Are you a stock picker who wonders whether you’re beating the market?

Or perhaps you’re a passive investor keen to see how the returns from your DIY ETF portfolio 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 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 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*, 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 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 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 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 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 (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 of calculating returns. 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, 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.

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 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:

- 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 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 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 that might help you understand if your returns are down to skill or risk taking.

Superb post TI – just the sort of simple but effective system I’m looking for. I will very likely use this idea in my own spreadsheets. I’ve been looking for a way to effectively track how each additional quarterly/monthly top-up of money to my portfolio performs in its own right over time, as well as my portfolio over all. Unitizing each lump sum seems like a very easy way to achieve this – rather than having to worry about how each proportion of the top-up, distributed across multiple funds, is performing.

I feel I posted too much on the last thread so I’ll keep quiet unless anyone encourages me otherwise!

Great post – something to think about – I’ll be putting a new tab in my finance s/s to try this method. At first glance it’s at a higher level than I’ve used before and I’m uncertain about these imaginary “units” rather than something more real.

I’m not a great fan of percentages in such calculations but they are used a lot.

However…your example:

500 units, with each unit being valued at a notional £100 = £50,000.

Portfolio values rises to £60,000 so your 500 units are now worth £120 each. 20% gain.

You add £6,000 of new funds with a unit price (your imaginary unit, not the unit of the fund you are buying) of £120, so you “buy” 50 more units.

You now have a portfolio worth £66,000 consisting of 550 of your imaginary units.

Your gain is still 20%. £66,000 / 550 = £120 per unit vs a “face value” of your unit of £100.

I would have said your gain was still £10,000 on a, now, £66,000 portfolio – 15%. The new money dilutes your overall percentage (but not £) gain. It’s one of the reasons I prefer to deal in £, not %. Either 20% or 15% can be regarded as correct, it just depends on what question you’re trying to answer. But if someone says to me they’re 20% up and their portfolio is worth £66,000, I’m going to think they’re £13k better off. I wouldn’t naturally think to ask them how they defined their %.

If your £66k portfolio then fell to £56,000 I think you’d tell me that you’re 2% up (£56,000 / 550 units = £102). I’d say you were break-even as you’ve put £56,000 in and your portfolio is worth £56,000.

Oh dear…obvious mathematical error in my last post. Blush. Please delete penultimate para in your minds…

How you treat dividends does matter, in that when you compare your portfolio to an index, you need to decide if you want to compare to a total return index ( where dividends are accumulated) or not ( I.e. dividends are withdrawn from the portfolio). Eg there is the FTSE all share index, and the FTSE all share TR ( total return ) index. If you assume that dividends are held within the portfolio, then you need to compare to the TR index.

You can of course calculate both – Also known as accumulation units or income units.

Richard: Mathematical error excused, but I’m confused why you’d say you were 2% up – unit price is not a measure of how successful your portfolio is, simply what it costs to “buy in”, relative to when you first started it. £56,000 is the same as what you’ve invested overall, so you are neither up nor down.

However, what *has* taken place is that your latter £6000 investment has dropped into the red (50 units now valued at £5090.91 total), while the original £50k investment is still slightly up (500 units valued at £50909.09). So one investment is ‘saving’ the other – but overall you are still back where you started. Only now it costs slightly more than before to buy in, relative to your original investment.

@Moongrazer

Hmmm…not sure. You’re now keeping track of separate lots of purchases – which is what I do (but for real shares not imaginary units).

I read the post as the unit price was the single number you needed to measure your portfolio’s return.

@all — I’ve just written 3,000+ words on this, so excuse me if I have a bit of a break from writing long replies.

However please note I fully expect(ed) people to turn up in the comments saying *this* does or doesn’t measure *that*. 🙂

There are myriad ways to calculate different kinds of returns. To draw attention to that, I included the section on “What about Net Present Value, or IRR, or CAGR and so on?”

It is an explicit nod to the fact that there are very many different ways to measure return, which are applicable in different circumstances.

