Tuesday, 3 June 2014

The five minute portfolio



If you make the mistake of telling people in a social situation you are 'in finance' then they will usually have a specific kind of follow up question. This is basically the equivalent of telling people you are a doctor, at which point they will ask you about this little niggle or mole that is worrying them. If you are in finance you will usually get 'Should I buy or sell X'? This post aims to answer the general question of that - what stuff should I hold in my portfolio?

To approach this problem we need to think about two questions

- Which assets I should hold?
- What proportion should I hold them in?

As a trailer for the second question I will be using some relatively interesting results using bootstrapping to optimise portfolios. So people for whom this entire question might seem trivial might want to skip ahead to the fun bit. This, and only this, is what separates this post from other 'lazy portfolios' you can find on the Internet – I will show you the 'moving parts'. 

For some other lazy portfolios this is a particularly good site and worth reading first if you really are a complete novice http://monevator.com/passive-investing-model-portfolio/.  

Essentially this is a post on how even quite ordinary people can make use of the results of some fairly funky quantitative techniques, without being experts. Or without having to pay for it.


Which assets should I hold?



For the first question I am going to assume a particular kind of person is doing the questioning. Since I don't tend to hang around with pension fund managers the person asking me is normally a relative novice at investment, with a relatively small amount of money and no time or interest in becoming an expert. For such a person I advocate a 'five minute portfolio'. Five minutes is how long it takes to construct, and then you might want to spend five minutes a year thinking about it. It may well take you longer than five minutes to read this initial post, but that isn't included. If you really don't want to spend any more time on this exercise then feel free to scroll to the end where the actual portfolio is shown.

First I am going to assume that you want to hold the best portfolio possible. Since the only free lunch in finance is diversification that means you want the most diversified thing possible.

If you have a relatively small amount of money I would say there is no value in holding individual stocks. The fixed costs of purchasing stocks mean that buying less than say £500 of something isn't economic. You will be lucky to pay dealing fees of £10 plus stamp duty of £2.50; so a 2.5% hit on your assets on day one. If you have £10K and you use it to buy 20 UK listed equities then you've got a portfolio that is just starting to be diversified within UK equity space; but has absolutely nothing outside UK equities. Using up those £500 chunks on individual stocks and bonds is just unnecessary.

As an individual there is also the advantage that you will feel less attachment if you aren't holding individual stocks. This abstraction is a way of reducing the cognitive bias of overconfidence and will reduce the chances of you wanting to over trade your portfolio.

I am going to assume that there is no skill in investment management, or at least that the price you pay for it isn't worth it. This puts unit trusts and investment trusts off the menu, as well as hedge funds (which in any case are inappropriate for the kind of people I meet at parties, since I don't tend to go drinking with wealthy oligarchs). Perhaps a bit harsh, especially given my former career, but this really cuts down on the menu of options and reduces the time you have to spend thinking about whether a particular portfolio manager is worth his 100bp or 2 and 20. I actually like investment trusts and you should consider using them for certain foreign holdings especially if they are trading at a discount to NAV. But the process of checking that discount bumps up the time required from 5 minutes, so bear that in mind.

So I would argue for a small relatively inexperienced investor that a highly diversified portfolio of Exchange Traded Funds (ETF's) is most appropriate. They are relatively cheap, passive trackers. Arguably this is likely to outperform in the long run a portfolio of individual stocks, particularly if they are focused on one country. Since that is all most active retail investors hold, you're already ahead of the competition.

I will ignore tax, so I don't mind if you are holding this stuff in your ISA, self invested pension, in a plain old brokerage account or in share certificates stuffed under the nearest matress. This isn't a question about which investment wrapper is best, but about which stuff you should put in your wrapper.


Which ETFs?



I am going to focus on the ETF's provided by Vanguard and iShares. This is because vanguard are very cheap on fees, but with a limited offering; and ishares have a very big offering (as well as quite a nice website) but tend to be more expensive. There are probably slightly cheaper ETF's out there and it might be worth doing the research on this. I will also assume you are a UK domiciled investor who wants to own assets listed on the London Stock Exchange only (though the funds might be listed in Ireland for example).

Disclosure: I have no connection with eithier firm, but I did partake of some iShares corporate hospitality several years ago. Other ETF's are available!

By the way this allocation amongst ETF's is something you can pay someone like nutmeg to do for you. Its not something I would personally bother with, but if five minutes is a bit too much of a commitment and you don't mind paying the additional fees involved then be my guest.

If we think about kinds of asset classes there are in the world then at the top level we potentially have:

- equities
- government bonds
- corporate bonds
- Property and land
- Foreign currency (FX)
- Commodities (Agricultural, Metals, Energies)
- Infrastructure
- Private equity / Venture capital


As an individual investor its quite hard to access many of the latter of these objects in a pure sense. The last two often require big minimum investments. In ETF land when you see these listed you are usually buying into listed companies holding these assets. This means you are just holding equity investments. Commodity indices have their own potential problems depending on if they hold the physical asset or trade futures. There is some argument over whether FX is even an asset class.

