Category Archives: Finance

Being concrete about the benefits of tax efficient index investment

In my last post I discussed the methods that a UK individual could use to make investments. There were plenty of different methods, all with their own unique tradeoffs.

In this post I'm going to focus just on the issue of tax efficiency. Let me remind you that I'm definitely not a tax professional and this post just reflects my current understanding of the situation. You probably shouldn't rely on it to be correct, and should seek independent advice before using any of this info.

That being said, what I have done is write a simulation of an unleveraged FTSE 100 investment from 1989 to 2016-11-01, as achieved via four methods:

  1. Index-tracking ETF
  2. Index future
  3. Spread bet
  4. CFD

With a 100,000 GBP initial investment, the most efficient investing method (spread betting) has a final account value of 610,718 GBP: 163k higher than the least efficient investment method (index futures), which had a final value of 447,629 GBP. That's a 36% difference!

CFDs and ETFs came somewhere in the middle: the CFD investor would have had 521,090 GBP at the end, while the ETF holder would have 491,957 GBP — and this is with the generous assumption that the fees charged by the ETF provider are 0%.

Spread bets win for a simple reason: they don't pay any capital gains or income tax at all. With an unleveraged investment, the high financing costs of a spread bet are irrelevant. Note that my model assumes that your spread bet provider pays you the full value of a dividend if you had a long position. It is by means guaranteed that this applies to your provider, but there are few companies out there that do do things this way: I will cover a few in the last part of this post.

Why are index futures so inefficient? The reason is that index future returns are net of the risk free rate. This means that you have to stick your unmargined money in a bank account to earn back the risk free rate, and that means you end up paying income tax — the most onerous of all the taxes. Over the sample period the futures strategy ends up paying 115,309 GBP in income tax alone. The capital gains tax obligations are a relatively modest 19,236 GBP. The trading costs of this option are also relatively high (thanks to the quarterly contract roll), at 2,156 GBP but this is dwarfed by the tax charges.

Note that my backtest period includes a period of rather high interest rates in the UK (rates fluctuated around 10% at the beginning of the period). It's likely that investing in futures is more tax-efficient nowadays than it was historically.

CFDs benefit from being able to treat dividend payments on the underlying as capital gains. The CFD investor would have paid only 49,914 GBP in capital gains tax over the period, and no income tax at all. The fact that this number is roughly half the total tax burden of the index future investor reflects the fact that the higher rate of income tax is about twice the rate of capital gains tax.

Finally, the ETF investor would have paid a mix: 46,314 GBP in income tax, and 16,897 GBP in capital gains. This is a total tax burden not much higher than that paid by the CFD investor, but it differs in that the CFD investor's capital gains liabilities mostly arise towards the end of the test (2013 and later), while the ETF is dribbling dividend income away to the taxman almost every year since inception (actually, 1994 is the first year in which the ETF dividend income exceeds the tax-free threshold).

Naturally, for those who are willing and able to invest all their money within an ISA, all of this discussion is irrelevant — in this case, all dividends and capital gains will be tax free anyway, so you may as well just buy an ETF. Individuals who have hit their ISA contribution cap, or who want to do things that are incompatible with ISAs (e.g. hold futures and options, or use leverage) may however find this information useful.

Note finally that my tests make a number of assumptions:

  • You are a UK higher rate taxpayer
  • Today's tax regime applies across all of history
  • For the index future results: that you can save in an easy-access account offering 0.5% above LIBOR
  • You realize your gains somehow to take full advantage of your annual tax free allowance
  • I couldn't find monthly FTSE 100 index returns anywhere (I know this sounds weird, but I really did try quite hard and they were nowhere to be found) so I backed them out from Quandl's FTSE 100 index future data by assuming an annual dividend yield of 3.83%. At least this should mean that my results aren't affected by shocks to the level of market-expected dividiends.

