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Ideal portfolio: Asset diversification is cheaper than you might think

Negative correlation between investments is the key to limiting downside
March 18, 2016

A basic tenet of modern portfolio theory (MPT) is that logical investors want to achieve an ‘efficient portfolio’; where no other combination of available assets carries a higher expected return for the same degree of risk. Harry Markowitz, the founding father of MPT, described diversification as “the only free lunch in investing” while the right mix of assets can reduce a portfolio’s volatility and improve the chance of achieving target returns within a desired timeframe.

So what is the best approach to diversification? Instinctively, one might think that allocating capital across as many different asset classes as possible is the best way to reduce overall risk. But this is not the case as many investments are influenced by the same factors and therefore positively correlated. For example, US and UK equity indices tend to move in the same direction, so exposure to the S&P 500 as well as the FTSE 100 will not necessarily make a portfolio less risky.

The optimal asset allocation will be a blend of investments with the potential to deliver the highest returns and where there is a good chance that when one asset underperforms, others will do well. In portfolio construction, we are concerned with the covariance between the returns of different asset classes. From this it is possible to work out the combination of assets that, in theory, offers the best trade-off between reward and risk.

 

21-year strategy real returns

 

To conduct this exercise, we’ve looked at indices tracked by US-listed exchange-traded funds (ETFs). The focus on US products is because enough historical data exists to check the end portfolios with risk management software. The asset universe is not exhaustive, as only indices with at least 21 years of history are considered (the products themselves are younger). For instance, large ETFs offering liquid exposure to high-yield and investment-grade corporate bonds are ignored as the indices they track do not go back far enough to be included in the covariance analysis.

Broad commodity indices, private equity, hedge funds, international government debt and currency exposures are also overlooked.

 

The American blueprint for an 'ideal portfolio'

Firstly, it is worth noting the relationship between indices. There is a strong positive correlation between equity returns in the US and in other countries. To a lesser extent, US share prices move in the same direction as US real estate. There is a negative correlation between shares and government bonds; and shares have very little correlation at all with the price of gold.

 

Equal weightMax. return at monthly vol. of 1.81%Min. vol. at monthly return of 0.82%Max Sharpe ratio
S&P 500 (equity)8.3322.8526.7315.41
Russell 2000 (US small-cap equity)8.331.07
MSCI UK (equity)8.33
MSCI Eurozone (equity)8.33
MSCI Japan (equity)8.33
MSCI Asia Ex Japan (equity)8.33
1-3 Year US Treasury bond8.33
3-7 Year US Treasury bond8.3353.31
7-10 Year US Treasury bond8.3361.8232.0621.99
Gold 8.331.641.81
US real estate8.3313.6941.216.41
Real CAGR4.606.177.424.95
Annual Volatility8.956.1810.774.36
Max drawdown -31.59-15.81-40.21-7.59

 

Three long-only portfolios have been generated from a variance-covariance matrix of risk-adjusted total returns for the indices. Each has a set of reward-risk optimisation criteria and there is also a fourth, benchmark portfolio, where the 12-index universe is equal-weighted. All four portfolios assume annual rebalancing, according to their specific allocation splits, every January.

The first portfolio targets the highest possible return at a minimum monthly standard deviation of 1.81 per cent, which is the level of volatility experienced by the index for US Treasuries with seven to 10 years until redemption. On this criteria, the algorithm suggested a simple asset split of large-cap equities, bonds, gold and real estate. The proportions of the allocations can be seen in the table, along with the diversification benefits, which include a compound annual growth rate (CAGR) for the portfolio of 6.17 per cent, after adjusting for US CPI inflation. Most impressively, this asset split would have suffered a maximum drawdown (ie the worst peak-to-trough fall in portfolio value) of only 15.81 per cent in the 2008-09 financial crisis.

The second portfolio aims to match the (arithmetic) mean monthly return of the S&P 500, which is 0.82 per cent over the period studied, with minimal volatility. According to the matrix, by investing in bonds and real estate as well as the S&P itself, this is possible. The drawdown in the financial crisis would still have been terrible (-40.21 per cent) but less so than for the equity index alone, which halved in value. The knock-on effect of lower drawdown in times of market stress, is a better annualised real rate of return for the three asset portfolio versus the S&P 500 (7.42 vs 6.70 per cent) over the whole period analysed.