So no, the article did not say: “the unit price was the single number you needed to measure your portfolio’s return”. 🙂

What it is saying is that it is the single number you need to track your portfolio’s unitized return, and hence over time to compare it with other funds, indices, benchmarks and so on.

If you want to work out some other kind of return in some other way for your own purposes — such as, for some reason, what percentage you happen to have more in total than when you started, irrespective of fund flows — then knock yourself out. 🙂

You can’t compare that to a return quoted by a tracker fund or Neil Woodford though.

@Nigel — Well really what you’re saying is “don’t compare a total return portfolio with a capital-only index” or similar, which is quite correct.

However from the point of view of unitization, all that matters is whether you keep the dividends in (/reinvest your dividends) or take it out (/you spend your dividends).

If you leave the money in, that’s fine.

If you take out/spend the dividends, you’ll need to track those withdrawals and reduce your unit count as you do so.

@Richard

The way I see it (if I think I’ve read TI’s post correctly), the aim of the exercise boils down to being able to illustrate “I invested £X on this date and this is how well that particular sum is doing now.”

If I did that with each of my individual funds every time I topped up my investment, I’d have to add 9 new entries to a spreadsheet every time (apportioning the lump sum to each according to weightings), in order to track what that particular investment was doing. To say nothing of what would happen with all the convoluted scenarios we were discussing in the previous blog post of selling old funds and buying new ones.

With this approach, each time I top up, I am locking in that new investment according to how my portfolio is doing at the current time. If my portfolio is currently in profit, then the new investment will have to do that much better to pull its weight. If my portfolio is currently in the red, then the new investment is going to (hopefully) yield a bigger reward in the future.

This, for me, solves a problem I’d been thinking about for a while. Each year I invest money with the intention of it being locked away for 25 years, and then after that time withdrawing the profit and living off that for a year (I hope!), whilst also leaving the original sum invested for another 25 years. The problem I needed to solve was how to differentiate money invested in year 1 vs. money invested in years 2, 3, 4, etc. so I could work out whether year 1 had done sufficiently well enough in 25 years’ time that I could live off the profit alone. Maybe thats a bit of a bonkers way of looking at it.

Nonetheless unitizing appears (to me) to be the answer to that, since I now have a way of crystalising the value of any given investment at the point in time it goes into my portfolio!

@Moongrazer — No, that’s wrong and I’m a bit dismayed if I’ve given that impression. (Are other people reading it this way? If so tell me where/why please so I can edit it).

Unitization is a method to track your whole porfolio’s performance when there is cash going in and out of the account, used by the industry, and hence best adopted if you want to compare your returns with the industry, in my view.

Perhaps this Wikipedia entry will help:

http://en.wikipedia.org/wiki/Unit_valuation_system

The reason I am a fan is I want to know how well my portfolio is performing in a directly comparable way to other funds. The best way to do that is to use the same system they use. If you want to figure something else out, then there are other methods to turn to such as IRR or NPV that are not the subject of this post. 🙂

TI is right to stress that there are many different ways of looking at returns. However, I do not think that unitisation is one that gives you a view of your “portfolio” return, its intention is to tell you about the return of your underlying assets in a way that can be compared with other indexes and funds. It does not tell you if your timing of inflows and outflows messed up the whole apple cart by selling low and buying high.

Consider this simple example…

1/1/2014 Invest £1000 in portfolio (1000 units at £1 each)

1/7/2014 Portfolio is now worth £2000. Yippee! You invest another £1000 (total of 1500 units at £2 each)

31/12/2014 Whoops! Portfolio has fallen to £1500. (total of 1500 units at £1 each).

I think most people would expect that their measure of “return” would be negative.

Yet for the year your unitised return is 0%. Your IRR however is -32%. And from a cash perspective, you have invested £2000 and have now only got £1500.

If you want to know if you are making any money or if your crap market timing is hurting you, then use IRR (or other versions thereof). If you want to compare your portfolio constituents with Neil Woodford independent of your market timings then use unitisation.

“There are myriad ways to calculate different kinds of returns.”

I think that just about sums everything up!