Spread-Betting Providers

From the above we can see that spread betting can be advantageous. However, this conclusion is sensitive to the amount of dividends that the provider passes on to the better. My computed final account value of 610,718 GBP assumes 100% of dividends are passed on, but if just 90% are passed on then you will have only 552,525 GBP at the end — still good, but not much better than a CFD investment. At 85% retention final value is 525,472 GBP, and if your provider is cheeky enough to retain 80% then final value would be 499,698 GBP — almost as bad as holding an ETF.

I gathered some info from around the web about the charges imposed by various spread-betting providers. For long term investors the relevant bits of info are the financing rate and the fraction of dividends that are passed through to you (for a long position). The below table compares a few providers on these criteria, again assuming an investment into the FTSE 100.

(Note that I expect that you would only pay the financing cost on the value of your position that exceeds your cash deposit, so the financing rate may not be at all important for a totally unleveraged investor.)

Provider Financing Cost Dividend Passthrough
Ayondo 2.5% 100%
CityIndex 2.5% I expect 90% given "net dividends", which matches another source
CMC Markets 3% 100%
CoreSpreads 2.5% 90%
ETX 3% 100% but another (older) source says 90%
GKFX ?? 100%?, see also here
IG 2.5% I expect 90% given "net dividends", but other sources say 85%
InterTrader 2.5% 80%
LCG 2.5% Perhaps 80%
SpreadEx ?? 100%

Without considering any other factors, Ayondo seems like the best deal, with full dividend passthrough and low financing costs.

Tax-efficient and financing-efficient UK individual investing

In my last post I gave an example of a situation where individual investors might want to borrow money for investment purposes. This post will give an overview of the methods that individuals can use to achieve that leverage efficiently. I will also cover tax considerations, some of which may be relevant even to unleveraged positions. Much of what I cover here will be UK specific, particularly when it comes to taxes.

Before we begin I should probably say that I'm not a tax accountant, a lawyer, a professional financial advisor, or anything else: I'm just a guy with access to Google and an interest in efficiency. You should probably speak to a professional before acting on any on the info in this article! I do work for an investment company, but I'm certainly not speaking for them here, and the information in this post has little-to-no relevance to their business. This is simply a summary of my understanding based on my research — I haven't actually tried most of these methods in practice. I would appreciate feedback if you notice any errors.

Secured Lending

A secured loan such as a mortage or HELOC is the form of borrowing that is probably most familiar to people. Because these loans are backed by an asset (i.e. probably your house), you can get very good interest rates: I see 2 year fixed teaser rates as low as 1.2% AER, which is less than 1% above the overnight GBP LIBOR rate of 0.225%.

The obvious downside of this form of borrowing is that the amount you can borrow is limited by the amount of home equity you have.

Margin

Many stock brokerages offer margin accounts to their customers. A margin account is one where you are allowed to borrow to invest more than you have deposited into the account. The borrowed capital is secured by the equity in the account, which must meet a minimum value threshold ("margin requirement"), normally defined as some fraction of the total notional value of the account.

The broker I'm most familiar with is Interactive Brokers (IB). Roughly speaking, their rules allow a margin account to borrow up to 100% of the value of the equity in the account (i.e. achieve 2x leverage). The interest rates charged are fairly low: right now, for GBP borrowing they charge 1.5% above LIBOR. The rates get more competitive if you borrow more — loans above GBP 80,000 only attract a charge of 1% over LIBOR.

If you're using a broker's margin facility you obviously need to accept their schedule of trading costs too. Luckily, IB's fees are just as competitive as their margin charges, and start at around 6 GBP for an equity trade.

Futures

If you want to invest in an asset on which a liquid futures contract exists, this can be a very cheap way to achieve leverage. At the time of writing, a single FTSE 100 index future contract has face value of around 73,000 GBP. The returns on this contract will closely match the returns on investing that same face value in an index tracking ETF. However, unlike with an ETF investment, if you purchase one of these futures contracts, you don't need to invest those tens of thousands of pounds upfront — instead, you just need to deposit a certain amount of margin with your broker. Right now, IB only require about 6,500 GBP of deposited margin for a FTSE position held overnight, so you can potentially achieve 10x leverage without paying any financing costs.

