Portfolio building: diversification with cash

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Last week I wrote about how all equity portfolios are not the same – some are more efficient – that is, they offer a better expected return for the same expected risk. And there are different sorts of efficient portfolios for investors with different appetites for risk. This week, I will add cash into the mix to show how cash opens up even more good choices for investors.

Cash and risk

We usually assume there is no risk in holding cash so that cash has zero volatility associated with it. Carrying over last week’s stylised discussion, cash was assumed to earn 3%.

Let us now assume that the investor is considering holding the equity portfolio denoted by the red circle in the chart below. That portfolio happens to have an expected return of 12.375% and an expected volatility of 12.5%.

Chart 1: Stylised efficient frontier with cash

If the investor chooses to hold a proportion of his or her wealth in cash (say 20%) and the rest in the red portfolio (80%), the expected return of the equity portfolio and cash falls to 10.5%, a simple weighted average.

(0.2 (3%) + 0.8 (12.375%) = 10.5%)

Reducing volatility

Since the volatility of cash is zero, the volatility of this new cash/equity portfolio is equal to 80% of the volatility of the red equity portfolio alone, which works out to be 10%.

(0.8 (12.5%) = 10%)

If we choose proportions in cash other than 80%, the risk-return alternatives follow the green dotted line in the chart. The line cannot go to the left of the returns axis, that is, negative volatility is not possible.

However, the green dotted line goes on forever towards the right. At any point to the right of the red circle on the green dotted line, the proportion of cash is negative – that is, the portfolio is geared by borrowing to invest.

Although standard gearing (or a margin loan) is not allowed in an SMSF portfolio, let me temporarily sidestep that one for a paragraph or two. From last week’s column we know that the portfolios above the dotted line and up to the black efficient frontier are not as efficient as those on the black line itself.

Preferable portfolios

However, had the investor chosen the yellow circle portfolio (the equities portfolio with the higher risk-adjusted return), we can see that all portfolios on the solid green line (being combinations of cash and the yellow portfolio) are preferable to those within or on the efficient frontier – except for the yellow portfolio itself which has no cash. If the green line was steeper there would be no feasible portfolio with which to blend it with cash.

The new efficient frontier

If the green line were shallower – say the dotted line – there is always a portfolio with higher expected returns, but with the same level of risk vertically above the dotted line on the (extended) green line. The yellow portfolio is the maximum Sharpe-ratio portfolio, so named after the Nobel Laureate who constructed the theory. The green line is the new efficient frontier when cash is included.

It follows for investors outside of super that there is only one equity portfolio for them if they are prepared to hold cash or borrow on loan. On the geared side, both expected risk and return climb up the green solid line as the investor swaps the risk inherent in the portfolio for the gearing risk that is amplified by borrowing. It makes no sense to gear up a portfolio that carries more expected risk than the yellow portfolio. Equity portfolios can carry too much risk – particularly if they are geared!

Using the strategy

For the SMSF investor, holding some cash is usually very wise. Since gearing is not allowed, the efficient frontier is the solid green line from the vertical axis up to the yellow circle – and then it follows the black line to the right.

Importantly, there are many opportunities for SMSF investors to hold cash and make significant gains in expected returns for the same level of risk on the dotted line as the equity portfolio directly below it on the black line – and there is nothing in between! So, if the SMSF has low volatility stocks and no cash, it might be worth exploring swapping some of the low equity return for riskless cash! It all depends upon expectations.

In the next set of articles, I will explore how one might choose the number of stocks an investor might hold in an SMSF.

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.

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