Monday, December 27, 2010

What it means to diversify your investment


Whenever you meet with a financial adviser, you'll be probably fed with the idea of diversification and its closely related idea of asset allocation. The concept, when fully expanded, is very convincing. The presentation may start with an introduction to Modern Portfolio Theory (MPT) as formulated by the Nobel laureate Harry Markowitz, and reach a conclusion to invest in a portfolio on the efficient frontier. Efficient portfolios in our world always consist of more than one asset class. Sometimes, a more knowledgeable adviser may also extend the presentation to include the Capital Asset Pricing model (CAPM) to explain the concept of "the market portfolio", diversifiable risk (also called security-specific / idiosyncratic risk), and non-diversifiable risk (also called systematic risk / market risk), where lies the essential merit of diversification. Rarely, the Security Market Line (SML) and stock beta may also be mentioned, though these concepts are more relevant to stock-pickers than portfolio investors.

Despite all the jargons and explanation, the recommended action for average investors often is to simply buy into the various "diversified" funds marketed by the company being represented. Now I'm not against investment in funds, for I'm also vested in funds. The key thing however, is to understand what diversification and asset allocation mean for you as an investor.

Diversification is often understood as buying many stocks instead of holding to one, and when you believed it as such you have done yourself a disservice. Truly efficient diversification involves selecting component stocks based on their relative correlation and giving proper weightage to each component stocks based on its value. When you define diversification this way, I say, even Warren Buffett will agree with diversification .

The merit of diversification can be shown using the risk-return plots of portfolios consisting of two perfectly negatively correlated assets S and B in various proportions, as in Figure 1. The result defies the conventional wisdom that risk (probability and magnitude of an adverse return) and expected return must be directly proportional to each other! As can be seen from Figure 1, negative correlation between the asset S and B creates a section in the portfolio risk-return graph where return and risk are inversely proportional to each other.


Figure 1 Portfolio risk-return plot

Some significant results from Figure 1 are tabulated in Table 1. Compare portfolio A and C, which have the same level of risk, and you find that portfolio C has higher expected return! Portfolio B does even better because it has both higher expected return and lower risk (in fact, riskless) than portfolio A!


Table 1 Portfolio risk-return



Alas, the results in Table 1 are not achievable because it requires asset classes that are perfectly negatively correlated that do not exist in the real world. However, the good news is imperfect correlation can also be used to achieve similar result! So, selecting component stocks based on carefully chosen correlation has more merit than you think!

The next challenge in efficient diversification is allocating the appropriate weights to the component stocks in your portfolio. The component stocks can be price weighted, market value-weighted, or un-weighted (equal weighted). If you invest in Dow index fund, your portfolio is price weighted. If you invest in STI ETF, your portfolio is market value-weighted. If you invest equal dollar in each component stock, your portfolio is un-weighted.

There are other weighting schemes, of course. For example, take a look at the publicly-traded U.S. stocks owned by Warren Buffett's holding company Berkshire Hathaway or its subsidiaries, as reported to the Securities and Exchange Commission in filings made available to the public (http://www.cnbc.com/id/22130601/). Clearly, Warren Buffett uses a weighting scheme for his diversified portfolio that’s non-conventional, and it’s this ability of his to separate the chaff from the wheat that makes him a legendary investor!

After all the discussion, I hope now you’ve a clearer picture of how to achieve efficient diversification. Though Warren Buffett doesn’t believe in index investing for himself, for those who are not on par with Warren Buffett (e.g. those who does not understand the economics of specific businesses but nevertheless believes it in his interest to be a long-term owner of global industry, i.e. most of us), he’s got an advice for us: own a large number of equities and space out our purchases. Ironically, the best way to do it when you have limited funds under $300,000 is still investing in funds.

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[1]  Warren Buffet has been widely quoted to have said that diversification is a protection against ignorance and it makes very little sense for those who know what they're doing. Upon investigation, you’ll know he’s referring to wide-diversification, not efficient diversification when he said that.

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