As long as we’re very clear about the question we’re answering everything should be fine. But if I want to compare “my” return to “your” return we need to be very clear that we’re talking the same methodology.

I’m pretty sure it is just my misreading of it. I think I’m going in a different direction with the maths than this particular system is meant to do.

Re-reading, where I went off on a tangent was the bit when you talk about working out your actual rate of return by using the present unit value (current portfolio value divided by total units) versus the original unit value.

In which case I appear to be in Richard’s camp in thinking that’s a bit strange – as he illustrated, if your investment dropped back to £56,000, the value of your portfolio would be equal to the money you put in, but your unit price would be £56,000 / 550 = £101.82 (ish), not £100, so it would be ‘up’ 1.82%, even though your portfolio’s current value is no higher or lower than the original money that went in.

I’m certainly not disputing its use in comparing your portfolio’s return to an industry index – but if that’s the case, then suddenly industry indices look a whole lot less useful (or I am still not getting something).

For me, tracking how my entire portfolio has performed versus the market over time, while interesting (and certainly useful to see if I’m off the mark), is less useful than seeing how each individual lump sum is currently doing in its own micro existence.

But unitizing still seems to work for my purposes (if not the ones you intend) – because when I put in new amounts of money, I can see how those individual sums go up and down easily (I could look at individual monies put into many differents real funds, but that’s just more time consuming).

Really, the maths behind my problem just requires me to know the fraction of my portfolio that my new investment is occupying versus the portfolio as a whole. Units is just a nicer way of representing it.

Sorry for the long ramble!

@helfordpirate:

Useful summary. Think that clears up the distinction for me, if I’m honest. So IRR is the manner in which I should measure how my portfolio is doing versus the money I put in, Unitization is what I need to see how my portfolio stacks up against other market indexes.

One can come up with quirky examples that ‘break’ all the different ways of calculating returns, I’ve noticed. And people always do when these discussions come up! 🙂

Unitization seems particularly suspect when small sums are involved relative to the cash inflows/outflows, and when the portfolio is liquidated. But in practice I find it perfectly usable, which isn’t a surprise given the financial industry — passive and active — also does, too.

Yes, I think you should be unitizing your returns. 🙂

At the end of the day, I’m not a statistics junkie and certainly not a statistics expert. Unitization struck me as a sensible and surprisingly simple way to track returns over time and deal with the cash I am regularly adding when it was first introduced to me several years ago, and the fact that it enabled direct comparison in an industry standard way was very appealing.

@Moongrazer

I think I got off lightly in my example. Poor Helfordpirate’s lost £500, had a -32% IRR and yet Mr Woodford’s telling him he’s breakeven.

Is it too late to retrain as a fund manager…?

@Richard

That gave me a good chuckle. Touché sir!

Having a set-up of different platforms and differing monthly inputs; I was looking for a solution to this problem at the end of last year. My research ended up taking me down the excel XIRR solution. But interesting to see another option – if only to double check my original spreadsheet calculations are correct!

After a quick test I see that there’s a minor difference to the XIRR v’s Unit figure – which is not surprising. (but good to know it’s only a minor difference)

And I’m guessing it is due to the that fact that I currently only check my Total Portfolio amounts (from the platforms/etc) some days after those monthly installments have been made. And I don’t record the Total Portfolio amount the day before the monthly installments – to give a better figure to calculate the Unit Value that will be used the following day. (As the XIRR formula only needs to know only the dates when the various inputs/outputs happened, and then the current Total Portfolio amount)

Would I be correct in my assumption for the small % difference between the 2 systems or am I barking up a wrong tree? (Hope the above makes sense 🙂 )

Thanks TI for clear explainations and revealing a different solution to the problem. And will be playing around further with this idea.

I’m struggling with the maths in thie following section. If unit value is£143 yet starting value was £160 then that’s a £17 loss ain’t it?:

“Let’s say at the end of next year a unit was worth £143.

You started the period with a unit value of £160. 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?”

