**A few weeks ago a reader asked me about the unit valuation system as he was thinking of using it to measure the performance of his investment portfolio.**

I knew what the unit valuation system was, but it wasn’t something I used myself so I said I would write a blog post about it once I’d looked into it.

However, as I researched the unit valuation system it became clear that a different metric, the internal rate of return, was generally preferred as a measure of portfolio performance. So in the rest of this post, I want to describe what these performance metrics are, why the internal rate of return is better and why it might be a good idea to use both.

**Free spreadsheet:**** **If you’re familiar with these portfolio performance metrics then take a look at the free resources page. You’ll find a spreadsheet that can calculate returns using both the unit valuation system and the internal rate of return.

## What is the unit valuation system?

The unit valuation system is a way to measure the underlying performance of an investment whilst excluding the impact of subsequent cash inflows and outflows.

In this context, cash inflows and outflows are just cash added *in* to or taken *out *of an investment, where the investment can be anything you want to track the performance of, such as an individual stock or an entire ISA or SIPP account.

Because it ignores cash inflows and outflows, the unit valuation system is mostly used to track the performance of open-ended investment funds and unit trusts. It works something like this:

Imagine a brand-new but really boring unit trust which will hold nothing but cash. The initial unit price is arbitrarily set at £100. Jack gives the fund manager £100,000 and the fund manager creates 1,000 units and gives them to Jack. On day one Jack is the only investor, so the fund’s total value is £100,000 and there are 1,000 units in total.

A week later, the fund is still worth £100,000 so each of the 1,000 units is still worth £100. Jill invests £200,000 into the fund. This increases the total value of the fund to £300,000.

The size of the fund has increased, but Jack is not any richer. That’s because Jill’s investment also increased the total number of units. When Jill invested the unit price was £100, so the fund manager created an additional 2,000 units and gave them to Jill. So there are now a total of 3,000 units in issue (1,000 belonging to Jack and 2,000 to Jill) and each unit is still worth £100.

As this example hopefully shows, the unit valuation system separates out changes to the value of the underlying investment(s) from changes to the value of the overall fund or portfolio. If you’re adding cash to or removing cash from your portfolio on a regular basis, then the unit valuation system will give you a better idea of your performance than simply measuring the absolute value of your portfolio.

The mechanics of the system aren’t complicated, but they do need a bit of explaining, so here’s a slightly more detailed example:

## How to calculate the unit value of a portfolio

Let’s say Bob invests £100,000 in a FTSE 100 tracker at the peak of the dot-com boom on 01/01/2000. Let’s also say the FTSE 100 was at 7,000 on that day. And for the sake of simplicity, let’s ignore dividends.

We can unitise Bob’s portfolio by setting an arbitrary unit value (£100 is a common starting value) and calculating how many of those units Bob has to start with (1,000 in this case, as he invested £100,000).

So on 01/01/2000, Bob owns 1,000 imaginary units, each unit is worth £100 and the portfolio is fully invested in a FTSE 100 tracker.

Let’s fast forward ten years. It’s 01/01/2009 and the FTSE 100 has fallen by 50% from 7,000 to 3,500 (it’s the middle of the global financial crisis). Bob’s portfolio is now worth £50,000, so it’s down 50% in line with the FTSE 100. Bob still owns 1,000 units, so the value of each unit has also fallen by 50%, to £50.

Bob decides to invest another £100,000 into the same FTSE 100 tracker. With a unitised portfolio, cash inflows change the number of units in the fund rather than the value of each unit. This is what allows the unit valuation system to ignore the impact of cash flows.

In this case, each unit is now worth £50, so Bob’s additional £100,000 cash inflow buys 2,000 additional units. The total value of the portfolio is now £150,000, the total number of units is 3,000, and so the value of each unit is unchanged at £50.

Let’s fast forward another ten years. It’s 01/01/2019 and the FTSE 100 is up 100% from 3,500 to 7,000. As a result, the total value of Bob’s portfolio has also increased by 100%, from £150,000 to £300,000.

The total number of units is still 3,000, so the value of each unit has increased by 100% to £100, in line with the FTSE 100. To finish off the example, Bob now makes a cash withdrawal of £100,000. Taking cash out of a unitised portfolio reduces the number of units rather than the value of each unit, effectively excluding cash outflows from the measure of performance.

In this case, the unit price is £100, so the £100,000 cash outflow sells (and deletes) 1,000 units. This leaves the portfolio with assets of £200,000, the number of total units at 2,000 and the value of each unit at £100.

This may seem like a lot of work, but with the help of a unit valuation spreadsheet it should take no more than a couple of minutes each month or year or whenever you revalue your portfolio. And there are a lot of benefits, especially if your cash inflows or outflows are large relative to the size of your portfolio.