If you use futures to make long-term investments in assets it is important to understand how the returns you earn on futures differs from that on the underlying asset. By an arbitrage argument you can show that the price of a futures contract should be equal to the forward price F:

Where S is the spot price of the underlying instrument (in our example, this would be the FTSE 100 index), T is the time to expiry of the contract, r is the risk-free rate and q is the "cost of carry". The cost of carry is essentially a measure of the return you earn just by holding a position in the underlying. For an equity index future like the FTSE the cost of carry will be positive because by holding the components of the FTSE you actually earn dividends. For commodity futures the cost of carry may be negative because you will actually have to pay to store your oil or whatever.

If the spot price of the underlying stays unchanged, the daily return R on the contract will be:

This illustrates the key difference between holding the underlying and the future. With the future, you don't just earn the returns of the underlying asset. — the value of your contract also decays each day by an amount related to the difference between the cost of carry and the risk free rate. If this decay costs you money, the future is said to be in "contango", otherwise it is in "backwardation". You can somewhat offset the decay due to the risk free rate part of this by depositing the notional amount of your investment in an account that earns the risk free rate. However, even if you do this, you wouldn't expect the returns on your position to perfectly match those of the ETF because the forward price is determined based on the expected risk free rate and cost of carry. If interest rates are unexpectedly low, or dividend payouts are unexpectedly high, then your futures investment will underperform the equivalent ETF, so you are bearing some additional risk with the futures investment.

The other issue with futures contracts is that if you hold them for the long term you will need to deal with the fact that they have a limited lifespan. For example, the June 2017 FTSE 100 contract expires on the 16th of June. On or before that date you will need to sell your position in the June contract and buy an equivalent one in a later one (e.g. the September 2017) contract, or else you'll stop earning any returns from the 17th June onwards. This regular roll process incurs transaction costs which acts as a drag on your investment. Thankfully, futures contracts are generally very cheap to trade: not only does the bid-ask spread tend to be tight, but brokerage fees are lower — IB only charge GBP 1.70 per contract to trade FTSE 100 futures, and most futures have extremely tight bid-ask spreads that are essentially negligible from the perspective of a long term investor.

One problem that makes index future investment particularly tricky for the individual investor is that these contracts generally have rather large notional value. The ~70k GBP value of one FTSE contract mentioned above is quite typical. So if you only have a small account, you can't really use futures unless you're willing to accept enormous leverage and all the risks that entails.

Contracts For Difference

Contracts For Difference (CFDs) are an instrument you can buy from a counterparty who specialises in them. Big UK names in this area are IG, CityIndex and CMC Markets, though IB also offers them. Like a futures contract, these products let you earn the returns on a big notional investment in an asset without putting down the full amount of that investment upfront — instead, you just need to deposit some margin. Depending on the provider and the reference asset, the margin requirements can be very low: CityIndex seems to only require 0.5% margin for a UK index investment, allowing for a frankly crazy 200x level of leverage. IB only require 5% margin.

Also like a future, CFDs are not available on just any underlying. It's easy to bet on equity indexes, FX, and big-cap stocks with CFDs. It is also reasonably common to find bond or commodity CFDs, but not all providers will offer a full range here (IB don't offer any). The other characteristic that CFDs share with futures is low trading costs: for index CFDs, providers commonly only charge a spread of 1 index point, i.e. about 0.01% for the FTSE 100. IB as usual offer a good price of only 0.005% per trade for version of the FTSE 100.

Now we turn to the differences between CFDs and futures. For starters, unlike futures, CFDs do have financing costs, and they are chunky: typical rates from CityIndex and friends are 2%-2.5% above LIBOR, with IB again offering an usually good deal by only charging a 1.5% spread. On the plus side, if you hold a position in an asset via a CFD you will recieve dividends on that underlying, something that is not true if using a future.

Spread Bets

Spread bets are a bit of a UK specific way to lever yourself up. Many companies offering CFDs in the UK also offer spread bets. These are essentially CFDs in all but name, and will face almost identical trading and financing costs as compared to the equivalent CFD product. They are also generally available on exactly the same set of underlyings. The key difference between a CFD and a spread bet is that spread bets are treated as gambling rather than investing by the tax system, with the consequence that earnings via one of these instruments are subject to neither capital gains nor income tax!

