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Someone once said that the first rule of investment is “don’t lose money” and the second rule is “don’t forget the first rule”. This sounds facile, yet it is a profound statement that is central to how we think about risk. The reason for this lies in the distinction between the calculation of arithmetic average versus geometric average returns and the fact that aggregate portfolio returns are compounded over time.
The chance of gain is by every man more or less overvalued, and the chance of loss is by most men undervalued
Imagine a coin flip where each outcome is equally likely, but heads pays 60 per cent, while tails loses 50 per cent. This sounds like an attractive bet since the expected return is the arithmetic average of 5 per cent. Indeed, some active fund managers would describe this return profile as asymmetric, offering greater upside than downside. But let’s roll the exercise forwards: a positive 60 per cent return followed by a negative 50 per cent loss followed by positive 60 per cent gain then negative 50 per cent. Despite the arithmetic average remaining at 5 per cent, the geometric average multiplies each outcome such that our errant coin flipper has lost 36 per cent of their starting capital.
What was presented as a seemingly attractive bet overlooks the fact that a 100 per cent return is required to return to breakeven after being down 50 per cent. When assessing a prospective investment it is not enough to merely quantify the upside because the mathematics of compounding returns make it very difficult to recover from catastrophic losses. Accordingly, our priority should be not to lose.
What is true at the individual stock level also holds true for a portfolio. An investor who receives 16 per cent annually for a decade end ups better off than an investor who earns 20 per cent a year for nine years and then loses 15 per cent the tenth year. Again, the mathematics of geometric compounding are responsible for the deleterious effect of one bad year on overall performance. This is what makes capture ratio a suitable metric for assessing fund returns on a risk-adjusted basis.
By giving attention to how a fund performs during negative periods for the market can show otherwise positive returns in a different light. For example, imagine a market that returns 16 per cent for nine years and loses 16 per cent in the tenth year. One fund unexcitingly performs in-line with the market during the up years but falls by half as much in the final year. Overall it beats the market by one percent annualised with a capture ratio of 2.00. Another fund excitingly beats the market by four percent during the up years but falls by twice as much in the down year. While it has outperformed by a similar amount, the far inferior capture ratio of 0.63 speaks to the risk-adjusted manner in which these returns where achieved.
