Please, see my first post

for more details regarding the portfolio strategy.

'MO' 'AMGN' 'BCR' 'BDX' 'CVS' 'CPB' 'CLX' 'ED' 'FDO'

'GIS' 'HRL' 'JNJ' 'K' 'KMB' 'LH' 'MKC' 'MCD' 'PEP' 'PG'

'RAI' 'SO' 'WEC'

Although I recommend a portfolio composition every week, it is desirable to maintain this composition for four weeks, and then rebalance with the new composition.

This portfolio consists of 22 stocks. Four weeks ago, the portfolio composition was the same except: now we have added ‘CPB’ and ‘LH’, and now we no longer have ‘AON’. In order to have again equal weights for all the stocks, the turnover respect to previous composition is 19% (due to the portfolio growth in the last month and the change of 3 stocks in the portfolio composition).

Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 10% (versus 17% of the S&P 500). The weekly 95%-VaR was 2.5% (versus 4.2% of the S&P 500). See this post for the details about the back-testing.

The last year annualized Sharpe ratio of the low vol strategy was 1.68 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the S&P 500 was 1.12 over the same period.

Finally, the correlation of the low vol strategy with the S&P 500 along the last 52 weeks was 85%.

Again, all these performance results are consistent over time.

In this case, I am going to talk a bit more about the performance results in order to understand better how the low volatility portfolios outperform market indexes.

In the next figure, you can see cumulative return over the last 52 weeks of the low vol portfolio (after transaction costs) and the S&P 500 (no costs).

It can be observed that the S&P 500 attains a bit better final return than that of the low vol portfolio. But we need to analyze this graph with caution. It depends on both the initial and final investment periods. Moreover, we need to focus on the associated risk too, not only on the final return.

For these reasons, I prefer to project the previous 1D trajectories into a 2D world: the risk-return space. That is, each of the two trajectories will be summarized by one point containing their corresponding mean returns and volatilities.

The next graph shows the risk-return space for the two considered portfolios.

Each blue point represents the mean return and volatility of the low vol portfolio over a given period of 52 past consecutive weeks. On the other hand, each red point represents the mean return and volatility of the S&P 500 index over the same periods of 52 consecutive weeks.

We say that, for a given period, the low vol portfolio

*dominates*the index market if its volatility is lower and the return is higher than that of the index.

In total, the graph contains 50 of such periods, corresponding to 50 different trajectories of cumulative returns for the two portfolios.

With this 2D vision, we can compare better the performance of the two strategies. We can see that the volatility of the low vol portfolio remains stable around 10%. The volatility of the S&P 500 is less stable and near 20%. But what happens with the associated return?

The S&P 500 does not attain a larger return. In contrast, most of the time, its return is worse than that of the low volatility portfolio.

More concretely, the volatility of the low vol portfolio is always less than that of the S&P 500. And more than 70% of the time, the corresponding return is better.

As a summary, the low vol portfolio

*dominates*the market index 70% of the time in the risk-return space, showing they attain consistently better risk-adjusted returns. At least, this is true for the last two years.