I'm also going to ignore property. This is because again the ETF's mostly include listed property equity rather than 'real' property, and also because most investors already own a house which gives them property exposure. Finally I am also ignoring various strategies 'smart beta', 'sustainability' and 'minimum volatility' ETF's. We want to keep it easy. All these more complex things also tend to be more expensive. 

The arguments about the rights and wrongs of sustainable investing is for another post. However if this does float your boat you can substitute sustainable ETF's where possible. This will reduce your choice and cost you more in fees; which may or may not be made up for in performance. I am not saying this is an ideal state of the world, just stating the facts.

So we are looking at a portfolio of:

- equities
- government bonds
- corporate bonds

For each of these I am going to want something which is geographically diversified. Ideally I would also want to be diversified around different sectors of the economy; but with a maximum of say a dozen ETF's that just won't be possible.

 

Portfolio optimisation 101


Do not worry if the following is gobbledygook. You can just skip ahead to the results if you find it hard going.

Considerations when allocating portfolios are:

- Expected gross return
- The correlation of returns
- The volatility of returns
- Fees

These are in order of unknowability. It is really hard to forecast returns. Correlations are a little more stable, volatility more so, and fees are known with certainty.

I am going to assume that we can't predict expected gross return. Like the rude comments about fund managers above this might be a little harsh. However this does simplify things immensely, and although there are models which do a reasonable job of forecasting returns they require some effort to implement.

To deal with fees is simple; where we have two ETF's that do roughly the same thing we will go for the cheapest. For example IUKD from ishares costs 0.4% and VUKE (Vanguard) costs 0.1% (note I am measuring fees on 'TER' which isn't perfect, but is simple). In practise this means we will use cheaper Vanguard funds for our equity ETF's, only turning to ishares for bonds.

When I actually do in my optimisation I am going to assume that everything I have has the same net Sharpe ratio, i.e. the returns scale precisely to the realised volatility. Of course this isn't quite the same as assuming the same unknown gross return and subtracting known fees; but it is neater. I am also going to assume that we have an annual risk threshold of 10%. This is about as risky as the FTSE 100 ETF returns over the last year (I will relax that assumption at the end). 


 The ETF menu

 


So all we are left to worry about is covariance - correlation and volatility. Essentially we want pretty much to choose the ETF's with the lowest correlations and offering the best diversification. Given our limited menu that means we won't able to buy ETF's for every country in the Eurozone for example, as they are likely to be quire correlated and that's a waste of our limited number of options.

Initially lets suppose we have £10,000. I want to buy my ETF's with say a minimum of £500 for any one in my theoretical £10K portfolio. It turns out that around eight fairly diversified ETF's will tend to have an allocation of at least 5%. So I will start with the following four Vanguard equity funds (all cheaper than their ishares counterparts):

VUKE FTSE 100 UK
VAPX FTSE Asia
VEUR FTSE Developed Europe
VUSA FTSE S&P500 US

And these four ishares bond funds:

IGLO ishare global government bonds
SEMB emerging markets $ government bonds
HYLD global high yield corporate bonds
CORP Global corporate bonds

I won't spend too much justifying this selection; particularly with ishares availability of choice we could have chosen a slightly different set of bond funds but it probably won't affect our performance too much.


The hard maths bit



Because some of these ETF's are quite new I've only got about a year of daily price data. This isn't much. Step one is to run a 'point estimate' optimisation of the above just to see what it gives us. I say point estimate because we are going to estimate a single covariance matrix of returns based on all the history we have. This is what people normally do when they do portfolio optimisation. This gives us a very unbalanced portfolio (some would say insane).

  • 0% VUKE FTSE 100 UK
  • 69% VAPX FTSE Asia
  • 0% VEUR FTSE Developed Europe
  • 0% VUSA FTSE S&P500 US
  • 3% SEMB emerging markets $ government bonds
  • 10% IGLO ishare global government bonds
  • 11% CORP Global corporate bonds 
  • 18% HYLD global high yield corporate bonds

Two questions we should ask; firstly am I comfortable with such an extreme portfolio based on only 12 months of data? (Answer for me: No). Secondly is the last year representative enough of likely future history?(Answer: Probably not).

Thinking about the first question; the problem is that by using a point estimate of the covariance matrix I am missing out on the fact that there is a lot of noise in the underlying data. A better method is to use bootstrapping. What we do is randomly select 30 days worth of returns and estimate our portfolio based on those. Note that this destroys any structure of returns through time, if that is important. What is nice about bootstrapping is that with more evidence: more history and the more structure in the data, the more the weights are allowed to deviate. So if the last year is unrepresentative it can't do too much harm.

We then take an average of the bootstrapped portfolios and voila.

The result is much more reasonable:

  • 6% VUKE FTSE 100 UK
  • 28% VAPX FTSE Asia
  • 21% VEUR FTSE Developed Europe
  • 10% VUSA FTSE S&P500 US
  •  7% SEMB emerging markets $ government bonds
  • 8% IGLO ishare global government bonds
  • 10% CORP Global corporate bonds 
  • 10% HYLD global high yield corporate bonds


The 65:35 split in bonds and equities is pretty similar to what you will see in many example portfolios around the internet. However this means that around 78% of the portfolio risk is coming from equities. The higher allocation to Asia and Europe reflects they are more diversifying; the US market has been too correlated to the UK but also to global bonds thanks to QE. If you believe the last year has been unrepresentative in that respect you might want to reallocate a little from other equity markets to the US. This can be done formally using something like Black litterman or shrinkage.


