Tuesday 22 August 2006

Stumbling towards the efficient frontier

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.

efficient frontier graph [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?


mOOm said...

The efficient frontier is constructed, excluding the returns on the risk-free asset. So including long or short positions in the risk-free asset can accelerate returns further. Shorting the rfa is borrowing cash. The fact that most investors must pay more to borrow than to lend means there is a different (higher return and more risky) portfolio that is appropriate when considering borrowing vs. when considering allocating to part cash, part investments. In other words there is a quantum leap in lower risk aversion needed to go from non-leveraged investment to leveraged investment which wouldn't be there if the two rates were the same. I might draw up a diagram of this on my blog.

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