Smart Portfolios 4 – Costs and Diversification

Smart Portfolios 4 – Costs and Diversification

Today’s post is our fourth visit to Rob Carver’s book Smart Portfolios.


Regular readers will know that I am very keen on keeping costs to a minimum.

  • It’s one area of investment that is relatively easy to control.

And in an era of low returns (and fortunately, lower costs than ever), costs will have more impact than usual.

  • Costs need to be measured not just against assets / net worth, but as a proportion of annual returns.

Let’s see what Rob has to say on the subject.

Here’s the effect of costs over the long run (60 years):

Costs over time

Costs over time

A relatively modest 0.10% reduces the final value of the portfolio by over 6%. Half a percent (50bp) drops it by a quarter. Finally an extra 1% (100bp) of costs nearly halves the final portfolio value!

I would call 0.1% impossible rather than relatively modest.

A simple ETF portfolio can be built for around 0.3%, with running costs of around 0.2%, but it’s hard to get much cheaper than that.

  • This ignores platform fees and costs hidden within funds.

Robo-advisers start around 0.3% (for pensions) to 0.5% (for ISAs), not including hidden costs.

Rob focuses on passive ETFs – which he says are the cheapest way to get market exposure – in comparison to direct share holdings.

He lists the sources of expense as follows:

  1. brokerage fees (commissions) – typically £5 to £12 in the UK
  2. taxes – 0.5% stamp duty on stocks (but not ETFs)
    • also an extra £1 (the takeovr panel levy) on deals over £10K
  3. annual management fees – from 0.07% on the cheapest ETFs to more than 2% on some active funds
    • some funds also have performance fees
  4. hidden fees – admin, custody, marketing and internal trading costs (watch out for churning in active funds)
    • there are also swap fees and spreads for synthetic ETFs
  5. the bid-offer spread – small for ETFs, large for small, illiquid stocks
    • this is a bigger problem for institutional investors who can impact the market (move the price) through the size of their trades (also known as slippage)

We can also look at charges through time:

  1. acquisition – shares are expensive
  2. holding – shares are free
  3. rebalancing – shares are expensive again

We’re ignoring taxes (on dividends and gains) at this stage.

We’re also ignoring platform costs.

  • Shares and ETFs need to be held in an account, and the tax-sheltered ones are often not free.

There are no free SIPPs; ISAs are usually free for shares and ETFs but not for OEICs.

  • Large investors should prefer flat fees (see below) whereas small investors might benefit from variable charges.
Rule of 20

Rob uses the rule of 20 to capitalise ongoing costs.

  • This comes from the way that annuities are valued, and is also the source of the UK government’s conversion of annual DB pension payments into a lump sum for LTA purposes (and the deprecation rule on company capital investments).

The true conversion factor depends on interest rates (and your time horizon, though this can be infinite).

  • The low rate which prevail today mean that the rule of 20 substantially underestimates the value (or cost) of ongoing payments.

A rule of 30 to 33 would be more appropriate (based on actual annuity values).

  • Let’s say 31, since neatly that is the reciprocal of the fail safe withdrawal rate of 3.25% pa.

Rob uses a 3% discount rate and a 30-year period to justify his rule of 20.

  • For 20 years he suggests a multiplier of 15, for 10 it’s 8.5 and for 5 its 4.5.

What Rob actually does is divide the initial charge by 20 and add it to the annual charge:

total annual cost = (initial cost ÷ 20) + holding cost

I worry about this as it implies a holding period of 30 years, which will be achieved by almost no-one.

Costs by trade size

Costs by trade size

Fixed and variable

We can also classify costs as fixed or variable, depending on whether they change with account size.

It’s important to be clear on whether we are assessing the fee or its impact as fixed / variable.

  • Rob uses the percentage impact, which I think is wrong.
  • This means that a fixed brokerage fee of £5 is a variable impact for him (it has less impact on a larger trade).

By my definition, brokerage fees at the PTM levy are fixed costs (variable impacts).

  • Stamp duty, the spread and annual management fees are variable costs (fixed impacts).

As noted above, platform fees can be fixed or variable.

FTSE 100 ETF costs

FTSE 100 ETF costs

Using Rob’s initial cost amortisation, the optimum trade size in a cheap ETF is £5K.

  • Using a more conservative discount approach won’t change the relative values too much, but I might err on the side of caution and aim for £8K to £10K (portfolio size allowing).

Comparing ETFs which track the same or similar benchmarks is easy, since the tracking error (underperformance) will include both the management fee and the hidden costs.

Keeping costs down

Rob recommends using direct access (DMA) to place limit orders inside the spread.

  • In fact, he generally recommends using limit orders and trying to trade inside the spread.

He also recommends splitting large orders in illiquid stocks.