@Mikkamakkamoo — Oops, sorry, my fault! It’s a typo, I was going to show an example loss calculation but then swapped it for a gain as the ‘minus’ sign is never very clear online so I thought it looked confusing. Not as confusing as leaving old numbers in! *red face*.

Fixed now. Thanks very much for the spot!

There is a major difference between XIRR and “unitization” as neatly described by The Investor, as is hinted at by the examples above from Moongrazer and helfordpirate.

XIRR gives what is known as a “money-weighted return” – 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.

Unitization gives what is known as a “time-weighted return” – all time periods are weighted equally, irrespective of how much money is invested and when. So this is just the underlying investment performance, with all the money in, out and inbetween stripped out.

Think about the another example:

– You invest £1,000 on 1 January 2014.

– Your portfolio goes up by 10% in the first six months of the year.

– The first contribution is therefore worth £1,100 on 1 July.

– This is a licence to print money, you think! You invest another £1,000 on 1 July.

– Your portfolio goes down by 5% in the second six months of the year.

– The first contribution is therefore worth £1,045 on 1 January 2015.

– And the second contribution is therefore worth £950 on 1 January 2015.

– So the whole portfolio is worth £1,995 on 1 January 2015, less than your £2,000 investment.

The unitized return is 4.5% (1.05 x 0.95 – 1), reflecting the fact that the underlying investment actually did just fine, leaving aside your poor timing.

The XIRR return is negative (at -0.33%), because you had more invested during the second six months when returns were much lower, reflecting the fact you’d have more money now having left it in your bank account all along.

Neither return is wrong, but you need to appreciate that time-weighted returns and money-weighted returns serve difference purposes.

Time-weighted returns tell you about relative investment performance only. You can directly compare the time-weighted return to that of any given index, fund or other investor’s time-weighted returns over the same period, and get a clue as to whether or not your investment strategy is doing what you expect it to be doing (whether that be accurately tracking an index, capturing a risk premium, or delivering active outperformance).

Your portfolio’s time-weighted return of 4.5% may actually have been quite respectable, if your benchmark returned only 3% over the year as a whole. Perhaps you’re good at picking your investments, though you’ll need a lot longer than a year to be sure!

Money-weighted returns tell you about the actual performance of your money taking into account the good, bad or indifferent timing of your contributions and withdrawals as well. No matter the validity of your investment strategy, that’s may be all for nought if you’re constantly buying high and selling low. And you need to take into account your actual returns to see if your money is on track to get you to your financial goals.

Clearly, -0.33% per year isn’t going to grow your money in a hurry, but perhaps the timing was just unlucky this time around.

Generally speaking, over a long enough time and with enough contributions and/or withdrawals, you would expect any good, bad or indifferent timing that is due just to luck (or lack thereof) to average out, and money-weighted returns to end up being very similar to time-weighted returns. But, even then, in some cases, that may require more time than you have, if the luck (or lack thereof) is big enough!

And if the timing of the contributions and/or withdrawals is not down to luck at all, but deliberate investor behaviour, then money-weighted returns may differ markedly to time-weighted returns (see the DALBAR studies, for example, that show that actual US investors have consistently earned lower returns than the market, due to buying high and selling low).

Perhaps it is worth also pointing out that you can use money-weighted returns for comparative purposes, but only if you apply the exact same money-weighting to whatever it is that you’re comparing your portfolio to – this involves calculating how many units in each and every comparator each of your contributions or withdrawals would theoretically have bought or sold on the same dates, and the end value of the sum of those units. Needless to say, that can be an awful lot of theoretical calculations.

On the other hand, to calculate time-weighted returns you need to know (or be able to calculate) exactly what your portfolio was worth at the time of each and every single contribution and withdrawal, which can also be easier said than done.