## Measuring unit value vs measuring total portfolio value

In the above example, if we simply measured the total value of the portfolio we would see it going from £100,000 in 2000 to a peak of £300,000 in 2019 (before the final cash withdrawal). That’s a maximum increase of 200%.

However, all of that growth was due to the cash inflow of £100,000 in 2009. While the total value of a portfolio is a very sensible thing to measure if you are, for example, saving towards your retirement, it doesn’t reflect the underlying growth rate of the things you were investing in; in this case the FTSE 100.

To track the performance of the underlying investments we need to strip out the impact of cash inflows and outflows, and that’s exactly what the unit valuation system does.

So in the example, the value of each unit was £100 in 2000, £50 in 2009 and £100 in 2019, accurately reflecting the fact that the FTSE 100 went from 7,000 in 2000 to 3,500 in 2009 and finally to 7,000 again in 2019.

Okay, if you’re invested in a single fund and don’t have much in the way of cash inflows and outflows then yes, unitising your portfolio is probably overkill.

But, if you hold 20 or 30 investments and you’re adding cash on a regular basis, tracking your investment performance is going to be much harder, and that’s where the unit valuation system can make a lot of sense.

So the unit valuation system is great if you want to see the performance of your investment(s) excluding the impact of cash inflows and outflows. But in the real world, the size and timing of cash inflows and outflows can matter a great deal.

## Why cash inflows and outflows matter

Looking back at the previous example again, we see no growth in the unit price between 2000 and 2019. This does reflect the zero growth seen in the FTSE 100 between 2000 and 2019, but it doesn’t reflect the actual returns achieved by the investor (Bob in the example).

How so? Well, Bob invested £100,000 in 2000 and another £100,000 in 2009. And yet by 2019, Bob’s portfolio was worth £300,000. In other words, the portfolio was worth £100,000 more than the amount Bob invested, giving a 50% return on investment over the period rather than the zero percent return suggested by the unit valuation system.

This difference arises because Bob invested in two separate chunks, and each chunk (even though both were invested in the same underlying investment) has its own rate of return whereas the unit valuation system only calculates the return of the first chunk.

The first £100,000 invested in 2000 saw no capital gains because the FTSE 100 was at 7,000 in both 2000 and 2019. But Bob invested another £100,000 in 2009 when the FTSE 100 was at 3,500. That second £100,000 was then worth £200,000 in 2019 because the FTSE 100 doubled to 7,000. The final value of the portfolio, £300,000, is the sum of those two separate investments.

So cash flows matter. They can provide a tailwind or a headwind, depending on their size and whether the corresponding purchases are at attractive or unattractive valuations.

Fortunately, there’s another way to measure portfolio performance which sits somewhere between the unit valuation system (which completely ignores cash flows) and simply measuring changes to a portfolio’s overall value (which is overly sensitive to cash flows).

This metric is known as the internal rate of return, and it’s super-easy to calculate with a spreadsheet.

## What is the internal rate of return?

The internal rate of return looks at your portfolio as if it’s a black box. You put cash in, you take cash out and at the end, there’s a certain amount of cash left inside the box. The internal rate of return tells you what annual rate of return the black box must be providing (internally), given that specific combination of cash inflows, cash outflows and final cash value.

Let’s go back to the second example. Bob put £100,000 into a black box on 01/01/2000 and another £100,000 ten years later on 01/01/2009. Another ten years later Bob opens the box and there’s £300,000 inside. The box contains 50% more cash than he put in, so clearly, the box’s internal rate of return is somewhere above the zero rate of return given by the unit valuation system.

Calculating the internal rate of return by hand is actually quite laborious. You have to make an initial estimate of the rate of return and then iteratively tweak your estimate until the results more or less match up with reality. Fortunately, it’s much easier to use the XIRR spreadsheet formula, which I won’t cover here as there are many good explanations online.

Entering the figures from the previous example into my Portfolio Performance Spreadsheet (available here) tells me that the internal rate of return of Bob’s portfolio was 2.78% over the period from 2000 to 2019. This is a useful amount more than the zero percent figure given by the unit valuation system, and it shows that cash inflows and outflows do matter.

This is especially true if you’re actively choosing when to add or remove cash in an attempt to boost returns.

## Why it could be a good idea to use both the unit valuation system and the internal rate of return

In general, the go-to measurement for portfolio performance should be the internal rate of return. That’s because it captures the impact of cash inflows and outflows, which do matter.

However, the unit valuation system is also useful because it allows you to track performance with the impact of cash flows completely excluded, and this can help you isolate and analyse the impact cash flows are having on your performance.

