The Arithmetic of Prudence, Part 1

This is the 1st part of a series where I will discuss the need for low-risk portfolios. Note I said risk and not volatility. In personal financial planning, risk is the likelihood of the portfolio not meeting one’s financial objectives, while in other financial decisions, “permanent loss of capital/purchasing power” is an acceptable definition. Academics like to use volatility as a proxy for risk, it can be easily calculated and lends to neat formulas but is a poor conveyor of real risk.

I personally have a pretty high psychological capacity for risk, no doubt conditioned by being a PM investor since 2002. I have been gainfully employed for most of my life except for 2007-2010 when I voluntarily quit to take care of my daughter and to pursue some ideas of my own. Before embarking on that I made a pact with my wife that I would contribute half of the expenses from my portfolio – unfortunately the great financial crisis was just around the corner. Forced to sell near the bottom was a visceral lesson that portfolio risk should be the LESSOR of indicated by psychological capacity and financial need. I had underestimated the risk characteristics as the portfolio transitioned from accumulation to withdrawal.

Let’s do a thought experiment. Suppose we are faced with a choice between

A. 50% chance of getting $10 million, 50% chance of nothing

B. 100% chance of getting $1 million

The choice can only be made once.

Which one The choice can only be made once. will you choose? I, and most people I know, would pick B in a nanosecond. Now, the expected value of A at $5 million is much higher than B, but expected value only matter when this choice can be made multiple times. When there is only one shot, the pain of getting nothing (losing $1 million vs. B) far outweighs the joy of getting $10 million (an additional $9 million vs. B). This is an extreme case of loss aversion. The dollar amounts need to be significant for this to work, i.e., if we’re talking about $1 and $10 instead, I may well pick A. But since we’re talking about retirement savings, the amounts are such that loss aversion is real and matters a great deal.

An analogous asymmetry exist in personal financial planning. Once we adjust to a certain life style, the “misery” of having to dial back is much greater than the extra “joy” from the same amount of additional spend. A famous passage in David Copperfield by Charles Dickens goes,

(Wilkins Micawber) Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds nought and six, result misery.

This preference for the current level of spending may be a case of status quo bias. Together with loss aversion, they are related to the prospect theory which “describes the way people choose between probabilistic alternatives that involve risk”. The crux of the theory is the value function: an asymmetrical S-curve, steeper for losses than for gains.

So how does this impact portfolio planning? Far too often we only compare the expected portfolio value, which by definition is the 50 percentile outcome, with our target number. Knowing how the pain from undershooting disproportionately outweigh the joy from overshooting, it behooves us to examine the lower percentile outcomes, i.e. the outcomes we’re more sure of achieving. As I will show in future installments of this series. This insight will lead one to trade potential upside for limited downside.

Leave a Reply

Your email address will not be published.