Notes, links and extra information to supplement episode 12 of the Oxford Risk podcast.

**The following is an explanation of the issues facing asset allocation by Xi Chen PhD.**

“Based on modern portfolio theory, an actively managed portfolio is established through the portfolio optimization process. It is a mathematically constructed process which, in effect, aims to look for the very combination of involved assets that can produce the maximum/minimum portfolio return/volatility subject to restrictions, if any. Hence, this process strictly depends on not just the asset classes but the actual return and volatility of each asset involved in the portfolio as well as the correlation estimates between these assets.

In the following two examples, we attempt to explain that assets from the same asset classes could contribute rather differently to the portfolio and so, two portfolios constructed with the same asset classes and the same associated weights may perform very differently from each other.

Let’s take shares of Apple and Nokia as two cases of growth assets (all costs ignored and naively based on historical performances in the following discussion). Apple shares have an average return of 22.33% and a volatility of 32.00% during the past ten years while Nokia shares have an average return of -12.38% and a volatility of 46.35%. Although both are growth assets, their performances differ significantly and would contribute to the portfolio returns and volatilities quite differently. Let’s assume we create a portfolio with one of these two growth assets as well as the iShares 7-10 Year Treasury Bond ETF. By setting the portfolio volatility at 8% throughout the portfolio optimisation process, the portfolio is estimated to either involve 89% of apple shares and to generate 20.45% expected return, or to involve 50% shorting of the Nokia shares and to generate 13.96% expected return. Clearly these portfolios have quite different return-volatility prospects and would hence suit people with significantly different risk appetite.

Another pair of examples would be SP500 and DAX as two cases of stock market indices. SP500 has an average return of 7.35% and a volatility of 20.70% during the past ten years while DAX has an average return of 4.63% and a volatility of 23.38%. While their overall return and risk look similar, their correlation is around 62%, meaning these two indices perform with rather different patterns and cannot be substitutes for each other. Let’s again assume we create a portfolio with SP500 and the iShares 7-10 Year Treasury Bond ETF. By setting the portfolio volatility at 8%, the portfolio is estimated to involve 131% of SP500 and to generate 8.05% expected return. Now if we replace the SP500 with DAX while holding the asset weights unchanged, the portfolio would generate only 4.48% expected return and a 10% portfolio volatility, half as profitable and yet 25% more than the portfolio involving SP500 instead of DAX. This change would certainly alter the categorical investors who would like to invest in the portfolio.

While it would be a very convenient practice to put together portfolios with similar asset classes involved with similar weights within the portfolio, we suggest strongly against some risk profilers’ practice of matching portfolios not based on their actual financial characteristics but based on their involved asset classes and the associated weights.”