumb money has actually beaten you…

More subtly, passive and active investors alike can be provoked into overtrading ^{[5]} or excessively fiddling with their portfolios by paying them too much attention.

You might even scared out of shares altogether, should you begin to more closely follow their ups and downs.

You could even get sick with stress.

Behavioural scientists have shown we hate losses much more than we love gains.

Yet as Nassim Taleb explained in *Fooled by Randomness ^{[6]}*, on any given day it’s a coin toss as to whether the market is up or down.

This means looking at your performance every day is a guaranteed downer.

You’ll be twice as miserable as you are happy!

### It all adds up

With willpower, you can accurately track your returns and avoid looking at your numbers every day – or even every month.

You can make up the rules.

Just don’t kid yourself by also making up your returns.

I have met many people who don’t take account of all the new money they add to their portfolio – yet they talk confidently about how well they’ve done through their active investing decisions in growing their wealth.

Only when you grill them do they admit to “top-ups” and the like.

This is all nonsense from the perspective of comparing performance.

Hint: If your portfolio starts the year at £10,000, you add £2,000, and at the end of the year you have £12,000, you did not earn 20%!

Your return was diddlysquat.

### You fooled you

You may decide not to obsess about returns, or even to ignore them altogether.

Good for you!

But if you don’t know your returns, don’t presume you do when somebody asks.

That includes you, when you ask yourself whether you’d be better off with index funds instead of active investing.

If you haven’t properly tracked your returns – taking into account all the new money you add, as well as all the capital gains and dividends – then don’t pretend you’re the next hot hedge fund manager.

You just don’t know.

### Unitize your portfolio to track your returns

Still want to know how you’re doing?

I believe the best way to track your returns is to **unitize your portfolio**.

Sure you can use online portfolio tools ^{[7]} or work out various numbers on-demand, but I think it’s better to take charge for yourself so you understand not just the numbers, but what is driving those numbers.

Unitization ^{[8]} is the method used by fund managers who must account for money that flows in and out of their open-ended funds.

As it’s the industry standard method of measuring returns, unitization means you can compare your performance with any existing fund.

You can also compare a unitized portfolio’s performance against a benchmark such as an index.

And unitization encourages you to keep decent records – also important if you’re trying not to kid yourself.

As physicist Richard Feynman warned: *“The first principle is that you must not fool yourself, and you are the easiest person to fool.”*

### Why open-ended funds are called unit trusts

So what is unitization?

You are probably already familiar with unit pricing when it comes to funds.

If not, here’s a quick refresher.

When you invest your money into an open-ended fund, you buy a certain amount of units in that fund with your money.

For instance, let’s say I have £18,420.58 in Legal & General’s European Index Trust.

The L&G website tells me how it calculates this:

Number of units I own: 6,564.712

Unit price Buy/Sell: 280.6p/280.6p

Value: £18,420.58 (i.e. 280.6 pence x 6,564.712 units)

All investors in the L&G fund would see exactly the same unit price. However they will own different numbers of units, depending on how much they have invested.

Whenever investors put additional money into the European Index Trust, L&G creates new units at the prevailing unit price.

The new money buys the right number of units at that price for the money invested.

For example, if the unit price were 280.6p, then investing £5,000 would buy you 1,781.9 additional units.

The new cash you’ve invested now comprises part of the assets of the unit trust, which offsets the creation of those new units.

The fund’s total Assets under Management have increased, but the returns haven’t changed just because new money has been added – and this is confirmed by the unchanged unit pricing.

Finally, the fund manager deploys your extra money to buy more holdings in order to keep the fund doing what it says on the tin.

In the case of this example, he or she buys more shares to match the European Index.

### Unit prices and new money

The crucial point is that adding new money does not change the price of a unit.

Only gains and losses on investments, dividends ^{[9]} and interest, and costs that are charged against the portfolio’s assets will change the price of a unit.

For example, if the companies owned by the European Index fund rose 10% in value, then the unit price would be expected to increase by 10%, too.