For example, the unit valuation system said the underlying performance of Bob’s portfolio was a gain of zero percent over 20 years.

In contrast, the internal rate of return said that Bob achieved a 2.78% annualised return from the same portfolio over the same period, thanks to the additional cash injected into the portfolio when the FTSE 100 was at a low point in 2009.

If that cash injection was pure luck (perhaps Bob had been made redundant in 2009 and was investing his £100,000 redundancy payment without really thinking about boosting returns), then by measuring both the unitised rate of return and the internal rate of return it’s possible to see *how *lucky Bob was (his luck was worth 2.78% annualised over 20 years).

But if that cash injection was intentional (perhaps Bob sold his Ferrari and invested the £100,000 proceeds into the market at a low point precisely because he thought it would boost returns) then we can see *how *skilled Bob was at market timing (his skill was worth 2.78% annualised over 20 years).

So although the internal rate of return is a better measure of actual performance, the unitised rate of return provided by the unit valuation system is probably also worth calculating as well, as is the gap between the two.

To help you (and me) with this, I’ve added a Portfolio Performance Spreadsheet to the free resources page which will do most of the legwork.

I’m sure it isn’t perfect, so if you spot any bugs, or have any feature requests, just get in touch or leave a comment below.

Very interesting John. Need to look through it a few times to get my head around it. One question. If the portfolio being measured is a SIPP or LTISA , then the tax rebate added… should that be counted as cash flow ? (even though the cash has not been put in by your self ie should it be treated as if it were a dividend in effect.) Regards

Hi Steve, personally I think I would add it as a cash inflow. It’s money coming into the portfolio from an outside source (the government) rather than from one of your investments, so in that regard it’s no different than cash paid in by you. If you don’t include it as a cash inflow then the unit valuation system will see it as an investment return and include it in the unit value. This will make you think you’re a better investor than you (already) are.

Good article. Personally I have been using both since 2015 and have found them to be relatively close. The Unit method is simpler with the aid of a spreadsheet and I find that it gives a satisfactory indication of performance. It really depends on the purpose behind this but unless you are a fund manager, this is not an area where precision really means much especially as random fluctuations in prices can change values considerably over short periods..

Hi Lemsip, thanks.

I think you’re right. Over time there is unlikely to be a large gap between UVS and IRR.

However, as you say they’re simple to calculate with a spreadsheet so there’s no harm and potentially some use in tracking both.

What really matters is the annualised number over the long-term (i.e. more than ten years). If that figure is markedly below the total returns from a similar index (the FTSE All-Share in my case) then something is going wrong with the investment process.

I think the time period for evaluation is a crucial issue. A year is too short but in my view 10 years is way to long to evaluate investment performance – for the simple reason that by then it is simply too late to recover since we have a small number of investment decades and the later ones tend to have fewer options for recovery via human capital.

I have found a 3 year period to be the bare minimum and a 5 year period useful. I evaluate performance at the end of each year for the preceding 3 year and 5 year periods. I have fought that investments that are losers over 3 years tend to be bad businesses which I generally ditch. Also as I live off investments and always carry a cash buffer, I expect to be directionally in line with all equity benchmarks ( MSCI world in my case) without needing to be close. Through luck I have somehow managed to keep ahead in every 3 year period since 2011 but am sure a stinker of a 3-year is going to come along one of these days

For me, ten years is the gold standard. If I’m not keeping pace with (and preferably beating) my benchmark over ten years then I should probably throw in the towel. But as you say it’s a long time, so I also look at five-year performance, where I hope to beat the market but wouldn’t shoot myself if I didn’t. I think anything less than five years isn’t worth worrying about, but the exact cut-off doesn’t really matter.

As long as an investor isn’t worrying about underperforming the market by 10% over a year then they’re probably on the right track.

Having said that, the magnitude of underperformance (and possibly outperformance) matters too.

For example, if I underperformed the All-Share by 50% in a year then that’s a pretty good clue that I’m doing something wrong. And if I beat the market by 50% in a year then either I’m a genius or I’m probably taking too much risk (the latter seems much more likely).

Given my fairly “normal” holdings I think either of those outcomes is highly unlikely, but for more risk-seeking investors it might be worth thinking about.

The problem with the IRR is that it is a forward looking indicator i.e. it shows an expected return if you are sitting at period 0, but it does not work well if you are 5-10 periods (e.g. years) down the line. This is because later cash flows are increasingly discounted and have decreasing effect in the calculation. After 10 years any improvement in the periodic returns have little effect in the overall IRR.

Hi Freddie, that’s true. A good example is Buffett where his long-term returns are skewed upwards by exceptional returns decades ago compared to slower returns in more recent years.

