23 Nov, 2021

Everything in moderation

INSIGHTS Market Insight

More is not always better. Eating four scoops of ice cream on a hot summer day is not necessarily more satisfactory than eating just two. The more ice cream you eat, the lower your marginal utility from one extra scoop becomes and higher the likelihood you regret your decision when on your weighing scale the next morning. This rationale underpins a decades old debate among financial market practitioners – that is how many stocks are enough to diversify your portfolio?  

Deciding on the number of stocks in a portfolio will ultimately depend on the level of risk an investor is willing to accept, as well as the transaction and opportunity costs involved. Holding too few stocks exposes the investor to stock specific, diversifiable risk (often termed ‘idiosyncratic risk’), while holding too many stocks increases both transaction costs and the opportunity cost associated with monitoring a larger portfolio. There is, therefore, a portfolio size beyond which the marginal diversification benefit of adding an extra position does not outweigh the associated costs – a point of ‘diminishing diversification’. 

We assess the number of stocks required to meaningfully reduce idiosyncratic risk across five Risk Premia: Momentum, Value, Carry, Size and Quality. As Figure 1 illustrates, a 100-stock developed market (DM) portfolio reduces volatility by 7% for Value and 5% for Momentum and Size compared to a 10-stock portfolio, with the diversification benefit being slightly less significant for Carry. The 100-stock portfolio can reduce idiosyncratic risk by at least 80% compared to the 10-stock portfolio for most of these Risk Premia. For the ‘less risky’ Quality Premium, peak diversification can be achieved through a 50-stock portfolio.  

Figure 1: The figure shows the annualized volatility for different sizes of a DM portfolio across five Risk Premia: Momentum, Value, Carry, Size and Quality. Portfolios are constructed using the following indicators: 12M Price Momentum (Momentum), Price-to-Book (Value), Dividend Yield (Carry), ROE (Quality) and Market Capitalization (Size). Constituents are equally weighted. All figures are shown in USD, from 2005-01-01 to 2020-12-31. Source: Arabesque Asset Management 

his is perhaps even clearer through a sector neutral lens (Figure 2). A sector neutral 80-stock portfolio removes c. 75% of diversifiable risk compared to a 10-stock portfolio for all Risk Premia except Quality, which again requires a lower number of stocks to diversify idiosyncratic risk. One can also see that all Premia have structurally lower volatility when sector constrains are imposed. This is supported by Kritzman and Page (2002), who show that diversification across countries and sectors provides the greatest diversification potential, after security selection. 

In practice, the optimal size of a diversified portfolio is a function of the scope of diversification, the desired risk reduction and the respective risk measure. However, a general rule of thumb is that holding 100 stocks cognizant of sector constraints can diversify away 90% of idiosyncratic risk, a rule supported by our own data.  

As Cleobulus, an ancient Greek philosopher and poet, said: “Μέτρον ‘Αριστον” or “Everything in moderation”. It is important to maintain balance and avoid unjustifiable extremes, be it when deciding how much ice cream to eat or when choosing how many stocks to hold in our portfolios. At Arabesque, we construct our portfolios in a similar manner, defining thresholds that offer our investors an appropriate trade-off between portfolio size and diversification. 100 stocks tends to be our 2 scoops of ice cream.  


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