**Compounding**

One of the things that surprised me more than I thought was the impact of costs on long term performance. It was not until I created a simple spreadsheet did the penny drop. Albert Einstein once said that ‘Compounding is the eighth wonder of the world’. And there in lies the real secret the financial industry would rather you did not see. Is it any wonder the financial services industry is so wealthy and hold such economic power.

We shall see. Let’s first of all understand what compounding actually means.

Essentially, in mathematics there are many types of series, but for practical purposes, I consider there to be two: Arithmetic & Geometric (as I was taught in A-Level pure maths). Pretty much everything else is a variation on themes. Arithmetic series are characterised by each number being separated by a fixed constant. For example, 1,3,5,7 and 2,8,14,20. Geometric series the gap between the numbers changes in a non-linear fashion (getting smaller or larger).

It is very easy to look at a holding and a target return and see it gives 3%, 4%, 5% return in a year. The issue is what happens the following year. Now that depends on whether the return is reinvested or removed. Fundamentally, that is the difference between a straight Arithmetic return and a Geometric (or compounded) one.

Just creating a simple model investing £10,000 with a yield of 5%.

- Option 1 – just take the yield and leave capital means taking £500 pa and at 10 years the capital and yield collected would have returned £15,000 .. 50% !! sounds great
- Option 2 – re-invest the yield. End of 10 years the capital is worth £16,289 .. +63% … even better

So on the face of it a slightly better worth by re-investing …. Oops … forgot about two factors (ignoring costs right now)… Inflation, and capital growth.

**Add in Inflation**

Lets assume inflation is a round 2%. This means that each year a fixed amount of money is worth less. If I have £100 today, in a year’s time in real terms it will be worth £98, the following year in real terms £96.04. That is ‘real terms in todays money’. Net Present Value (NPV is a simple concept – it tries to model the real value of forward cash flows to allow investment choices to be compared, but can be tricky to be really accurate. In the end, I use KISS (Keep It Simple Stupid). As a private Investor (PI), I just want a pretty good idea – I am not getting it to the exact penny for a tax return !.

So, with inflation at 2%,

__Option 1 (NPV)__– Total return of £12,911__Option 2(NPV)__– Total capital value of £13,581

Again .. this really does not sound a lot of difference

What about if I use a basic fund growth rate of the same as inflation (2%)

__Option 1 (NPV)__– Total return of £15,154__Option 2(NPV)__– Total capital value of £16,401

Mmmmhhh … still not showing a lot of total return difference. Well, maybe that is because Total return is not the only picture.

For the last simulation (2% growth + 2% inflation), the NPV of the respective yields relative to the initial investment is 5.0% and 7.7% respectively (ie, still £500 for option 1, but £766 for option 2: almost 54% more yield in real terms).

The power of compounding is not in growth . Growth is growth and based a wide variety of market factors. The power of compounding is to create greater future income streams.

**What about a basic Idea of Cost impact**

Perhaps more on costs another time, but for a quick look, if I assume the platform and transaction costs run at 0.8% pa and just deduct this from growth (just as its simple to see the effect) then the effective growth rate would be 1.2%.

__Option 1 (NPV)__– Total return of £14,212 (6.2% less), Yield (NPV) £464 (7.2% less)__Option 2(NPV)__– Total capital value of £15,215 (7.2% less), Yield (NPV £716 (6.4% less)

It is not hard to see the impact of costs. And interestingly, the balance of Yield rates, Growth rates and relative investment risk along with costs governs what the real returns can be. It is not hard with a simple spreadsheet to show that a very low cost holding with a modest growth and yield could outperform a higher growth holding with a higher set of costs. This is why the phrase ‘you cannot beat the market in the long run’ is used by passive investors so much. Active management can and does give very high returns … but not forever. Just look at how Woodford has performed since setting up his own fund. It is also why firms like Vanguard have taken so much market share – KISS and keep the costs low.

As I intend exploring in the future, simulation is a very useful way of evaluating the impact of costs, or risks and of particular approaches to re-investment and divestment. I found that trying to create something that would ‘predict’ is futile, and it was only when I started to try and understand behaviour of the numbers that the picture sharpened for me. Ultimately leading to ideas such as ‘Bucket Strategy’, Modelling future personal income needs and the like.

**In Summary**

- Compounding is not about increasing fund value (that is a mere effect)
- Compounding is a means to secure Higher real terms income and mitigate against inflation and random negative growth periods

I feel sure may have a different view – but so far, this one works for me and helps me keep a focus on long term goals and not short term fluctuations