Investment Mindset Bootcamp. Stop Gambling. Start Accumulating Long Term Wealth. Step 4.

Step4. The Simple And Essential Math Of Investing.

Very little is more important, when it comes to investing than understanding the basic dynamics of risk and return and how to use these two crucial concepts to your best advantage.

In order to get there, however, it is important to actually do the work, and be ready to discard preconceived notions and embrace new ideas. Make sure that you are truly grounded in the simple and essential math of investing, so you can stay consistently focused on what is really the key to accumulating long term wealth.

In step 3, the LTCM example showed why sole use of returns as an assessment of investment success is potentially disastrous. So, just for this reason, but there are other reasons too,  returns, by themselves, should be discarded as a sole  investment assessment metric.

In step 4, it is important to start examining risk in relation to long term returns. Remember our objective is to maximise returns through the full economic cycle.

In step 5 the key investment metrics will be defined.

Risk and returns


In very few human occupations do people embrace risk in isolation of some purpose. After all risk means embracing the possibility of an adverse outcome not in your control. It seems that no one would want more of that, without some prospect of gain.

However, when it comes to investing I find that some people do embrace risk! I believe that the only reason for this is that for many they have an equation in mind. If they want high returns, which they do, they believe/think they need to commit to higher risk.

In the very short term this has validity to the extent that high volatility assets by definition go up and down more in the short term. You will obviously make or lose more in the short term in a high volatility asset.

However, for our stated objective a portfolio of assets is chosen, and it usually takes several years to complete an economic cycle. Is it really the case that what is true for individual assets in the short term is also true for asset portfolios over many years?

It is crucial to examine this thought extension, because this simple concept lies at the root of so many decisions and discussions. What if this theory is simply wrong?


This is a huge and dangerous assumption. Does more portfolio risk really equate to a higher return? To the extent that’s not true then many investors are taking far too much risk, and are increasing the likelihood of sub-optimal outcomes or worse.

I believe that what we cover below will change the way most investors approach investing, as simple and essential math takes us on a different journey away from commonly believed investment myths about the relationship between risk and long term returns.

The Math

The starting point is to confirm that one of the most powerful forces in investing is simply:

1.Consistently compounding positive returns.

The chart below shows the exponential growth assuming 6% growth, and the importance of time in building your savings.

https://www.businessinsider.com/saving-at-25-vs-saving-at-35-2014-3

If only it was just that simple!

Naturally, there are big assumptions here, that money can be made consistently at a constant positive rate every year without risk.  

Historically, this has sometimes seemed to be a reasonable proxy for the general investment environment. With high enough interest rates and good yields on government bonds, and stable to low inflation, you might get close to those ideal conditions.

However, low and rising interest rates over the last decade mean that the current environment has a very different dynamic.

Nevertheless, this is a good start for how to think about the purpose of investing and how compounding consistently positive investment returns can work out very well. This is what most investors have in mind when they think about investing.

What happens in reality when losses are a possibility?

2.The “power of compounding” ONLY WORKS when you do not lose money.

Once you introduce losses the whole dynamic changes.

These results show the advantage to an investor’s long-term wealth of finding a manager with consistently positive returns, even if these returns are all in single digits.

Manager A at first glance may seem very uninspiring. This manager never has outstanding up years like the other managers. However, every year is positive, and despite some small volatility, he is the only manager who actually experiences a compounded return above the sum of the annual returns, which are the same for each manager.

Manager B and especially Manager C may have much more exciting returns, or so it may seem. At first glance, just viewing the last 3 years of returns, might suggest they may be better managers of your wealth even though they both lost money in year 4.

A 5-year analysis, however, suggests that in this case, that conclusion could be very wrong! Manager A outperformed both Manager B and Manager C, while also preserving the wealth of the investor much better. In fact, Manager A managed to both lower the investor’s risk AND produce a higher return over 5 years. This brings us much closer to the initial ideal  above on both counts.

This also shows how a LOW RISK approach can be part of what it takes to accumulate HIGHER long term wealth.


3.Losses are far more harmful to long term returns than most investors understand. A loss is asymmetrically worse than the same amount of gain for your long term wealth accumulation.

The 5-year compounded return comparisons show that losses in any year can be devastating for an investor’s long-term return. They are disproportionately damaging as they require disproportionate gains to offset the losses.

Even then no account has been made for the time it took for both the drawdown and the full recovery. There was a zero return for that time period. So a further additional gain is then required to make up for no return over the whole period.