But that isn’t a fault with IRR, it’s a problem with the period being measured. So I think it’s probably a good idea to track IRR (or any rate of return measure) over various periods such as the most recent five or ten years, as well as from ‘inception’ (or as far back as you have data).

I have unitised since the beginning of PEPs. I learnt the method from our investment club in the mid 80s, where we used accumulation units to deal with people joining and leaving. We were shown how to do it by a visiting speaker from the City.

I run two portfolios myself, plus do the record keep for another three. All are unitised, both for accumulation and income units, since once set up the spreadsheet does it all.

There are no violent cash injections or withdrawals in any of these portfolios, (which would throw XIRR into a temporary wobbly) although some reinvest Divis, some take income, some add monthly sums, some irregular amount, some don’t.

In all instances after about 8-10 years the XIRR and compound growth in Accumulation units have basically converged and will stay very close unless vast cash movements (in relation to portfolio value)occur, no surprise since they both attempt to calculate TR. For example in my ISA, since January 1987, the XIRR is 11.32% at tonight’s update, the acc units have compounded at 11.37%. Basically identical and no surprise. Since my ISA invests for highish yield, the important figure to compute is the growth of Divis per income units, which must be above RPI imho. Over the period these have compounded at 6.13%.

I have looked at a few web sites where people unitise, but I must say lots of unitisers make a pig’s ear of it. The most common mistake is when there is a special attached to a share consolidation, which is NOT a portfolio event which leads to any unitisation computation, being an internal reorganisation of one’s capital base. There are a few other mistakes, another common one is to fail to compute acc units properly when all income is withdrawn:in that instance it is important to first pay the dividend in the portfolio, which increases the value of the acc units, and withdraw the divi cash as a separate operation, which decreases the number of units, if that is not done properly acc units will undershoot their true value.

MGH

Hi MGH, thanks for highlighting some common unitisation errors. I just double checked the unitisation spreadsheet mentioned in the article and it doesn’t seem to fall foul of the dividend withdrawal issue you mentioned, so that’s a relief.

To be honest, I’m quite new to unitisation, having been too lazy to do it with my personal portfolios. I’m in the process of digging up as much historic data as I can in order to unitise as far back as possible, so I’ll keep your comment in mind and try to avoid some of the more obvious mistakes.

Hi John,

Forgot to say, since you presumably have my email address, if you are interested I can send you a complete write up covering all aspects of Unitisation from which you are free to build an article. I have run many workshops on Unitisation many years ago.

I must remain anonymous though.

Regards

MGH

Okay, thanks. I’ll send you an email.

Hi John,

I’m focusing on measuring investment performance so thank you for this article. I’d like to share with you what I intend to do and I’d be very grateful if you could confirm if I am along the right lines. Apologies if this is very newbie. I have decided to calculate the individual investment performance of all my stocks using XIRR where I have any purchase investment as a negative values, all income from dividends as positive and the last row as the present value of the stock along with today’s date and previous dates for everything before. This is repeated for all stocks i own. In order to find portfolio return, I intend to calculate the weight of each holding in the portfolio by dividing the individual stock value by the entire portfolio value and then multiplying this weight by the XIRR figure provided for each stock. Finally, I intend to add all these weighted returns up which I’m led to believe will give me my portfolio return. Is this correct? Thank you for your help; I just want to make sure I understand this!

Hi Liam

Your calculation of IRR for individual holdings sounds right. As for calculating overall portfolio return, I prefer to use IRR at the portfolio level too. So the portfolio value (including cash) on a date would be entered as a negative, cash in/out would be recorded as negative/positive amounts and then the current portfolio value (including cash) would be recorded as a positive amount.

For example:

01/01/2010 : -£100,000 (portfolio value)

01/01/2011 : £5,000 (cash withdrawn)

01/01/2012 : £6,000 (cash withdrawn)

01/01/2013 : -£20,000 (cash added)

01/01/2014 : £150,000 (portfolio value)

That gives an IRR of about 9.1% for that portfolio.

I think your idea about summing up weighted returns of individual holdings could work you’d need to be careful about what weightings you’re using, whereas we know that IRR works for individual stocks and whole portfolios.

Great, thanks John. Based on that I’ve actually gone and used IRR at a portfolio level. I have a sheet with all my purchases, sales and dividend payments and just performed the IRR on that data using a few formulas in Google Sheets. Sadly, the return isn’t looking great; it’s been a torrid few years since I started in 2018!

Yes it’s been a bumpy and disappointing few years, but 2018 is only yesterday in investment terms so you’ll need a few more years in the game before you really have an idea of how things are panning out!