A third asset split was made to achieve a maximum Sharpe ratio from the opportunity set. The Sharpe ratio is a measure of excess returns (gains above a ‘risk-free’ rate) relative to the volatility of the portfolio. The ‘risk-free’ rate chosen here was the mean monthly return on US Treasuries with one to three years until redemption. The optimal Sharpe ratio portfolio is a mix of large-cap equities (S&P 500), small-caps (Russell 2000), different bond exposures, gold and real estate. The 4.95 per cent real annual returns are unspectacular but drawdown in bear markets was much lower than for the other portfolios.

The results show all three of the optimisation strategies, even though they were concentrated in fewer assets, would have achieved better risk-adjusted returns than the equal-weighted benchmark. This is good news for investors, as it goes to show a well-diversified portfolio can be created using a handful of low-cost ETFs, with just a few rebalancing trades once a year.

 

ETFs and a more robust risk analysis

As mentioned, all of the indices included in the covariance study are now tracked by large New York-listed ETFs. For the second part of this analysis, we will switch to talking about the performance of the actual ETFs, so there may be slight discrepancies between the performance figures of the funds and the indices they track.

So far, we have followed the convention of using standard deviation as a proxy measure for risk, but this has serious limitations. Assuming that asset returns are normally distributed about the mean return value can distort the perception of risk. This is because, in reality, high-magnitude price movements occur more frequently than the normal distribution suggests.

Significant advances have, however, been made in the computational techniques for quantifying risk. PrairieSmarts is a US company with a proprietary model that assigns a higher probability to large daily falls in asset prices. There is always the danger of unprecedented events that fundamentally alter statistical understanding but PrairieSmarts’ model fits empirical returns far more accurately.

Running PrairieSmarts software against ETF portfolios based on our allocation splits gives a more robust assessment of their riskiness. Encouragingly, the results support the findings of the first part of the study, with the least risky portfolios being the Sharpe-optimised and equivalent volatility (to the seven-10 year bond index) selections.

According to PrairieSmarts, the average loss a Sharpe-optimised asset split would suffer in a very bad month is -5.07 per cent. The model estimates the average returns on the worst 0.5 per cent of days and this is extrapolated to give a monthly figure. Looking at past returns, the worst period for the back-tested portfolio was between April and November 2008, when it fell 10.14 per cent from peak, so the risk estimate is plausible.

 

Equal weightMax. return at monthly vol. of 1.81%Min. vol. at monthly return of 0.82%Max Sharpe ratio
Total risk (worst of months)-11.26%-7.77%-14.96%-5.07%
Reward:Risk ratio1.452.011.532.37
PS Diversification score16391848
Drawdown 2008-9-33.85%-19.83%-44.88%-10.14%

 

As well as absolute risk estimates and reward-to-risk ratios for all of the portfolios (results are summarised in the table), PrairieSmarts calculates a diversification score. This number shows the percentage of risk eliminated at the portfolio level thanks to the co-movement of assets. By this measure, the Sharpe-optimised portfolio and the equivalent volatility portfolio achieve greater reduction in risk, compared with the equal-weight portfolio.

 

Are these really the ideal portfolios?

Does this mean these efficient asset allocation splits are the ideal portfolios? Certainly, in the past better diversification could have been achieved by focusing on correlations. But there is a danger that relationships observed between securities can weaken or break down, so in the future it might be better to diversify more widely and not just rely on past patterns of co-movement.

Another concern is that by ignoring markets and asset classes entirely, because they are positively correlated with core holdings, we may leave returns on the table, which can be frustrating. For example, although a 2006 investment of $100 in the Sharpe-optimised ETF portfolio analysed by PrairieSmarts would not have fallen below the starting value even in the financial crisis (it would now be worth $171), the reality is that investors bemoan underperformance compared with more aggressive strategies in good years for risk assets.

Depending on horizon and objectives, it may be profitable over time to make tactical asset allocations. This means adding risk to the portfolio when the probability of pay-off is highest. Of course, market timing is perilous and most people will get it badly wrong on occasions. Another way, therefore, is to take a rules-based approach to capture well-attested risk premiums from factors such as momentum, minimum volatility, quality or value. The key is to understand how much extra risk you are taking on, whether you are on course to achieve objectives without adding risk and if an adverse outcome is likely to jeopardise those goals? Ultimately it is personal factors that will decide an investor's portfolio composition, but the approach should be to manage risk, rather than chase returns.