i

Tuesday, 8 April 2014

Diversification is a Second Order Effect

Diversification is commonly understood as one of the cornerstones of Modern Portfolio Theory. The most basic MPT models (which are taught in schools and therefore represent the way most people think about MPT), are single-period models in which the inputs (most importantly expected returns, covariance matrix and investor preferences), are assumed to be known in advance and to remain constant over this time period. In this world, diversification is then perceived as the benefit of holding a portfolio of imperfectly correlated assets and is expected to result in improved risk-adjusted returns for the investor.

Real-world investing is about running portfolios in a dynamic world characterized by time-varying and asset risk and return characteristics which are subject to significant forecasting uncertainty (as opposed to forecasting risk). The chart below plots the rebased trajectories of the two important asset classes equities and bonds, as measured by two popular market indices (total returns, monthly data 1985-2012, base currency USD)...


In order to visualize the risk dynamics, we calculate annualized rolling 24 month asset volatilities and 24 month rolling asset correlation...


We see that neither correlations nor volatilities are stable. Plotting correlations against average volatility reveals a relatively week relationship between the two...


In order to assess the relative importance of volatility dynamics versus correlation dynamics, we create a 50/50 monthly rebalanced paper portfolio and calculate its 24 month rolling volatility over time and create scatter plots against asset volatilities and asset correlations...

 
 
We see that the risk of the 50/50 strategy is driven much more by asset risk dynamics than asset correlations. The difference is so pronounced that we can conclude that time-variations in the diversification potential is a minor second order effect compared to time-variations in asset risk. This stylized fact can be easily reproduced with more sophisticated statistical methods, different asset universes and different historical time periods. This fact has important consequences for real-world investment practice like asset allocation, portfolio construction and risk management.