The last Zero fighter pilot has one final battle. Telling the Japanese public about the horrors of war.

Essentially Japan's war government had only one big idea to improve their people's welfare. Enslaving the rest of Asia.

It's the equivalent of wagering your house on a single bet - then as well as losing a house, you get caught up in a skin melting firestorm.

Of course, 20-20 hindsight is a wonderful thing and any Japanese politician at the time would have given a more nuanced picture. But at it's heart, it boiled down to total domination or annihilation.

More recently, Japan's old whipping boy, China, has been whittling down their own idea diversity. Experienced China watchers say that president Xi is now the most powerful Chinese leader since Mao, by an unprecedented jailing of every senior opponent.

Multiple Attack Vectors

Multiple opinions can weigh decision making down, but simultaneously working on different approaches to a problem is common sense in a complicated world.

In finance, this is formalised by asset classes. Bonds, equity, real estate and commodities for example. E.g. lend the government money to build roads and earn a small yield; or invest in the next Facebook to help them gain market share.

Each asset class represents a different idea about how to earn a return.

We can go one step further however, by mathematically counting and measuring the money making 'ideas' (aka PCA) contained in a portfolio's returns. Moreover, every idea we find is mutually exclusive (orthogonal) from another.

Would you rather invest in a one idea shop or a fund brimming with creative ways to generate returns? The latter right?


Let's count the ideas of a broadly diversified fund, holding equal parts equities (IWV) and investment grade corporate bonds (LQD).

The maths shows us that there is one idea which explains 90% of returns.

Hard to know for sure, but I would guess that it's a beta bet - rising company value increases stocks prices and bond credit worthiness (note there is not a one-to-one mapping between ideas and assets, these ideas are mutually exclusive, remember!).

Adding commodities (GSG) into the mix gives us another idea. Now 2 ideas are explaining 95% of our returns. Teasing out what these ideas actually mean will take some further analysis.

Real estate (VNQ) adds another strong source of returns. 97% of data is explained with 3 ideas.

Removing the bonds from the portfolio, eliminates the smallest idea. I suspect it was related to interest yield returns. Note how the other three ideas remain more or less steady.


Of the final 3 ideas, one dominates. As suggested above, this might be a beta bet - a good economy raising all boats - which benefits every asset class.

The two smaller ideas are more interesting. They may be related to idiosyncratic situations where real estate and commodities move irrespective of what the wider economy is doing - more analysis would be needed to make this anything but a shot in the dark.

We removed the bonds, but we could have increased their weighting to give us a better spread of ideas and a more balanced portfolio.

Another interesting case would be taking a collection of equity ETFs which claim to be idiosyncratic ideas (value, momentum, small cap, global etc.) and see how significant they are compared to a 'beta bet'.

The essence of investing is systematically generating returns; having as many ideas as possible ensures that you can do that consistently.