Asset Allocation - The retail equity investor’s guide

What is risk?

Last year I wrote about my personal approach to managing my own capital which we got a lot of positive feedback from. Given equities would peak a few months later the note was quite timely. With equities significantly lower from their recent peak and the recent bounce in equities, we are taking a slightly different angle to risk management. We are laying out what risk is and what the typical retail equity investor can do to avoid having too much risk should equities begin falling again.

First we need to distinguish between risk and uncertainty. Risk can formally be described as process that is quantifiable with a certain confidence bound related to the sampling size; in other words, a process in which can have statistics. Uncertainty is defined as unquantifiable such as the invasion of Ukraine, because the event is unique and thus has no meaningful prior.

If we look broader at risk it all starts with the ultimate definition of risk which is avoidance of ruin. While being an important concept and something that can be avoided if an investor refrain from using leverage, ruin can also be losing 98% of wealth; it is just not complete ruin. But it is ruin enough that you need a 4900% gain to get back illuminating the asymmetry between gains and losses.

The most normal definition of risk is the variance of some underlying process (for instance a stock) which is a statistically measure of how much a process varies around its mean value. The higher the variance the higher probability of big moves in either direction. Since most retail investors are equity investors, and thus long-only investors, we should care more about the downside risk than the upside risk (gains) as I want as much variance if its lower bound is above zero return.

Focusing on downside risk/returns leads to a concept called semi-variance which only focuses on the returns below a certain threshold, often zero, and describes the downside risk. The problem with this approach is that the underlying assumption is a well-behaved distribution of negative returns. Now, we know financial markets and equities are fat-tailed meaning that we observe many more big moves (both gains and losses) than what the normal distribution would indicated. This means that the semi-variance will underestimate the true risk because of the asymmetry in returns.

These observations have lead to concepts such as conditional value-at-risk which is a fancy word for calculating the average return of the say 1% or 5% worst returns. This measure has many wonderful statistical properties with one of them being that it is less sensitive to the assumptions of the underlying distribution of returns.

A somewhat related concept which is easier to understand is maximum drawdown which is defined as the decline in portfolio value from the maximum value to the lowest value over the entire investment period. Because of the asymmetry of gains and losses, traders focus a lot on this measure and cut losses to avoid big drawdowns or large single period losses (daily, weekly, monthly).

How can the typical equity investor reduce risk?

The typical return investor has limited capital and thus often end up with portfolios holding only 3-5 stocks as minimum commission otherwise would equates to high transaction costs. The first plot shows the returns of a 5-stock portfolio in European equities in which we select randomly five stocks in January 2010 and let them run through time. If one stock is delisted or bought we just place the weight in cash. We do this 1,000 times to the intrinsic variance in outcomes of such portfolios.

A considerable percentage of these 1,000 portfolio end up with a negative return over this 12,5 year period which in itself is remarkable, but the number of portfolios that end with extremely high total returns is also surprisingly high. In other words, a 5-stock portfolio is a lottery ticket with an extreme variance in outcome. The blue line and area represent the median total return path and its variance if these random 5-stock portfolios are blended 50/50 with a the STOXX 600 Index. The striking result is that the median expected return is not changed but total risk (both gains and losses) is reduced considerably. The sharpe ratio, which measures the annualised return relative to the annualised volatility, improves 20% on average by adding an equity market component. So most retail investors can drastically improve their risk-adjusted returns by adding an ETF that tracks the overall equity market without sacrificing the expected return.