So here the new unit cost would be:

280.6*1.1 = 308.66p.

Measuring changes in the value of units like this – as opposed to measuring the total monetary size of the fund – enables the manager to maintain a consistent record of performance.

This record is not distorted by money coming in and going out.

Also, when an investor wants to cash out from the fund, there’s no confusion about what percentage of the assets they own or anything like that.

They’ll own a certain number of units. To cash out, they sell them back to the fund manager at the prevailing unit price.

For instance, let’s say you own 600 units.

At 280.6p per unit, you’d cash out with:

£2.806 x 600 = £1,683.60

By **unitizing your portfolio**, you can use the same principle to measure your own returns – whether you’re saving and investing extra cash or you’re withdrawing money from the portfolio.

### Interlude: A pep talk

So far, so boring.

Well, we are talking about accountancy here!

I’ll level with you. Things aren’t going to get any more exciting.

However the good news is that unitizing your portfolio is a very easy process.

Read on to discover how to do it.

### How to unitize your portfolio

For something that has the letter ‘z’ in it, unitization is very simple to do.

Admittedly, trying to retrospectively see your unitized performance over previous non-unitized years is a nightmare.

It’s such a nightmare, in fact, that I didn’t bother trying when I started to track my returns properly a few years ago, and I wouldn’t suggest you do, either.

If instead you take a leaf out of the Khmer Rouge’s generally best-avoided playbook and declare today to be “Year Zero” for your portfolio then it’s straightforward to get started.

**1. First decide on an arbitrary unit value**

The first thing you need to do is to decide what one unit in ‘your fund’ is worth.

It’s a totally arbitrary decision, as it will just be used as the base for future return calculations.

Many people choose £1.

I chose £100 for egomaniacal reasons.

**2. Calculate how many units you currently have**

As it’s Year Zero for unitizing your returns, you need to work out how many units you currently have.

This is based on the total value of **everything in the portfolio** you’re tracking, together with the unit value you just came up with.

You simply divide the former by the latter.

Let’s say your portfolio is £50,000 and your unit value is £100.

This means you have 500 units to begin with, like so:

£50,000/£100 = 500 units

Make a note of this number, together with your arbitrary unit value.

I track all this on a Web-enabled spreadsheet that constantly tells me what my portfolio is worth right now, what one unit is worth, and how many units I have.

From this it also works out and tells me my returns over various periods.

But if you want you can just write these numbers in a notebook. It’s only when you add new money that further calculation is mandatory.

**3. If you don’t add new money you can now easily track your returns**

Let’s say you never did add or remove another penny from your portfolio.

You know how many units you have, and you know the starting unit value.

You can now easily work out your unitized returns.

For example, let’s say your portfolio increases to £60,000.

The unit value is now:

£60,000/500 = £120

Your return to-date is the change in unit value.

£120-£100/£100 = 20%

However you hardly needed to unitize to see that…

**4. Adjust your total units as you add new money**

The whole point of unitizing is to properly take into account money added or removed from the portfolio.

Every time you add new money, you need to calculate and take note of the value of one unit.

For instance, let’s say that when your portfolio hits £60,000 you decide this investing lark is a piece of cake, and so decide to add in another £6,000.

The unit value before the additional cash is added, as above, is £120.

Now we need to calculate how many units our new money buys:

New money added / unit cost = number of new units

£6,000/ £120 = 50 new units

This means your £66,000 portfolio now comprises 550 units.

Again, you note it down ready for next time.

**5. Keeping ‘buying’ new units as you add money**

This process is simply repeated over your investing lifetime.

Let’s say the value of your portfolio increases to £69,850, and you decide to add a full ISA contribute of £15,240.

First:

Unit value = Portfolio value / number of units

Unit value = £69,850/550

Unit value = £127

Number of new units that £15,240 buys:

New money added/ unit cost = number of new units

£15,240/£127 = 120 new units

With the new ISA money your portfolio is now worth £85,090, and is comprised of 670 units (that is, 550+120).

