Modern Portfolio Theory 2.0 – The Most Diversified Portfolio!

(wi = portfolio weight in asset i, σi = the risk of asset i, σp is the total risk of the portfolio)

Moreover, for a given set of underlying assets, there is only one portfolio combination that has the highest diversification ratio and thus represents the most diversified portfolio. In other words, it is possible to put the maximum weight into each asset class whereas the overall portfolio volatility is not being increased at all.

In our article, we would like to review a maximum diversification portfolio with the following investment universe:

• Vanguard Total Stock Market ETF (VTI)
• Vanguard MSCI Europe ETF (VGK)
• Vanguard MSCI Emerging Markets ETF (VWO)
• SPDR Gold Shares (GLD)
• Vanguard REIT Index ETF (VNQ)
• Barclays iPath DJ UBS Commodity TR ETN (DJP)
• iShares Barclays TIPS Bond (TIP)
• iShares Barclays 20+ Year Treasury Bond (TLT)
• iShares Barclays Aggregate Bond (AGG)
• iShares iBoxx $ Invest Grade Corp Bond (LQD)

 

In our example, there is no allowance for transaction costs or brokerage fees. In order to minimize transaction costs, we rebalance the portfolio on a monthly basis, whereas 1 day slippage is included. By applying the maximum diversification approach, it is absolute necessary to determine the weightings of each asset class on a regular basis, since the correlation among asset classes is not stable over time! We have used a rolling variance/co-variance matrix to determine the optimal diversification weights.

If we have a look at the diversification benefits this portfolio has utilized in the past, we can see that the diversification ratio reached a maximum score of 6, meaning that the overall portfolio risk was reduced by 500 percent! In this specific time period, the correlation among the underlying asset classes was extremely low. On average, the overall risk within the portfolio can be reduced by a factor of 2.7, while the minimum diversification factor was 1.5 in September 2006. Apart from October 2008, where the financial crisis hit the markets, the portfolio volatility itself swung between 2 and 9 percent, whereas the average volatility is around 5.5 percent. Since it is possible to put the most weight to each underlying asset class without increasing the total portfolio volatility, the expected returns of each security and thus the expected return of the portfolio remains unchanged.

 

 

 

 

 

 

 

Another interesting fact is that the weighting of each asset class is mainly driven by its diversification characteristic. In other words, if the correlation coefficient of an underlying security increases, the less weighting it will receive, since its diversification benefits are decreasing (according to the diversification factor).  Therefore it can be possible, that certain high correlated securities will have no weight at all, or the other way round. As a result of this, it can be theoretically possible, that equities have a higher weighting than bonds, in times when the correlation coefficient of stocks to the overall portfolio tends to be lower than bonds.  That is one of the main advantages versus the risk parity approach, where every asset class has the same contribution risk, whatever the correlation of those looks like! Another main advantage of this “All Weather Portfolio” over a risk parity strategy is the fact that it does not need leverage to achieve an attractive return profile.

Since we have only focused on risk and portfolio weightings so far, we would like to examine how this portfolio has performed so far versus the IVV (S&P 500).

The maximum diversification approach has an annualized return of 8.2% while the IVV (S&P 500) has only generated an annualized rate of return of 5%. More importantly, on a risk-adjusted basis (Sharpe Ratio), this “All Weather Portfolio” is strongly outperforming the broad benchmark. However, it was only slightly underperforming the IVV (S&P 500), when equity markets have been in a strong bull market (2006).

 

 

 

 

 

 

If we have a closer look on the diversification benefits (reducing risk during turbulent market conditions), we can see that this amazing portfolio construction approach has also shown significant lower draw-downs in the past. The maximum draw down for the so called “All Weather Portfolio” was only 15.1 percent, compared with 56.8 percent for the IVV (S&P 500). That makes roughly 3.5 times more. In total, the maximum diversification portfolio was reaching a new high after 150 days.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The bottom line:the maximum diversification approach is a perfect tool if investors who are searching for a highly diversified portfolio which tends to perform reasonable well in every market environment.  Since it can fully utilize the benefits of diversification, so then the portfolio is able to reduce draw-downs considerably, especially in times of market turbulences. Therefore this asset allocation approach is perfectly suitable for investors who are searching for compound returns instead of a strategy that tries to capture every gain when equity markets are strong. Nevertheless, the outcome of the strategy depends mainly by chosen asset classes, as this investment strategy allocates the most to those ETFs which have the lowest correlation coefficient. Therefore please bear in mind, that any approach is only as good as the expected future value of its underlying asset classes as well as their future diversification characteristics.