The Balanced Portfolio Theory Andrew Porter - 28 May 2008 This article is for information purposes only and does not form a recommendation to invest. The value of an investment may fall. Investing in shares and bonds may not be suitable for all investors, and if in doubt, an investor should seek advice from a qualified investment adviser. A simple rule of investing states that the higher the risk of an investment the higher the return. This is the Risk Premium: The amount you get paid for taking the extra risk. So if you want to make lots of money you need to take more risks. It is however possible to reduce the risk by building a balanced portfolio. The risk of buying a single share is high with many possible unknown influences on the share-price and future dividends. Buying two shares results in some reduction of risk because a crash in one share price may not affect the other one adversely. Many shares are highly correlated to each other, so having two shares in the same field (e.g. BP and Shell) does not reduce the risk as much as two shares in unrelated industries (e.g. BP and Lloyds) Similarly mixing shares with other asset-classes will also improve volatility of the over-all portfolio (e.g. mixing shares, bonds, property and gold bars) The risk of the portfolio of N assets can be expressed as follows: N N σp2 = Σxi2σi2 + 2Σxixjσij i=1 i<j where: σi2 = risk associated with asset i (variance) σij2 = covariance of ith and jth asset xi and xj= weights of ith and jth asset in portfolio Unfortunately these parameters are not readily available so accurately determining the optimum values for relative weights in the portfolio is difficult, but the equation does highlight the importance of uncorrelated assets. As the number of assets increases the value of xi2 gets far smaller and the first term of the equation far less significant and if the covariance σij is small the second term is also small: If N >> 1 then xi << 1 A portfolio with equally weighted investments in 10 uncorrelated assets (i.e. xi=0.1, N=10, σij=0) would result in a risk of: N=10 N=10 Σσi2 σp2 = Σxi2σi2 + 2Σxixjσij = ---- i=1 i<j 100 i.e. If each asset has equal risk (σi = σj for all i and j) The total risk is just a tenth of the risk of the individual assets. This of course is an extreme example, but does demonstrate the principle. Many people made the mistake of ignoring the equity and bond markets in favour of buy-to-let, making their portfolio extremely highly correlated to the property market, and heavily geared (mortgaged) to improve returns or increase losses. Property may have seemed like a one-way bet, but most people have more than enough exposure to the property market through their own home. Having no exposure to property and a large equity exposure could also be risky. Financial advisors often provide a range of different suggested portfolio distributions depending on the income requirements and risk profile of the investor, how long before the money is required and what volatility or losses could be tolerated. Generally higher risk portfolios will consist of smaller shares or foreign equities and high-yield or emerging market bonds, income portfolios are usually blue-chip shares and bonds and low risk portfolios mostly government bonds and cash. In all cases mixing many assets with low correlation from different countries and different industries will reduce the risk.
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