Explain how diversification of assets eliminates specific risk. Use a numeric example to illustrate your reasoning. (Do NOT use the same numerical example as in the textbook or lecture notes and seminars!) Use an example of two assets, one with higher return and volatility than the other. (i) Calculate the expected return and standard deviation for each asset and compare. Every asset has an expected return on it as they are forward looking and has a risk attached also. Risk refers to the possibility that the actual return may differ from the expected return of an asset be it more than or less than what was expected. The risk is subject to a combination of both the specific and market risk.
Diversification is a strategy that investors can use to reduce the risk each asset. It is done by investing in a percentage of each asset and placing it into one portfolio. As investors are assumed to be rational and risk averse. Risk by nature is symmetric, meaning return can be higher or lower than expected however, risk aversion is an asymmetric attitude that investors have to holding financial assets i.e. they are more concerned with the possibility of losing a given amount than the possibility of gaining the same amount. This attitude can be depicted on the diminishing marginal utility of wealth diagram, where the utility (u) from an added amount of wealth is far less than the decrease in utility from a reduction in wealth of the same amount.
Source: Richard G Lipsey and K Alec Chrystal, 2007 This means investors look for the highest return possible for a given risk and look for the lowest risk for a given return. Also, they would not be interested in a risky investment offering the same rate of return as a higher investment; they’d want a higher return for a risky investment than that of a safe investment. So that investors know better what assets to hold they predict from past results the expected return on each asset for the different states in an economy. The variance in an asset’s rate of return measures the asset’s risk as the more volatile the return, the more difficult it is to predict. However the variance is ex-post as opposed to ex-ante which is the basis of investor’s decision. The standard deviation for each asset tells us the amount of risk that comes with the expected rate of return expressed as a percentage.
This means that the variance of asset B being over 3 times more than that of asset A for not that much more expected rate of return 15.6 to 17.95, investors, due to the law of diminishing marginal utility of wealth would normally favour asset A out of the 2 as it less risky expressed by a lower standard deviation of 2.29% in comparison to 4.01%. If investors replace A with B they will have more risk but also a higher return, the risk will increase by 1.72% and the expected return by 2.35%. The expected return gained per unit of risk is then 1.37. If Investors replace B with A, they will have less risk and have a lower rate of return; risk will decrease by 1.72% and expected return by 2.35%. Expected return lost per unit of risk is then 1.37.
(ii) Construct a portfolio of the two assets in such a way that the portfolio consists of 50% of each asset. As noted earlier investors can include a percentage of each asset (all must equal 100%) into the portfolio but for this example we will be using 50% of each. To find the expected portfolio return of such we use the formula, As = 15.6 and = 17.95, Wj is the percentage amount invested as a proportion of the portfolio.
This figure is the weighted average for the expected rate of return on the assets that make up the portfolio. With this figure we can find the co-variance which measures the degree of co-movement of both assets in the portfolio. The formula is expressed as = 0.25(19-15.6)(20-17.95) + 0.65(15-15.6)(19-17.95) + 0.1(11-15.6)(6-17.95) = 6.83 Now with this figure of 6.83 we can find the standard deviation as a measure of risk for this portfolio. However to find this we use the formula below.
To measure the co-movement of both assets in the portfolio is called we use the correlation coefficient which tells us the degree to which the returns on each of the assets move together. This is a very important measure as it can let us know how effective diversification would be. The correlation coefficient is always between -1 and 1 where the closer the figure is to -1, the less correlated the assets are which means the more effective diversification will be. Diversification will be most effective however when the correlation coefficient is -1.