Two versus one

VWRL costs

VWRL costs

Rob compares the costs of using VWRL (the vanguard World ETF) with those of using multiple ETFs for the same coverage.

  • You might want to do this to vary the allocation to emerging markets, for example.



Rob uses 17% AUEM, compared to 7% in the single fund.

The two fund solution works out slightly cheaper here, because the annual fees are lower.

  • This offsets the higher initial costs.

Diversification is more expensive for smaller accounts, and I tend to take a top down approach.

  •  I set a minimum trade size (£2K to £10K, depending on your portfolio size) and don’t diversify below this size.

This turns out to be Rob’s approach as well (see below).

Diversification benefits

Diversification and returns

Diversification and returns

In Chapter Six, Rob looks at whether the costs of diversification (buying and holding more funds / stocks) are outweighed by the benefits.

Diversification and returns 2

Diversification and returns 2

Diversification boosts the geometric return of a portfolio by reducing its volatility (standard deviation of returns).

  • It also boosts the Sharpe ratio.

Diversification and Sharpe

Diversification and Sharpe

So all types of investors (max SR, max return and compromise portfolios) should like more diversification.

Diversification and Sharpe 2

Diversification and Sharpe 2

The benefits of diversification depend primarily on the number of assets in the portfolio and the average correlation between them.

  • The benefits from increasing numbers of assets are diminishing (10 assets are not twice as good as five).

Rob uses the same classification of asset classes that I do: equities, bonds and alternatives.

  • I lump cash and annuity-like investments (such as DB pensions) in with bonds.
Diversification costs

Rob’s next example compares buying a single UK stock for £1, versus buying 11 stocks, one from each main sector.

  • Initial costs are 1.1% vs 6.55%, or 0.06% pa vs 0.33% pa over 20 years.

I estimated that the correlation of shares within the same country but from different sectors is 0.75. Going from 1 share to 11 will boost your geometric returns from around 1.36% to 2.18% a year.

That is a benefit of 2.18% – 1.36% = 0.82% versus extra costs of 0.27%; a net improvement of more than half a percent. In this particular example diversification is definitely worth doing.

Looked at another way, you would need to hold the stocks for around 7 years until the diversification benefits outweighed the higher initial costs.

  • But of course, no-one would split a £1,100 trade down into 11 x £100 trades.

A more realistic test would be on a £50K portfolio, with £10 trades of £5K vs one big trade.

  • At that size, I estimate that you only need to hold the portfolio for a few months to be ahead.
Uncertainty of returns

Rob points out that extra costs are certain, whereas extra returns from diversification are uncertain.

  • In the example above, the uncertainty would be about future correlations.

We had this debate about the trade-off between returns and costs at AHL, the quantitative hedge fund where I used to work.

A more expensive trading system needed to earn twice as much more in pre-cost returns than the extra costs it attracted.

In the example above, the ratio was just above three, so that diversification step would have passed.

Diversification uncertainty

Diversification uncertainty

Clearly the breakeven correlation of around 0.92 is very extreme; there is almost no chance that the past correlation was actually higher than this.

Generally in the book, Rob uses 75% confidence intervals for correlation assumptions:

This is lower than the 95% usually used in statistical testing, as I want to be “pretty confident” not “nearly absolutely sure”.

Portfolio size

Rob starts his look at the effects of portfolio size by looking at the cost of buying one share.

Costs and returns

Costs and returns

I don’t find this table particularly useful as it tops out at a deal size of £1,100.

Here’s the table for 11 stocks:

Costs and returns 11 shares

Costs and returns 11 shares

The net geometric return after costs are identical at 1.25% when we have a portfolio value of £365. This is the breakeven value at which the portfolio of 11 stocks becomes more attractive than the single stock portfolio.

The Sharpe Ratio breakeven is shown in bold in the final column of each table, at a portfolio value of around £309.

ETFs vs shares

Here we would be basically trading off higher buying costs of shares against higher holding costs of ETFs.

It’s crazy to think that an investor can replicate what an ETF manager does more cheaply if they’re trying to do exactly what they are doing: buying the same shares and then doing the same trades.

Running large passive index trackers is a mechanistic process with mostly fixed costs which becomes much cheaper if you’re doing it at a very large scale.

Weighting options

There is an advantage to building your own portfolios of individual equities, which is that you can choose the weightings.

Owning a market cap weighted portfolio makes sense if all the investors in the world have collectively come to the right decision about the value of each and every company.

This is the key assumption of the Capital Asset Pricing Model.

And it is, of course, not true.

The problem is that the larger firms will tend to have goods news factored into their valuations, and the smaller firms with have bad news included.

  • In theory, market cap weighting is a “buy high, sell low” style.
  • It should be a particularly bad approach when the portfolio is heavily concentrated in the largest few firms.

