In considering portfolio management and the implications of diversification, it is important to understand the investor’s intrinsic values and their subsequent actions. Investors seek to maximise their utility, which is determined by their responsiveness to risk. Both Kevin and Julia’s risk aversion coefficient is important in determining their utility through investing in securities and evaluating the effectiveness of diversification to meet each individual investors’ needs. The utility function is represented by U = E(R) – ½Aσ^2. By incorporating expected returns and variance, this adjusts for investors’ willingness to adopt risk and consequently, Kevin will seek higher rates of return, whereas Julia will seek to minimise variances through diversification.
When considering whether to diversify, it is also important to understand the individual securities and the relationships with other stocks to determine the positive outcomes from selecting additional stocks. By using Telstra, Sydney Airport, Carsales.com, Flight Centre and Amcor, five stocks from unique industries with varying levels of returns and standard deviations, Kevin and Julia may receive positive benefits from choosing portfolios combining these stocks by dispelling unique firm-specific risks. As seen above, volatile stocks like Flight Centre are usually compensated with a higher premium for the additional risk.
As evidenced through the calculations, diversifying a portfolio helps lower portfolio risk for any given level of expected return. This is highlighted by the negative utility experienced by Julia if she invests 100% into each stock due to her preference to avoid risk against the high variances of Carsales.com and Flight Centre despite their higher associated returns. Whilst maximising expected returns, Julia’s negative utility from investing 100% in each of the 5 stocks is a reflection of the additional risk she must undertake and adjusted against her tendency for risk outweighs the additional returns she can expect. Similarly, Kevin also receives the lowest utility by investing 100% into both Carsales.com and Flight Centre and despite his propensity for risk with a risk-aversion coefficient of 12, implies that investors expect to receive a higher premium for Carsales.com and Flight Centre’s stocks due to the higher standard deviations of their returns.
Whilst Julia cannot match the returns of fully investing into Flight Centre, by holding additional stocks she is able to achieve a similarly high level of return at a much lower variance. On the other hand, Kevin welcomes Flight Centre’s high returns allocating a heavier weight than Julia, using Amcor’s low variance to offset Flight Centre’s high variance. These examples emphasise the importance of an investor’s levels of risk aversion to their allocation of weights and…