In portfolio theory, an efficient frontier is the collection of optimal, or efficient, portfolios, mapped according to their expected return and volatility. Efficient frontier analysis, aiming at selecting the best risk/return portfolios, could until recently only be performed using “classical” assets, but this can now be undertaken on a portfolio containing structured products.
Before considering the usefulness of an efficient frontier calculation, it is necessary to explore the theories behind the concept.
The object of an investment in a portfolio rather than a position in a single underlying is to diversify an investment, and minimise risk. However some portfolios are better than others, depending on the underlying assets, and their weights, within the portfolio itself.
Until revolutionised by Harry Markowitz, founder of modern portfolio theory, investment portfolios were largely selected according to an individual analysis of their constituent assets, selecting stocks and bonds for instance, which had attractive risk-reward profiles individually, rather than selecting an overall portfolio.
In 1952, Mr Markowitz introduced the idea that a portfolio should be judged at the portfolio level, treating the assets as random variables. This enabled the calculation of expected values, standard deviations and correlations between the constituent assets, and provided the means to draw an efficient frontier – a way of optimising a portfolio’s risk and return.
When analysing multiple portfolio combinations, there may be many portfolios that have the same volatility. Portfolio theory assumes that for a specified volatility, a rational investor would choose the portfolio with the highest return. Similarly, there may be multiple portfolios that have the same return, and portfolio theory assumes that, for a specified level of return, a rational investor would choose the portfolio with the lowest volatility.
An efficient portfolio is the unique portfolio that has the highest expected return for a given volatility, and likewise the lowest volatility for a given return. Point X, for instance, corresponds to the portfolio displaying the highest rate of return for a volatility of 10 per cent. The efficient frontier is the collection of all efficient portfolios.
Including a structured product
Our approach to the determination of an efficient frontier features the inclusion of a structured product held to maturity, in a manner fully consistent with the same analysis performed on the underlying assets.
This approach is illustrated on one particular structured product, the LookBack. The LookBack offers return at maturity based on the highest performance of an underlying asset on any observation date, with no cap on the upside and 100 per cent capital protection. The most obvious qualitative advantage of the LookBack is to solve market timing issues, thus avoiding stop-loss selling in a downturn of the market.
From a quantitative point of view, the LookBack can improve the efficiency of a portfolio by delivering returns close to those of equities, while lowering volatility/risk.
- Individually, the return of the LookBack increases with volatility, as it registers the highest point reached over the life of the product. Unlike a direct investment in equity however, the LookBack does not pay dividends, thus slightly lowering the potential for higher return compared with equities.
- In terms of risk, the LookBack is significantly less volatile than a direct investment in equity, as it provides full capital protection, and retains the highest level reached by the underlying throughout its life.
It is this powerful mechanism which serves to highlight the relevance of products such as the LookBack in the modern portfolio.
Efficiency analysis provides a useful measure for determining the optimum allocation to an investor’s portfolio. The innovative employment of a structured product component as part of our efficient frontier calculations advertises the versatility and practicality of structured products as part of an optimised portfolio. Unique models have been developed to conduct advanced portfolio analyses with structured products. Part II next month will concentrate on techniques used to measure portfolio risk and return in those models.
Wojtek Nabialek is head of structuring and new products group at BNP Paribas London.
In association with BNP Paribas.
FIGURE ONE: EFFICIENT FRONTIER
Note: An efficient frontier associated with standard portfolio of equities and bonds with the Look-back (orange) and without the Lookback (red)
Source: BNP Paribas
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