I will return to the issue of tax later, as there is quite a lot to say on the topic.

Options

Options are a slightly more complex way to gain leverage than the above alternatives. The idea here is that if you want to make a leveraged long bet on e.g. the FTSE, you can achieve that by buying a long-dated call option with a strike price somewhere around the current level of the index. Because the strike price is high, you will be able to purchase the option relatively cheaply, but you can potentially recieve a very high return. For example, let's say the FTSE is around 7000: you might be able to buy an option on 1x the index expiring in two years with a strike of 7000 for around 400 GBP. If the index is up 10% to 7700 at that time, then you will earn a profit of 700-400 = 300 GBP i.e. a 75% return on your investment, so you have effectively have 7.5x leverage.

Like futures or CFDs, options are only available on certain underlying assets. In the US, you can buy options on equity indexes with expiries up to three years in the future: these are known as LEAPs. Exchange-traded options with long expiries are also available in other countries: for example, the ICE lists FTSE 100 options expiring a couple of years ahead.

Also like with futures, investments via options won't earn any dividends, but neither will they attract financing charges. Individual investors may have difficulty with the fact that these options have notional values in excess of 50,000 GBP (in the US, S&P 500 mini options with smaller notionals are available, but they only list about 1 year out).

There are two other ways of purchasing options that may be more suitable for the UK small investor as they let you take a position in a smaller size. Firstly, companies offering spread bets tend to also sell options. I haven't looked into this, but given how expensive their spread bet financing is, I would not be surprised if their options were substantially overpriced. Secondly, you can purchase a "covered warrant", which is essentially an exchange-listed option targeted at individual investors. Societe Generale offers them via the London Stock Exchange: i.e. these options can be purchased just like a regular stock.

I did have a brief look into whether covered warrants offered good value for money. Specifically, I looked into the cost of SE91, a call option on the FTSE 100 with strike price 8000 and expiry December 2018 (the longest dated option available at the time of writing). When I looked at it, the warrant was quoting at around 0.25 GBP with a spread of 0.002 GBP (1%):

The equivalent exchange-traded option was had a mid price of about 156 GBP on a spread of about 50 GBP (32%):

The exchange-traded option is for a notional exposure 1000x larger than the warrant, which explains the order-of-magnitude difference between the prices. Taking this into account, the warrant looks pretty expensive, with even the bid price of 0.2488 GBP being higher than the equivalent exchange-traded option ask of 0.1805 GBP.

We can quantify exactly how much more expensive the warrant is by using the Black-Scholes option valuation model. Given the level and volatility of the FTSE at the time, the model implies a fair market value for the option of 153 GBP, which lies within the bid-ask spread we actually observe on the exchange:

SocGen are trying to charge us about 250 GBP for equivalent exposure. To put this in the same terms as the financing costs for the other instruments (i.e. as a spread to LIBOR), we can tweak the borrow cost assumption in this model until we get the right price out:

So it looks like the SocGen options are effectively offering leverage at a cost of LIBOR plus 2.75%, which is not a good deal. Trading them might still make sense so long as you are intending to hold them short-term, because they have much narrower bid-ask spreads than the exchange-traded equivalent, but in this case you'd probably end up better off buying the options OTC from a spread betting company.

I won't consider options further as frankly speaking I find them harder to analyse than the alternatives.

UK Taxes On Investments

There are four forms of tax that are relevant to investors operating in the UK:

  • Stamp duty: payable upon purchasing an asset
  • Dividend tax: payable upon recieving dividends from an asset
  • Income tax: payable upon recieving non-dividend income from an asset
  • Capital gains tax: payable upon sale of an asset

Stamp duty is the simplest of the three. It's a flat 0.5% charge upon the purchase of shares in individual companies. It is not payable on the purchase of ETFs, futures contracts, or spread bets, so mostly not very relevant.

The amount of dividend tax you pay depends on your total income in a year, and can range from 0% (if your dividends amount to less than the current tax-free allowance of 5,000 GBP) to 38.1% (if you pay "additional rate" tax of 45% on income above 150,000 GBP).

