Banking and Finance

The correlation coefficient as we calculated earlier is also 0.74, an important figure that we’ll revisit later. So now we can choose to invest 100% in asset A or 100% in asset B or 50% in each as per the weightings of the previously constructed portfolio. First and foremost we can see the benefits of diversification with the portfolio risk being 2.96% which is lower than the weighted average of the asset risk of 3.15% derived from, (0.5×2.29) + (0.5×4.01). In replacing asset B with asset A we reduce risk at a rate of 0.73 (4.01-2.29) / (17.95-15.6) for every unit reduction in return but, if we replace asset B with a 50/50 portfolio we ‘buy’ the reduction of risk (diversify) at the rate of 0.9 (0.897435) derived from (4.01-2.96) / (17.95-16.78) for every one-point reduction in return.
Investing 100% in asset B will get an annual rate of return of 17.95% with a standard deviation on the returns of 4.01. This is where they could get their highest return. If they invested 100% in asset A, they will get an annual rate of return of 15.6% and with a smaller standard deviation on the returns of 2.29 so risk is reduced but so is the expected rate of return. If we diversify with equal weighting as per the previously constructed portfolio then our expected rate of return is 16.78% pa but with a standard deviation of 2.96. If investors diversify 50% into A the risk decreases by 1.05 and the expected return by 1.17 and so the expected return lost per unit of risk is 1.11 (1.17/1.05). If investors diversify 50% into asset B the risk will increase by 0.67 and the expected return by 1.18 (16.78-15.6) so the expected return gain per unit of risk is 1.76. All of this shows diversification gives a better risk to return trade-off.
However, diversification is not at its most effective in this portfolio with a correlation coefficient of 0.74 even though this shows a small reduction in risk. For it to be a zero-risk portfolio the correlation coefficient must be -1. However, even in this scenario, the total risk is not eliminated, only the specific risk and the returns on the assets will still be subjected to market risk. Total risk (standard deviation) is the combination of specific risk + market risk. Only the specific risk is reduced by diversification because it is a risk unique to each asset in the portfolio. For example, if asset A is gold and there’s a discovery of a new, rarer, more precious metal, this will affect the risk of this particular asset. Specific risk is therefore the deviation in the returns of an asset caused by events that affect that particular asset.

Market risk cannot be reduced with diversification as all assets are sensitive to market risk, some more than others. Market risk is the risk arising from factors that affect the economy as a whole like the economic cycle, a change in the price of borrowing, or a change in the price of the currency. The diagram shows that the more assets added to the portfolio for diversification the more the total risk is reduced because of the reduction in specific risk as to the curve slopes downward. This is because as you add more assets to the portfolio there is more chance of the correlation coefficient reducing or becoming negatively correlated. This adding of assets to the portfolio works up until all that is left is the market risk where the slope straightens out and is then pointless to diversify anymore. With this diagram, we can tell that our example of 2 assets of equal weighting is not enough to eliminate specific risks. We can see that it normally takes around 20 assets to eliminate specific risks in a portfolio.
Investors will look to diversify until the specific risk is eliminated through the right number of and weighting of different assets in a portfolio. They’ll have a zero-risk portfolio and the reward they get for the remaining risk will be related to the market risk. This isn’t easy to measure but with the CAPM (Capital Asset Pricing Model) we can measure an individual asset or security’s market risk relative to its expected return with the SML (Security Market Line) equation. In the CAPM the beta is the measure of market risk. Diversification reduces risk to an extent and can remove specific risk depending on the correlation coefficient of the return of assets in the portfolio. The more negatively correlated the better. However, it can’t remove TOTAL risk as the assets will be subject to market risks. A good strategy may be to diversify internationally as suggested by Bruno H. Solnik, to reduce market risk to some degree through offsetting.
Reference

Howells & Bain (2009), The Economics of Money, Banking and Finance, A European Text, Prentice Hall 4th Edition
Bodie, Kane, Marcus (2008), Essentials of Investments, McGraw-Hill, 7th Edition
Rugman (1996), The theory of multinational enterprises: The selected scientific papers of Alan M. Rugman, Edward Elgar Publishing, 1st Edition
Richard G Lipsey and K Alec Chrystal (2007), The Demand for Insurance, http://www.oup.com/uk/orc/bin/9780199286416/01student/interactive/lipsey_extra_ch12b/page_06.htm