So if you’re intent upon making meaningful comparisons of a portfolio’s performance relative to any other, there tends to be quite a bit of work to do either way!

while i’ve gone for using IRR instead of unitization (let’s not go into that), what struck me is that you’re counting cash held with your broker/platform as part of the portfolio, and i’ve never counted cash as part of the portfolio (i.e. the portfolio is just all the funds, shares, and so on, that i hold).

your approach has the advantage of making the returns look worse if an investor foolishly holds lots of cash with their broker (earning minimal interest) while markets soar (not that i’ve ever done that … well, not any more :)).

and it may make the calculations simpler – assuming you add or remove cash from your broker account less frequently than you buy or sell investments, or receive dividends.

@TI Thanks for this very well explained method of unitization and all the helpful coaching in the preamble. I did get a bit stuck at point 3

Whoops! My emoji crashed out the rest of my comment! I re read point 3 and got it. The comments were another matter… Isn’t is more a matter of avoiding comparing apples with pears? 🙂

Just to say that I use a programme call Fund Manager (https://www.fundmanagersoftware.com). It’s not the easiest programme to get to know, but once set up I just add my transactions, and then I can monitor the performance according to all the above options, and more. I think ‘Time-Weighted Return’ is similar to the unitization, but I’m a little beyond my pay grade here.

The programme is also nice as, again if set up right, it will work out capital gains and makes rebalancing a doddle. It’s a little more than I need in general, and a lay persons guide to the programme would be very nice, but it does make adding data easier, and any later analysis simple to do (and provides a lot of performance measures to do it). I can recommend it.

I’ve now created a nice, simple spreadsheet to complement my other (fund-specific) sheet. It contains entries for each investment sum I make into my portfolio, how many units of Moongrazer Fund that has purchased, and the IRR of that specific sum relative to the whole portfolio.

I then have total IRR for the portfolio (calculated across all the sums invested) so I can see clearly how my portfolio is doing for me personally, and the Unitized Return (current unit value / inception unit value) so I can compare how the choices I make inside portfolio are affecting it versus the market and other funds.

So I have a peaceful coexistence of Unitized Return and IRR that should hopefully suit my needs. I guess I’ll find out in years to come once the additions to my portfolio start going in. 🙂

@TI Great article; thanks.

In para 3 “track your performance” may be a seed of some of the confusion in the comments. Maybe it would be more accurate to say something like “*compare* your performance. And to compare your performance against industry funds and indexes, you need to use the same performance measurement tequnique as them”. I can see the post being a useful one in the archive so heading the confusion off at the pass might be worth the effort.

@John Hill — Superbly clear explanation that beats mine, thank you. (Fancy a gig writing the odd article for Monevator? Please contact me if so!) You’ve done such a good job explaining XIRR in fact that I just rewrote the section in my post and took the liberty of adding a few of your words, with a note to readers to jump down here and read the rest of them.

Thank goodness for John Hill’s excellent post above: I thought I was going to have to dust-off the mathmo books to explain the difference.

I struggle slighlty (as a poster above notes) with defining the edges of the portfolio. I do include cash in a brokerage account (and have an asset allocation for cash). I also include the cash float in a Santander current account. But I exclude the cash in my Lloyds account. I don’t include my rental property or mortgage, although I consider it a working asset (unlike my dwelling).

It comes down to what you want to measure, as stated above. There’s not much I can do about property allocation but I can play with the more liquid assets. I focus on allocation rather than return as my actions are determined by it.

In terms of measuring progress, I forecast retirement income, since that is the goal.

If I were a hobbyist active investor then I’d focus on unit return as a measure of my hobby.

@NearlyThere — I think I see what you’re saying, and have mad a tweak according — thanks. However I do want to push back at the implication (perhaps?) that unitization isn’t enabling you to *track* your returns. It is, but it is just one of a few different ways of doing so.

Perhaps it is my active bent that makes unitization so attractive to me. Clearly I need to see that my nefarious stock picking activities are adding value. If you’re a pure passive investor, then money-weighted returns might be a superior first port of call as you’re comparing more directly with just having the money in a bank account or similar.

That said, this discussion has made me appreciate more that I should probably track both in an ideal world. Possibly a future project!

Thanks very much for posting this, TI and also to people commenting.

I think I’ll give this a go and have a play around.

