I often find new investors think of choosing a basket of equally weighted stocks as being diversification – it ain’t necessarily so! Risk and return should also be taken into account.
In my previous column, I mapped out the risk-return characteristics of the 11 sectors of the ASX 200, the index itself, and the characteristics of a particular portfolio of sectors. This week I aim to show you that there is so much more to diversification than just selecting a bunch of stocks or sectors. I propose to demonstrate this using two charts, hypothetical data and the term ‘risk’ rather than ‘expected volatility’ for brevity.
So let’s begin. In Chart 1, I have plotted three red symbols: one for each of the hypothetical stocks A, B and C.
Decoding the chart
In the chart of stylised risk-return, ‘C’ is the high risk/high return stock, ‘A’ is low risk/low return and ‘B’ is medium in terms of both risks and returns. The yellow symbols represent three equally-weighted ‘portfolios’ of each pair of stocks (ie, A and B, B and C, and C and A), while the black circle is an equally weighted ‘portfolio’ of all three ( A, B and C).
Let’s calculate the return of the yellow and black portfolios. To do this, one simply takes a weighted average of the returns of each individual stock, and this will put the yellow diamond halfway up (in a vertical sense) between A and C’s return. Note: the risk in this framework is not an average of the individual risks. It also depends on the correlations between the stocks or sectors. In this hypothetical example, I have set all correlations to 0.4, which means there is some degree of co-movement – but not a lot. Negative correlations are the best to gain risk benefits from combining stocks, but they rarely exist. There is a market effect that is common to many stocks and that is what I am trying to capture by the 0.4 assumption.
Notice that stock B has a higher return than the portfolio of A, B and C (the black dot) and just about the same risk. If the risks were identical, B would dominate the portfolio, as I discussed in my previous column. Obviously, the portfolio is inferior – in that sense – to having not ‘diversified’ by just holding stock B. Similarly, the A, B portfolio dominates A alone, etc.
The opportunities
If we start to think about not having equal weights, the opportunities to diversify increase dramatically. To start this thought process, I have ‘randomly’ created a number of ‘blue dot’ portfolios in Chart 1 to give some impression of how the process works. I take this to an extreme in Chart 2 by adding even more blue dot portfolios.
The blue dots start to form a cloud that will eventually get filled in as I add different portfolios. It hopefully doesn’t take too much imagination to see that two curved (continuous) lines – one on the top of the cloud and one on the bottom – envelope all of the portfolios.
Understanding domination
All portfolios on the top curved line to the right of where it starts to bend under near stock A dominate all of those vertically below them in a risk-return sense. The ones on this top portion of the curve are all ‘efficient’ in a mean-variance sense (see the previous issue) and, because they each have a different risk, each portfolio is suitable for an investor with a different risk profile.
I don’t have the space in this issue to discuss in detail where the green line comes from – but it is a straight line from the ‘risk-free return’ (like a bank bill rate) – which in this example is about 3% – that just touches the cloud. The portfolio at that touching point has the highest risk-adjusted return of them all. There are complicated mathematical procedures that ‘optimise’ this process using equations and computer programming methods.
The efficient frontier
All of the portfolios in the cloud below the ‘efficient frontier’ (as the top curved line is called) might be diversified in that sense that they contain more than one stock (except for the portfolio just with B) but they are inefficient. We always prefer a portfolio with a higher return for a given risk, and these lie along the efficient frontier. And we prefer a portfolio with a lower risk for the same return.
Not only is the maths complicated, but one has to forecast risk and return! I’ll discuss that later, but it was precisely because my risk forecast for Consumer Discretionary stocks (like Harvey Norman and JB Hi-Fi) jumped enough to take me out of that sector in May as I discussed in one of my early columns. My optimiser chose a zero weight for that sector. And after recent days in the market, I couldn’t be happier about that decision.
Ron Bewley is the Executive Director of Woodhall Investment Research.
Important information: This content has been prepared without taking account of the objectives, financial situation or needs of any particular individual. It does not constitute formal advice. For this reason, any individual should, before acting, consider the appropriateness of the information, having regard to the individual’s objectives, financial situation and needs and, if necessary, seek appropriate professional advice.