Income tax is payable on income from an asset that is not considered to be a dividend. Basically, if the asset is a bond, or a fund more than 60% invested in bonds, you will have to pay income tax instead of dividend tax. Income tax can range from 0% (if you earn less than the current Personal Allowance of 11,500 GBP) to 60% (if the income from dividends pushes you into the 100,000 GBP to 123,000 GBP band where the Personal Allowance is withdrawn). For more info see HMRC and this discussion of the marginal tax rate. It's not 100% clear to me what the tax treatment is on the final repayment of principal made by a bond issuer. I suspect the final repayment is treated as a capital gain, and for UK government debt at least it seems that no capital gains tax is payable.

Capital gains tax is payable on realised gains in excess of the annual 11,300 GBP threshold. Higher rate taxpayers (i.e. those earning above 45,000 GBP) will pay 20% on anything above this. Those who don't pay higher rate tax may only pay 10% on some amount of their gains.

Capital gains tax is perhaps the trickiest of the taxes. Firstly, you need to know that it's calculated based on your net realized loss during a year. So if you make a gain by selling some asset, you can avoid paying tax on that by selling another asset on which you have booked a loss. If you realise a net loss during a year, that can be carried forward indefinitely to be set against future capital gains.

Secondly, note that that the tax free amount of 11,300 GBP is a "use it or lose it" proposition: if you don't have 11,300 GBP of gains to report in a year then you won't be able to make use of it, and it will vanish forever. This ends up being another reason to invest in a diversified portfolio of assets: if you are diversified then you're likely to have some asset that you can liquidate during a tax year to take advantage of the allowance (just be careful that you don't fall foul of the "bed and breakfasting" rules — see this guide to realizing capital gains for more info).

One general theme of all this is that you generally end up paying less tax on capital appreciation than on dividends.

Tax Efficient Investing

For concreteness, let's say we are interested in making a (either leveraged or unleveraged) investment in equity indexes. How do these taxes apply to the investing methods discussed above, i.e. ETFs, futures, CFDs and spread bets? As already mentioned, none of these assets attract stamp duty. But what about dividend and capital gains tax?

ETFs are relatively straightforward: you pay dividend tax on the distributions, and capital gains tax upon selling an ETF that has increased in value. This may mean that it is more tax efficient to purchase an ETF that reinvests divends for you (like CUKX) rather than one that distributes them (such as ISF).

Futures contracts are straightforward: there are no dividends, so you simply pay capital gains tax. One potential problem is that you won't have much control over when you realise gains for capital gains purposes because you'll probably be rolling the contracts quarterly anyway. Furthermore, if you have taken that portion of your equity that does not go towards the margin requirement, and invested it in an interest-bearing account, then you will have to pay income tax on any interest income. For tax purposes it might be most efficient to invest in a zero-coupon government bond which will not attract either income tax or capital gains tax, but this might be more trouble than it is worth.

The tax treatment of CFDs is interesting. All cashflows due to the CFD are considered to be capital gains by HMRC — what's surprising is that this this includes both the interest you pay to support the position, and any payments you receive as a result of the underlying making a dividend payment. This makes CFDs rather attractive: you can end up paying capital gains tax rates on dividend income, and benefit from being able to use you interest payments to reduce capital gains liability, reducing the effective cost of margin by up to 20%.

Finally we come to spread bets: as mentioned earlier, bets are subject to different rules, so you don't pay any tax at all on these. The flip side to this is if of course that if you make a loss, you aren't able to offset it against capital gains elsewhere. It's not totally clear to me whether this treatment applies to payments made on the spread bet as a result of dividend adjustment, but it looks like it may do. This is why some spread betting providers (e.g. CoreSpreads) only pay out 80% or 90% of the value of any dividend to the punter. One last thing to note is that the spread betting providers themselves pay a betting duty of 3% on the difference between punter's losses and profits: this will of course be passed on to you in the form of higher fees.

Summary

This is a lot of info to take in, so I've tried to summarize the most important points below. Trading costs assume a 100,000 GBP investment in the FTSE 100.