From a purely mathematical point of view, unitization is just the reciprocal of the profit/loss of your portfolio since inception, when flowing money in or out of it.

In other words, you could achieve the same calculation by multiplying any newly-added (or removed) funds by the reciprocal of the portfolio’s growth since inception, and treating that value as what you added to the portfolio. So adding money when the portfolio has grown 10% means you actually added £money/1.1 – thus £1000 would be treated as having added £909.09 at inception.

But I suspect measuring in units is a good deal easier than befuddling yourself with time-adjusted investment values!

What’s the objection to “comparing apples with pears”? Comparing apples to Tuesday now, that would be silly.

Great post, been reading Monevator for a while but never commented – but wanted to thank you for this 🙂

I’d been looking to track my returns recently and couldn’t get my head around the different methods – this makes it all clear to me, and the unitization method is nice and simple.

Now the hard bit is to ignore it 🙂

Interesting idea – thanks

We can also say – that the BIG gaps between investor (money weighted) returns and the average (unitised) return on a fund over time do not reflect investor mistakes (or genius) but simply the shape (‘path’) that the fund price takes over time.

This can be tricky to get ones head around – so I wrote a couple of plain English articles on this matter (one on savings and one on drawing down money) for investor’s chronicle last year.

Hope this is of interest

Hi

Very good and timely article for me as I’m trying to get to grips with tracking my investment returns.

Does anybody have an working example spreadsheet to get me started?

Thanks

Paul

Sorry for the ignorance but for passive i. e. lazy investors, isn’t Morningstar’s free portfolio tracker more than sufficient for calculating pretty much all of the above?

@TI

Thank you for this piece. I didn’t know there was XIRR at hand, and this addresses my problems :). I had tried to come up with something like that. From what I understand having played with it for a while, it calculates the returns both time- and money-weighted which is exactly what everyone should do to calculate their portfolio’s internal returns. And then you can compare it with anything you please.

On a side note there is one comparison I find useful for some who drip feed their portfolio every month or every quarter. Divide your total contributions by the number of months, you now have the average monthly contribution. Plug it into a simple smooth growth calculator and it will show you what annualized return was necessary to get to the current value of your portfolio. Your XIRR will likely be different unless you really contributed the exact same amount every month.

Unitization complements XIRR in my view. It can give you an idea as to why your internal returns are or aren’t similar to annualized unit price change.

For future projections XIRR may prove not as useful as your averaged out unit price change unless you are actively playing on volatility (market timing 🙂 and expect to be as lucky or as unlucky as before.

Internal rate of return (IRR) should not be used to track portfolio return if you are adding significant amounts of cash to your portfolio. Unitization as explained in the article is likely to be much more appropriate, but not without drawbacks as others have commented on. The idea that IRR is the same as “Money Weighted Return” is plain wrong, probably some rubbish put out by a wealth manager who misunderstood a basic financial arithmetic lecture. This misinformation has unfortunately spread like a joke that went wrong, much as Sinclair’s “Quantum Leap” did.

In some circumstances, internal rate of return may approximate a “Money Weighted Return”, but this is not the general case.

The internal rate of return of a series of cash flows is simply the discount rate that makes the net present value of the flows zero. For example, you invest £1000 in a deposit account and a year later receive £100 interest and the year after that another £100 interest plus your money back £1000. The flows are -£1000 (money into deposit account), +£100 after 1 year, +£100 after 2 years and +£1000 return of capital after the 2 years. Unsurprisingly, the internal rate of return is 10%, more formally this is because the net present value of all the flows, discounted at 10% pa, is zero: -1000 + 100/(1 + 10%) + 100/(1 + 10%)^2 + 1000/(1 + 10%)^2 = 0

IRR and Excel’s dangerous XIRR function, makes perfect sense when used as above and you want to calculate a single value that represents the rate of return achieved after making a single point in time investment. It is however extremely dangerous when used with multiple investments and withdrawals and may not have any useful meaning when used in these circumstances.

