The efficient frontier is a nice idea that actually makes a lot of sense - for any particular level of risk there is a maximum expected return that can be achieved. The efficient frontier is found by plotting the risk and return for the universe of all possible combinations of assets that you want to include in your portfolio, and joining the dots of the ones with the highest return for a particular standard deviation.

[graphic from styleadvisor.com]

For a good explanation of this see www.efficientfrontier.com or read this chapter from "Investment Strategies for the 21st Century" by Frank Armstrong [available free online!]

My difficulty is that my portfolio includes more than just equity funds, bond funds and fixed interest - I have direct property investments, alternative investments (agricultural trusts and hedge funds), direct share investments (local and US), and make use of leverage through property and margin loans. Aside from difficulty in calculating expected return and risk values for some of these investments, there doesn't seem to be much analysis of how gearing (the the risk associated with the loans) gets incorporated into modelling of the efficient frontier.

Wikipedia mentions that the use of leverage can actually lift you ABOVE the efficient frontier - but I'm not sure exactly why. To quote:
"An investor can add leverage to the portfolio by holding the risk-free asset. The addition of the risk-free asset allows for a position in the region above the efficient frontier. Thus, by combining a risk-free asset with risky assets, it is possible to construct portfolios whose risk-return profiles are superior to those on the efficient frontier.
* The investor who borrows money to fund his/her purchase of the risky assets has a negative risk-free weighting -i.e a leveraged portfolio. Here the return is geared to the risky portfolio. This combination will again offer a return superior to those on the frontier."

Unfortunately I haven't yet found a more detailed treatment of this elsewhere on the net. Also, in practice, your gearing uses margin loans or home equity loans at 2-3% above the risk free rate, so I'm not sure how this ties in with the presumption of leveraged investments utilizing the risk-free asset.

Any comments or references?

Had a nice, cheap evening out tonight. Vanguard Australia had arranged for Dr. Burton Malkiel to give a talk in Sydney. There was quite a good turnout, and the setting was great - in the Ballroom of the Westin Hotel in Sydney.

If you've read his famous book "A random walk down wall street" (and the Vanguard product brochures) there was nothing new in the one hour session. But the professor is a very entertaining speaker, and it gave my wife a quick overview of efficient market theory and how it suggests index funds are a good 'core' choice for your portfolio.

Afterwards I bought a new copy of the book, and had it signed by the Author. I also got to ask the Vanguard officials how come the US parent has low, low fees (around 0.25%) while the Australia version starts at 0.9% and only gets cheap (0.35%) for amounts above $100,000 that are invested in a single fund. With Dr. Malkiel predicting single digit returns are likely in the future, an extra 0.5% fee off your 9% total return will have a big impact over time. The suits from Vaguard said that the Australian Fund is smaller than the US one, but that they were "looking into" the fees. I won't be holding my breath. In the US "no load" funds can only charge a certain maximum for advertising before they can't call themselves "no load" - here there's no such rule, so I think the current Vaguard Australia customers are paying for the companies growth strategy.

All in all, a very economical and enjoyable night out.
ps.
Total costs (2 persons)
Lecture - free
Parking - $4 at Pyrmont (a healthy walk through Darling Harbour to the city)
Entrees and drinks before - free
Dinner afterwards - $17 (OK, it was actually 2x take-away)

total = $21.00!