Secured Lending Margin Futures CFDs Spread Bets
Available underlying Anything Anything Equity indexes, debt, commodities, FX, certain equities (though liquidity may be limited) Equity indexes, debt (sometimes), commodities (sometimes), FX, certain equities
Approximate max leverage 4x (assuming 75% LTV) 2x 10x 200x 200x
Financing cost above LIBOR 1% 1% to 1.5% 0% 1.5% to 2.5% (20% less if treatable as capital loss) 2% to 2.5%
Other holding costs 0.09% (Vanguard's VUKE ongoing charge)

0.014% (quarterly roll costs) 0% 0%
Trading costs (FTSE 100) 0.09% (VUKE 0.06% bid-ask spread, 0.03% commission) 0.0017% 0.005% 0.01%
Dividend treatment Paid in full by ETF provider None, but expected dividends become a positive carry on holding the contract Paid in full Generally paid in full but some providers may withhold 10%-20%

A return-boosting idea

As a final note, here's something I just noticed and haven't seen mentioned anywhere else. If investing via a CFD, spread bet or futures contract, you only need to deposit margin with your broker. If you're only using 1x leverage, this means that 90% of the notional value of your investment is free for use elsewhere, so long as you are able to move it back to the margin account if needed.

What's interesting is that as an individual investor it's straightforward to find bank accounts that pay more than the risk free rate — even though these accounts do enjoy full backing from a sovereign government, and so are risk free in practice. For example, right now I can see an easy-access (aka demand deposit) account from RCI Bank accruing interest daily and paying an AER of 1.1% on balances up to 1 million pounds — i.e. about 0.9% above LIBOR. This is higher than the financing cost of a futures position (though not a CFD or spread bet), so it seems to me that there is reason to believe that the returns on a futures investment will actually beat out the equivalent ETF, so long as you do invest the "spare" equity in this way.

The case for leverage in personal investing

The standard advice for personal investing that I see all around the web is to put your money into one or more low cost equity index tracking funds. Commentators also sometimes recommend an allocation to bonds (e.g. a 60/40 split between stocks and bonds), though the popularity of this advice seems to become less common with every passing month of the bull market.

However, the more I learn about investment, the more I come to think that this answer is suboptimal. To see why, let's consider a simplified world where we have exactly two assets to which we can allocate our wealth: stocks and bonds.

Portfolio Theory

The historical evidence (see e.g. the excellent book Expected Returns) is that the returns on bonds and equities are uncorrelated, with bonds having lower volatility (aka standard deviation) than equities — US treasuries experienced an annualized volatility of 4.7% a year between 1990 and 2009, while US equities had a volatility of 15.5% over the same period.

Given their lower volatility, bonds are clearly less risky than equities. However, you would hope that if you invest in equities rather than bonds, then your willingness to accept the inherently higher risks is compensated for by a higher expected return. This idea of can be captured mathematically as the Sharpe ratio, which measures the reward you receive per unit risk taken. Specifically, the Sharpe ratio S is equal to the ratio between the expected "excess return" of the investment, and the standard deviation of those returns. The excess return is defined as the amount of the expected return R above a risk-free rate Rf (e.g. the rate of return you can get by lending overnight in the money markets). Putting it all together we get this formula for S:

Thanks Wikipedia :)

All other things being equal, you probably want to invest in assets with as high a Sharpe ratio as possible.

It can be tricky to figure out what the Sharpe ratio is for investments of interest, but history suggests that stocks and bonds both have similar Sharpe ratios of roughly 0.3. What's more, the correlation between their returns is close to 0. This last fact is important because portfolio theory shows that you can form an investment with high Sharpe ratio by holding a diversified portfolio of two or more uncorrelated assets with low Sharpe ratios. Assuming that historical returns, volatilities and correlations are good guides to the future, the portfolio of stocks and bonds with highest Sharpe is one that holds roughly $3 of bonds for every $1 of stocks: this ratio comes about because the volatility of stocks is approximately 3 times that of bonds. This optimal portfolio has Sharpe ratio of about 0.42 i.e. 1.41 (= sqrt(2)) times higher than that either asset class by itself.