As an admittedly extreme example, consider an initial portfolio investment of £1000 that does very well over the following year and you take £3600 out. Then on the second anniversary you invest another £4310, but disaster strikes and over the following year the entire portfolio value drops to only £1716. What is the internal rate of return? The answer is that there are 3 perfectly valid answers of 10%, 20% and 30%. i.e.

-1000 + 3600/(1+10%) – 4310/(1+10%)^2 + 1716/(1+10%)^3 = 0

-1000 + 3600/(1+20%) – 4310/(1+20%)^2 + 1716/(1+20%)^3 = 0

-1000 + 3600/(1+30%) – 4310/(1+30%)^2 + 1716/(1+30%)^3 = 0

This illustrates one reason why it can be inappropriate to ask what the internal rate of return is when you have multiple positive and negative cash flows. If someone really wants to know a “Money Weighted Return”, it should at least be calculated in a way that can only give a single result. I would suggest calculating the internal rate of return of each investment (each set of “units” purchased if unitizing) and then calculating the weighted average of those IRRs.

However, sometimes it is far better to accept that it is misleading to represent a population by a single average value, which is what we are doing when we try to distil the performance of a portfolio with multiple in and out cash flows down to a single rate of return.

A most excellent post and replies, thank you all.

@HRP

I agree that in some scenarios (huge volatility, short investment period) asking about average annual return could be inappropriate. I can’t see, however, anything wrong with multiple discount rates XIRR returns when operating on alternating inflows and outflows.

Let’s have a look at your example. Initial investment is £1000, then after a year there is a withdrawal of £3600. What happened to that money then during the following year? If it’s invested elsewhere at 10% and you’ve got £3960 after a year then it would be like leaving that money in your original investment and adding only £350 instead of withdrawing £3600 and adding £4310 after a year. This way we can make sense of the discount rate returned by XIRR. The same goes for 20% and 30%.

Arguments passed to XIRR can be amended to achieve a single result.

@HRP

I am essentially already doing as you suggest in my spreadsheet. I am isolating each payment I invest in my portfolio (along with portfolio ‘units’ purchased) and tracking its IRR separately from any others.

I am not yet concrete about how to represent outflows from my portfolio. Since I have a 20 year minimum horizon this won’t be an issue for some time, but I am curious about how to best represent it. At the moment there is a line for each payment into my portfolio along the lines of Sum Invested / Unit Price At Purchase / Units Purchased / Current Value.

Your point about not using the entire portfolio as a basis for IRR seems perfectly logical to me. A sum invested in year 1 is clearly going to have gone on a far bigger journey by year 21 than a sum invested at year 19.

On that basis I would probably ‘sell off’ the oldest units/purchases in my portfolio first. Or perhaps as time advances and I move closer to retiring I would evaluate which sums invested in my portfolio have achieved well thus far (i.e. met the target growth I am hoping to achieve) and crystalise them so as to stem their volatility, whilst leaving funds that have performed below target to hopefully grow a little longer.

Is there anything worth reading on crystalising/reducing volatility in older investments as one gets older? I know the more general thinking is “increase bond %, decrease equity %” but that seems like a broad-strokes approach and I get the feeling there must be something better if I am taking the time to track how each individual sum I invest is doing.

@Paul W,

“If it’s invested elsewhere at 10% and you’ve got £3960 after a year then it would be like leaving that money in your original investment and adding only £350 instead of withdrawing £3600 and adding £4310 after a year.”

You are solving a different problem – initial investment £1000, no withdrawal after 1 year, add £350 in year 2 and take out 1716 after 3 years – this conveniently has only 1 IRR. What if the money withdrawn after the first year was spent?

The point I was trying to make is that in certain situations there can be multiple internal rates of return and using XIRR and variants to calculate a money weighted rate of return is inappropriate in these circumstances. If someone blindly creates a spreadsheet of flows and uses XIRR to calculate an internal rate of return, XIRR will usually oblige with an answer, but that answer can be misleading if it is one of many. IMHO investors are better off steering clear of XIRR unless they also check that there are not multiple internal rates of return. If there is only a single initial investment, there can only be single IRR and as such XIRR is fine.