It was this observation that led to the birth of the alternative indexing / smart beta approach some years ago.

The two main alternatives to market cap are equal weighting, and Rob’s hand-crafting approach.

  • Here, hand-crafting would split the index in to equal size industry groups, and allocate equally to all firms within that industry group.

Unfortunately, only market cap ETFs are readily available (in the UK – the US has equal-weight ETFs).

Handcrafting is the best theoretical approach, since sectors are likely to vary in terms of size, number of firms and correlations.

To examine the three approaches, Rob uses a fairly relative extreme index as an example:

  • The Canadian TSX index, with 60 firms, of which 12 are in the Materials sector and 14 in the Energy sector.
  • Note that some emerging markets country indices will be “worse” than this.

Here are results:

Weighting schemes

Weighting schemes

There’s not much to choose between them, even in an extreme index.

  • But they are in the order that we expect.

What about costs? [The next table] sums my findings once I include the effect of different cost levels.

TSX allocation

TSX allocation

A directly held, hand-crafted stock portfolio takes over from the market cap ETF for portfolios large than $15K.

  • For the FTSE-100, this break even is a massive £750K, and its $325K for the S&P 500.

Note that the equal-weighted ETF is too expensive to out-perform the market cap version.

I wouldn’t invest in an equal weighted ETF unless I expected it to have similar holding costs to a market cap weighted fund.

Rob notes that academic research produces stronger evidence in favour of equal weights and hand-crafting.

Bearing in mind the uncertainty around correlation estimates, I’ve used conservative figures that I think are realistic and achievable in the future.

I’m still not convinced that the benefits will be large enough to compensate when costs are significantly higher. Stick to a market cap weighted ETF except in the unlikely event that you can find an equal weight ETF that is at least 0.3% cheaper in annual management fees.

The required margin of safety comes from the extra trading costs in equal-weight ETFs.

Capped indices

Capped indices typically limit the weight allocated to any single firm, and to the largest 5% in aggregate.

  • 25/50 and 10/40 are common options.

Again I’d only consider a capped index if they had a lower management fee than a market cap weighted alternative. A discount of 0.1% a year in annual fees should be enough to compensate for the higher trading costs inside the fund.

The Brazilian 25/50 EWZ ETF has a management fee of 0.48% which, unusually, is cheaper than the nearest market cap weighted competitor fund: DBBR with an annual fee of 0.6%. In this case the capped fund is clearly the smarter option.


Next Rob looks at the practice of buying just a single stock from each sector.

  • Rob recommends picking the largest firm in each sector, to stay as close as possible to the market cap index.

Rob looks at the S&P 500 for this one.

Handcrafted S&P

Handcrafted S&P

Owning one stock per industry sector reduces returns versus full handcrafting, but not by much.

After costs:

You need at least $66,000 to invest in a given country to buy three shares in each of the 11 industry sectors, and $44,000 to justify buying two shares in each sector.

With less than that, it makes sense to buy just 11 shares, one in each sector.

Or looked at from my “minimum buy” perspective:

Don’t buy less than $2,000 of each share. With less than $22,000 an ETF might make more sense.

The smart approach

Below a certain threshold of total investment size, investors should stick to buying a market cap weighted ETF.

Breakeven for direct holding

Breakeven for direct holding

This breakeven figure depends on the holding cost of the ETF (including hidden costs), and the brokerage fee.

[The next table] shows the minimum investment per share to justify buying additional shares in each sector for both the US and the UK.

Minimum for extra shares

Minimum for extra shares

Even with a £6 brokerage fee, you would need to have 22 x £10K = £220K to invest in the UK to justify holding two stocks per sector.

  • Note that the decision to buy the second share has a much higher hurdle than the decision to switch from an ETF to one share per sector.
Minimum ETF size

This is an elaboration of the “two versus one” section from the previous chapter.

Rob estimates that the minimum investment per fund to avoid paying excessive costs is £1.8K for a £6 fee.

  • That’s £1.5K for a £5 fee, £3K for a £10 fee and £3.6K for a £12 fee (these are the most common fees that I’m aware of).

That’s fine by me as I’m not likely to put less than £2K into a fund.

  • It might cause problems for investors with less than £100K, though.

Today we’ve seen that diversification is a good thing, but that it costs money.

  • There are few constraints on the use of hand-crafting with ETFs.
  • But using stocks to replicate a market will restrict most investors to the largest stock in each sector.

We’ve also learned that although equal weighting beats market cap, the relevant ETFs aren’t usually cheap enough for us to take advantage.

That’s it for Part One of the book – what I call the theory.

  • In our next visit we’ll start constructing portfolios.

Until next time.

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Mike Rawson

Mike is the owner of 7 Circles, and a private investor living in London. He has been managing his own money for 35 years, with some success.

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