You can get a feel for how this optimization process works by playing with my online portfolio theory tool.

Leverage

What's striking about this optimal portfolio is that it's very different from the normal advice: it puts 75% of capital into bonds, much more than even the most conservative conventional advice of a 40% allocation. The obvious objection to the bond-heavy optimal portfolio is of course that it will have very low expected return compared to one with a bigger weighting on equities. This is absolutely true: we expect the volatility of the optimal portfolio to be around 0.75*(bond volatility) + 0.25*(stock volatility) = 0.75*4.7% + 0.25*15.5% = 7.4%. Because this is roughly half the volatility of equities by themselves, we'd expect the excess return on the portfolio to therefore only be about (0.42/0.3)/2 = 1.41/2 = 0.7 times that of a pure-equity allocation, which definitely sounds like bad news for the optimal portfolio.

However, this is a solvable problem — to recover the high expected returns we desire, we simply have to borrow money to invest greater notional amounts into the portfolio. If we borrow, then using 2x leverage (i.e. borrowing so as to invest $2 for every $1 of capital we actually control) would scale the volatility on our portfolio up from 7.4% to the equity-like levels of 14.8%. If we assume that we could borrow at the risk-free rate, then because our portfolio has Sharpe ratio higher than that of plain equities, the expected excess return in this scenario would be 41% higher than that of equities alone. So we earn better returns than with a pure-equity play even though we are running similar risks.

Everyone has probably been told at some point that diversification is good, but the way it is usually explained is by saying that diversification reduces your risk, which sounds worthy but sort of boring ☺. When you realise that this risk reduction means that you free up some "risk budget" which you can use to achieve extra returns via leverage, diversification starts sounding more exciting!

Of course, in reality we are unlikely to be able to borrow at the risk-free rate, but there are ways to borrow that are only just slightly more expensive than this — depending on the currency, companies and investment funds regularly borrow at rates as low as 0.5% above the risk-free rate. Even as an individual investor, there are ways in which you can borrow quite cost-effectively — this is a topic I will cover in a future post. The cost of leverage is of course a constraint that we should bear in bind, though: the fact that we face lending costs rules out activities such as levering up short term bonds (e.g. US treasury bills) which have very low volatility (because they take on very little interest rate risk).

Risk Parity

The approach to investing outlined above can be roughly summarized as:

  1. Assume that all investible assets have the same Sharpe ratio
  2. Therefore decide to allocate to them in an amount inversely proportional to their volatility (following the advice of portfolio theory and mean-variance optimization for Sharpe ratio maximization)
  3. Leverage up the resulting portfolio to achieve a particular desired level of risk

This method is also known as "risk parity". Famously, it's the strategy used by Bridgewater's All Weather hedge fund, which has returned a Sharpe of roughly 0.5 since inception in 1996. (All Weather invests in asset classes other than stocks and bonds, so we would expect it to have a higher Sharpe than our earlier prediction of 0.42, simply due to the extra diversification.)

What's particularly interesting about risk parity is that it's not actually immediately obvious that taking bigger risks with your money leads to a sufficient extra level of return to compensate you for those risks. For example, take the case of stocks and bonds. From 1990 to 2009, US equities returned a (geometric) mean of 8.5% per year while treasuries returned 6.8%: so equities did earn a higher return, but one that doesn't seem commensurate with the 3 times higher volatility experienced. Furthermore, global equities (which had similar volatility to US equities) actually only returned 5.9% i.e. considerably less than US bonds!

The fact that risk-taking is under-compensated is actually a well-known anomaly: an excellent paper on the subject is Betting Against Beta which suggests the reason may be because many investors are either unwilling or unable to use leverage. Whatever the cause, it's good news for risk parity, because this means that the low-risk assets you are levering up actually have a higher Sharpe ratio than the high-risk assets that you (relatively speaking) disprefer, so your portfolio's Sharpe ratio will be even better than you would naively expect. This subject is explored further in this readable paper on risk parity from AQR.