As always you note down the total unit number for next time.

**6. What happens when you remove some money?**

When money is removed entirely from the portfolio, the principle is exactly the same as when money as added – the number of units changes as consequence, but not the unit value.

You are effectively ‘selling’ units in your own fund to free up the cash. Obviously this procedure doesn’t change the returns you have achieved on the mix of assets you happen to hold.

For example, let’s say your portfolio continues to motor on and breaks through six figures to hit £100,165.

At this point you get collywobbles (I told you there was a downside to tracking your returns) and you decide to spend £10k of it while you’ve still got your teeth.

You know from your records that your portfolio currently consists of 670 units.

This means the unit value currently is:

£100,165/670= £149.50

You decide to remove £10,016.50 from the portfolio to keep the sums simple:

£10,016.50/£149.50 = 67 units

After the withdrawal you have £90,148.50 in your portfolio represented by 603 units (670-67).

**7. Work out your unitized return at any point**

At any moment in time you can see exactly what your return is by looking at your unit value.

For instance, let’s say that after all of the above, your portfolio ends the year with a value of £90,450.

Your unit value is:

£90,450/603= £150

So your unitized return since you unitized your portfolio is:

£150-£100/£100 = 50%

This is the return that you can compare with trackers ^{[10]} and other funds and benchmarks that report their returns over the same period.

Let’s say at the end of next year a unit was worth £160.

You started the period with a unit value of £150. So your return over the year is:

£160-150/150= 6.7%

You see how easy it is to calculate and note down your annual return figures every year, for instance?

### Actually it all seems a lot of work

It’s really not, once you’ve set it up properly.

My spreadsheet tells me my current portfolio and unit value at any time.

A sheet also tracks money added and subtracted over the year, and calculates the number of units added or subtracted when I do so, which gets added to the ongoing tally.

At the end of the year I simply record all the relevant values for my records.

Then, on the first trading day of the New Year, I hard-update the spreadsheet with my starting unit value and the total number of units.

This makes it easy to see and record my discrete total return figures every year.

### When should I calculate my returns? And what else?

Up to you. I take regular snapshots, and as discussed above I work out the annual figures as I go.

I also work out things like my Total Expense Ratio ^{[11]} (TER) – based on another sheet tracking all my trading costs – and my total portfolio turnover.

If you take monthly snapshots then you can track your volatility, and start to look into other more esoteric ratios if you want to, such as the Sharpe Ratio or the Information Ratio.

I don’t bother. (Despite having written over 3,000 words on it here, I’m neither an expert nor an enthusiast for data crunching!)

### What about Net Present Value or Internal Rate of Return or CAGR etc?

There are many different ways ^{[12]} of calculating returns ^{[13]}. They all have value in different circumstances. And they usually deliver different numbers.

The advantage of unitization is it gives you the appropriate numbers to compare with any fund or index out there. That’s most important when tracking your own performance.

### What if I have multiple dealing accounts, SIPPs, and so on?

If I were you I would track all the different holdings on one spreadsheet.

I’d then unitize the returns on this entire portfolio, and also track expenses, portfolio turnover ^{[14]}, and other interesting figures across the entire piece.

This is exactly how I measure my own total returns across half a dozen different platforms and brokers ^{[15]}.

There’s not a lot of point in tracking the returns in a SIPP separately from returns in an ISA, in my view.

Ultimately it’s all your net worth. They’re just different baskets.

However if you did want to track how particular accounts are doing – perhaps because you employ different investing strategies in one versus another – then you could create separate spreadsheets to follow them.

You’d also have to track separate money flows in and out of each them, and generate unitized return figures for each ‘pot’ of cash.

Remember, you’d still want to unitize the entire portfolio to properly track your overall returns (rather than, say, averaging the returns on the different accounts, as this would not account for the different amount of money in each – though you could create a weighted average I suppose).

### What about dividends, spin-offs, dealing fees, stamp duty, rights issues and so on?

None of this matters, so long as all the incoming money (from sources such as dividends and spin-offs) and expenses (such as dealing fees and stamp duty) are retained or paid from within the portfolio.