For example, let’s assume that a 4% gain per year is the benchmark for the managers above. However, what if in one of the years a 20% loss is made by one of the managers. How much return would he have to make in the following year to get back on track with a 4% compound rate over the full 2 year period?

Answer: A 20% loss takes the value of 100 down to 80. To return to 100 the manager needs a 25% return (100/80 = 1.25). Then the investor would still lose 2 years of 4% compounded return to achieve the benchmark. So to get back to the benchmark the manager would need to make 35% (1.25 x 1.04 x 1.04 = 1.352) to make up for a 20% loss. Almost twice the loss!

That is a tall order for just a year, but if the manager can’t do it the deficit keeps rising at 4% a year, and the make up gain gets bigger! It then becomes 40% (1.25 x 1.04 x 1.04 x 1.04 = 1.406). Note the make up gain rose by 5%, which is higher than the 4% benchmark required each year. The compound returns required will get further and further behind the longer it takes to make them back!

Most likely the loss may never be recovered without excessive risk taking which could land the investor in a deeper hole!

Even with the 38% return in year 5, Manager C still only had a 5-year return of around 1% over the whole period.
It is very hard to recover from losses. For this reason, losses are devastating to long term returns.

So a lower risk manager may, in fact, increase the likelihood of long term wealth accumulation! Not what many investors understand or believe!


4. Reinforcing this point, there is an additional observation to be made from the example above. Not just losses but consistency of return through any investment conditions compounds at a faster rate of return than highly variable returns!

Manager A outperformed the other managers but failed to beat the 4% compound rate over 5 years of 21.67%. That was only a small miss, compared to 21.5%, but the more variable the returns are the greater the miss, and over long periods of time with greater variability, this can become a much wider gap.

Once again a low risk manager will outperform in the long term just on the basis of lower return variability.

5.Many Investment Strategies make more money simply through understanding that a lower risk strategy produces higher returns! 

Rather than embracing risk wouldn’t it be better to figure out how to make higher returns with lower risk? There are many examples of this that most investors are unaware of. Surely, this is a far more productive discussion for investors to have. This begins to happen when an investor starts to appreciate that return relative to risk may lead to a better investing metric.

“The fact that low risk stocks have higher expected returns is a remarkable anomaly in the field of finance. It is remarkable because it is persistent – existing now and as far back in time as we can see. It is also remarkable because it is comprehensive. We shall show here that it extends to all equity markets in the world. And finally, it is remarkable because it contradicts the very core of finance: that risk bearing can be expected to produce a reward.”   Nardin L. Baker and Robert A. Haugen.

Source:  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2055431

https://www.fundsmith.co.uk/news/article/2018/08/31/financial-times—busting-the-myths-of-investment

Low risk equities make higher returns!

Investors and advisors, who are unaware of this research may well be embracing higher risk equities in their allocation expecting it to produce higher returns.

This comprehensive research suggests that in reality they should expect not only higher risk, but also lower returns!

Furthermore, we now have compelling evidence that the core concept of most investors and advisors is simply wrong!

The research above can then be taken a step further. Tradestops, introduce a series of adjustments to equity investing that lower risk further, and also at the same time increase returns.

STS and Equal Risk Strategies on True Wealth

Money Management Systems are crucial to Investment returns.

Source: https://tradesmith.wistia.com/medias/enfb4obmj4

The purpose of investing

Most of us are attracted to the idea of taking risks and winning big. It’s easy to be envious of someone else who claims great riches from investing and want the same. It’s exciting to many just to play the game of investing and trading. No doubt there are many other reasons why investors are drawn to investing, but I believe that the purpose needs to be stated clearly to have any chance of long term success.

Our objective or purpose has already been stated. To maximise our return over the whole economic cycle of the 4 quadrants of growth and inflation directional combinations.  

The math above speaks very powerfully that CONTAINING RISK, NOT INCREASING IT, has an indispensable role to play in accumulating long term wealth.

Point 3 above makes the point that losses simply must be contained in order for any long term compounding to work.

Point 5 demonstrates that lowering equity asset risk can even add to long term compounding returns. The simple risk return relationship assumption simply does not apply to individual equities, as measured over multiple decades across 21 developed countries.

The points made here are sufficiently compelling for us to fully reject the investment myth that higher long term returns always require higher levels of risk taking for asset portfolios over the full economic cycle.

Investors and their financial advisors need a new framework and whole new level of thinking, behavior and discussion if they are going to achieve our investment  objective.

In step 5 I will set out the investment metrics that I believe lead in a better direction, not just in order to achieve our objective but also to enable a better platform for financial planning and even lifestyle benefits resulting from lower stress and a more stable financial platform.

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