@Moongrazer, what you are doing sounds sensible, but it sounds as though you might be mixing up the calculation of a historical rate of return and a strategy to reduce forward volatility. The 2 are entirely unrelated.

I think there are 2 possible ways of doing the calculation. The first is the “first in first out” (FIFO) method, as you have described. This will give you 2 sets of IRRs and sometimes a partially closed out deal. One set of IRRs will be completely fixed, as earlier unit purchases are closed out. The other set of still open investments will have IRRs that will vary according to unit value. You could then calculate an average IRR by weighting according to the number of units. For example, if you received an IRR of 5% on 10 units, 10% on 3 units and -20% on 2 units, your weighted average IRR would be (5%*10 + 10%*3 – 20%*2)/(10 + 3 + 2) = 2.67%.

The other approach would be to keep every investment alive and apply the same percentage withdrawal across all of them. For example, if you are selling 5% of units and had made 2 investments, A of 20 units and B of 10 units, you would sell 5%*20 = 1 unit from investment A and 0.5 of a unit from investment B. Then calculate the weighted average IRR as with the FIFO method. This approach would give you a result that is closer to what people are aiming for with XIRR.

Personally I don’t do any of this. I doubt it would be of any use to me if I did as the investment risks I have taken have varied enormously over time. I also hate admin 😉

@Moongrazer, forgot to mention, in your case as you making multiple investments, but not taking money out, IRR is fine as well as there can only be a single IRR that will “fit” your situation. Just be careful with it if you start making withdrawals AND subsequent investments.

@HRP

“You are solving a different problem – initial investment £1000, no withdrawal after 1 year, add £350 in year 2 and take out 1716 after 3 years – this conveniently has only 1 IRR. What if the money withdrawn after the first year was spent?”

Then still one of the three discount rates return by XIRR has to be arbitrary chosen by the investor, because XIRR can’t know how much of the subsequently invested £4310 is/would be new money. It’s tricky to blindly use XIRR, I agree.

” If there is only a single initial investment, there can only be single IRR and as such XIRR is fine.”

Wouldn’t there be single IRR also when there are multiple investments followed by multiple withdrawals i.e. only one change of sign?

*returned and *arbitrarily

Hey guys,

I feel we’re overcomplicating things here.

XIRR copes fine with both money in and money out transactions and it gives you an equivalent (smooth) internal rate of return – that you would have required to hit the same end result.

The key concept here is that the the IRR can vary massively from the average annual return on the unitised fund prices over time where money is being put in (or withdrawn) over time.

This is due entirely to pound cost / Dollar cost averaging or it’s inverse.

Where your saving for the future – putting money in- then a big dip in your unit price followed by recovery will amplify your average returns whereas if prices race ahead and then fall back this will drag down your average returns.

As i said above – this can be a tricky concept to get ones head around but one of two plain English article that i wrote (for investor’s chronicle last year) to explain it – can be found here http://wp.me/p45vXF-ts

Hope this is of interest

Yeah Paul, I’ve seen your articles, but you clearly oversimplify things, seems like you didn’t read the comments here. With alternating withdrawals and investments things do get complicated to the point where XIRR does not give a single result because multiple are possible and some understanding is required to be able to draw conclusions and maybe pick one of these.

To Paul W.

Well I do try to simplify problems and communicate in plain English. As Einstein said, we should try to reduce all problems to their simplest form – but no further.

My concern is that some comments here overcomplicate the issue.

Are you really saying that (for a given start value, end value and series of inputs and withdrawals) there are multiple solutions to an IRR calculation ?

That would certainly be news to me.

@HRP

” You could then calculate an average IRR by weighting according to the number of units. For example, if you received an IRR of 5% on 10 units, 10% on 3 units and -20% on 2 units, your weighted average IRR would be (5%*10 + 10%*3 – 20%*2)/(10 + 3 + 2) = 2.67%.”

But that would be unit-weighted average regardless of unit prices paid. Had the prices differed significantly you would get a result very different from money-weighted-average and this is ultimately what we invest – money.