The number of units you own doesn’t change because you were paid a dividend – no more than if one of your shares went up by 20p.

But your units do now represent more assets, in the form of that extra dividend cash. That increases the value of each of your units.

Similarly, dealing fees and stamp duty are no different to seeing the price of one of your holdings go down, in terms of their impact on unit value.

Expenses subtract from your total assets, and therefore they reduce the value of a unit.

**The golden rule:** It’s only when external money is added or when you take money out of your portfolio that you need to adjust the number of units you own. Such additions or withdrawals are as if an investor was buying or selling units in your fund.

Of course none of this is to say that dealing fees and dividends don’t matter from an investing and return standpoint. They matter a great deal.

The point is simply that unitization is capturing their impact on returns, so you don’t need to adjust for them. They are not ‘extra’ money added or subtracted.

### XIRR, time-, and money-weighted returns

From previous discussions elsewhere, I know some people prefer to plug numbers into Excel than to unitize and track their portfolios.

As I understand it – because they have told me so – such people usually get very similar results by using Excel’s XIRR function.

I won’t go into the details of using XIRR here because, frankly, I’ve never done it.

There are various ^{[16]} tutorials on the Web.

However you should note that while the results you get from unitization and XIRR may often appear very similar, they will sometimes diverge markedly.

That’s because they are calculating different kinds of return.

- Unitization gives what is known as a
**time-weighted return**– all time periods are weighted equally, irrespective of how much money is invested when. Unitization tells you the underlying investment performance, and strips out the impact of money flowing in and out.

- XIRR gives what is known as a
**money-weighted return**– this means that time periods in which more money is invested have more of an impact on the overall return than equivalent time periods in which less money is invested.

XIRR calculates the Annualized Internal Rate of Return on a portfolio. The gist is that you supply the XIRR function with a column in your spreadsheet that lists these cash additions and withdrawals. The function then uses an iterative process to hone in on your returns.

It makes sense for the fund industry to use unitization because a fund manager typically has no control over when money is added or removed from their fund – it comes from the fund’s customers – and also because it’s the choice and performance of the underlying assets that matters when evaluating how skillful a manager is. (The same reason I unitize my returns).

However some would argue that a money-weighted return like XIRR is at least as illuminating from the perspective of a private investor, since you are in control of money flows and what matters is your personal rate of return.

Many private investors do derail their results with poor market timing. By calculating and comparing both the unitized return and a money-weighted return you can spot the impact of poor (or perhaps good) market decisions timing on your portfolio.

The *Henry Wirth* Investing blog explains ^{[17]}:

- If your Money Weighted Return Rate is greater than your Time Weighted Return Rate, then your market timing is adding value to your portfolio.

- If your Time Weighted Return Rate is greater than your Money Weighted Return Rate, then your market timing is subtracting value from your portfolio.

You should also read the excellent comments from John Hill ^{[18]} that follow today’s post.

### Do it for yourself

Personally I think if you’re going to keep track of the money flows in and out of your account, you might as well go the whole hog and unitize your portfolio.

Once you’ve setup a spreadsheet to do the sums it’s very easy to stay on top of things, and you have the satisfaction of knowing your returns are directly comparable with those reported by fund managers.

That’s not to say there’s a right or wrong way to measure returns.

It all depends on context, and on knowing what you’re measuring and why.

Also remember that in itself a return figure tells you nothing about the volatility or risk ^{[19]} you took to get those returns, nor about the maximum troughs (aka drawdown, or losses at the portfolio level) that you endured along the way.

But if you unitize your portfolio and keep records of, say, the daily unit price, then you can go ahead and calculate and track that sort of thing for yourself.

Indeed, once you’ve unitized your portfolio, you can go crazy if you want to and use it as the basis for calculating all kinds of extra stuff – such as the Sharp Ratio ^{[20]} that might help you understand if your returns are down to skill or risk taking.