I repeat the process with 6.5% and 7.5% risk targets. The first gives us half our portfolio risk in equities. So its closest to a 'risk parity' portfolio. The second gives us half our weight in equities, but about two thirds in portfolio risk terms. Going higher than 10% risk target is possible; but assumes that the Asian ETF will continue to show more volatility than the others. I wouldn't bet on it, and having more than 80% of my risk allocation in equities seems quite undiversified.


For investors with between £500 and £10K


If you have less than £10K then 6% for one position seems too low for one allocation. You won't do much harm by redistributing the weights a little. For example you could move 1% of the Asia equity allocation to the UK so all the portfolios are 7% at least. More radical surgery, i.e. a minimum of 10% in any position requires a little more effort. Since you will have 40% in bonds with a 10% minimum per position you need to eithier lower your risk target or remove one of the bonds from your portfolio; perhaps SEMB as that has the lowest weight amongst the bonds indicating it isn't very diversifying. The results of this are shown below.

Finally for investors with perhaps £5K or less having all eight or even just seven ETF's is going to result in quite uneconomic allocations. For less than £1500 I would invest just in VWRL, the Vanguard 'All world equity' index. With more than that I would advocate splitting between VWRL and IGLO. Again these portfolios are in the tables below.

 

Those who only want to know the results; skip to here.



£10K or over to invest: A portfolio with half its expected risk in bonds and half in equities (6.0% expected risk target)



  • 7% VUKE FTSE 100 UK
  • 13% VAPX FTSE Asia
  • 9% VEUR FTSE Developed Europe
  • 6% VUSA FTSE S&P500 US
  • 8% SEMB emerging markets $ government bonds
  • 20% IGLO ishare global government bonds
  • 22% CORP Global corporate bonds 
  • 15% HYLD global high yield corporate bonds

 

 

£10K or over to invest:A portfolio with half its funds in bonds and half in equities (7.5% expected risk target)



  • 8% VUKE FTSE 100 UK
  • 20% VAPX FTSE Asia
  • 14% VEUR FTSE Developed Europe
  • 7% VUSA FTSE S&P500 US
  •  8% SEMB emerging markets $ government bonds
  • 15% IGLO ishare global government bonds
  • 16% CORP Global corporate bonds 
  • 12% HYLD global high yield corporate bonds


£10K or over to invest: A portfolio with about the same expected risk as the FTSE 100 (10% expected risk target)


  • 8% VUKE FTSE 100 UK
  • 26% VAPX FTSE Asia
  • 19% VEUR FTSE Developed Europe
  • 10% VUSA FTSE S&P500 US
  •  7% SEMB emerging markets $ government bonds
  • 8% IGLO ishare global government bonds
  • 10% CORP Global corporate bonds 
  • 10% HYLD global high yield corporate bonds

 

£5K or over to invest: A portfolio with about the same expected risk as the FTSE 100 (10% expected risk target), and at least 10% in each ETF


  • 12% VUKE FTSE 100 UK
  • 25% VAPX FTSE Asia
  • 19% VEUR FTSE Developed Europe
  • 11% VUSA FTSE S&P500 US
  • 12% IGLO ishare global government bonds
  • 11% CORP Global corporate bonds 
  • 10% HYLD global high yield corporate bonds

 

£1500 to £5K to invest: A portfolio with a bit less expected risk than the FTSE 100


  • 65% in VWRL FTSE All world ETF
  • 35% in IGLO ishare global government bonds

 

£500 to £1500 to invest: A portfolio with about the same expected risk as the FTSE 100


  • 100% in VWRL FTSE All world ETF


Personally I would be happy holding any of these portfolios for the given risk tolerance. I also wouldn't get anal; feel free to round up or down a couple of % to get nicer and rounder numbers. It won't affect the results in any meaningful way.

It should now take you less than 5 minutes to buy the chosen menu, assuming you have already got a brokerage account. In future posts I will talk about making buy and sell decisions with these portfolios.

Happy investing and good luck!

4 comments:

  1. Nice post sir. Quick question.

    When you write the following: "When I actually do in my optimisation I am going to assume that everything I have has the same net Sharpe ratio, i.e. the returns scale precisely to the realised volatility."

    Do I understand correctly that rather then using mean historical return for each ETF you use (std*some_fixed_sharpe/16) as the expected return?

    ReplyDelete
    Replies
    1. Yes, exactly that. Use the average sharpe across all assets, or just an arbitrary figure like 0.25.

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  2. I think I managed to code it up in python.

    https://gist.github.com/schalekamp/adb1439af824a12f58a3.js

    I'd be interested to if you agree with this implementation.

    Thanks for writing this blog, very inspiring.

    ReplyDelete
    Replies
    1. I can't test this as I seem to be missing a library but it certainly looks okay to me.

      I'll be posting some optimisation code of my own soon, so keep an eye out for that.

      Delete