Commodities are a valued addition to an equity portfolio due to the dual benefits of decorrelation from equities and historically high returns.

Over the last five years, commodities have returned a healthy 13 per cent annualised total return, and close to 7.5 per cent over the last 10 years – reason enough to have a second look at this increasingly relevant asset class.

The most popular approach to including commodities in a strategic asset allocation is purely based on historical returns, where one calculates a historical expected return, volatility and correlation to other asset classes and performs a straightforward mean-variance optimisation. However, this approach does not present a consistent method to assess different types of commodity-linked investments.

Modelling commodity returns

Apart from actually stockpiling physical commodities, which for the average investor is impractical, or investing in shares of commodity-related companies, which is a poor proxy, the main method to invest in commodities is to use exchange-traded commodity futures.

For a long-term investment in a particular commodity future, there are two means:

• Buy the nearest expiring future (the ‘front month’ future) and switch to the next one on approach of the expiry date – this is the way commodity indices are calculated;
• Buy a long-term future directly (or for that matter a long term structured product linked to the commodity).

These two methods, however, do not have the same price. Similar to the forward yield curve for interest rates, there is a forward curve for commodities. Usually, long-term futures are cheaper than front month futures, this is known as backwardation, which allows attractive structured product pricing. Backwardation hence means that the spot price is above the forward price, for example when there is a shortage of inventories compared to demand.

The UK market has thus seen capital protected commodity-linked notes with participation in the upside as high as 300 per cent, while participation is usually in the region of 100 per cent for a capital protected note linked to the FTSE index.

The return on the rolling future investment can be analysed as:

• The ‘spot effect’ whereby the future tracks the commodity spot price;

• The return on the cash which is put up as collateral for the investment; investments in futures are usually fully collaterised, i.e. an amount equivalent to the notional investment has been set aside as collateral;

• The ‘roll effect’, which is the amount you will earn (or lose) each time you switch to the next future expiry, due to the difference in prices of different expiry futures. A backwardated forward curve will result in a positive roll yield, i.e. you will be making money each time you switch to the next expiry.

On the other hand, the structured product will have a return that will be simply the greater of zero and of the spot return until maturity, multiplied by the gearing.

To be able to compare the two of them, and this is where we really add innovation into the subject, we model jointly each component, i.e. the spot, the cash return and the cumulated effect of the rolls with realistic parameters. We also add an element of randomness to the process, allowing not only the spot but also the interest rate and the roll to move in a constrained random fashion over time.

The expected spot returns are in the region of 2.5-5 per cent (which is not far from general inflation), but when added to cash return and roll effect, we end up with an expected return for the GSCI Total Return index in the region of 8.5 per cent per year, which is encouragingly realistic.

Including commodities (structured products on commodities) in a portfolio analysis.

Now that we have a consistent way of modelling both index-tracking commodity investments and commodity-linked structured products, we can perform a portfolio optimisation.

The products that we will include are the following:

• Call commodities: a capital protected 5Y Note on a basket composed of 50 per cent WTI, 16.7 per cent gold, 16.7 per cent aluminium and 16.7 per cent copper

• Call FTSE: a capital protected 5Y Note linked to the FTSE 100.

We observe a significant impact of the inclusion of the commodities in the asset set.

Also, even with quite harsh assumptions on the commodity spot return, we observe that the capital protected commodity-linked note receives very significant allocations in all medium-risk portfolios, while the direct commodity index tracking investment appears mainly in the high-end in terms of risk.

The inclusion of structured products indeed has a huge impact on volatility. With their capital protection feature, their downside risk is non-existent. Therefore, they provide a toolbox to design return-seeking portfolios with tailored level of risk.

Wojtek Nabialek is head of the Global Structuring Group at BNP Paribas London.

In association with BNP Paribas.