The portfolio recommendation is based on two
low-volatility strategies: a

**long-only minimum-variance portfolio**and a**“130:30” minimum-variance portfolio**, which is long 130% and short 30%.
These strategies use advanced

**Optimization**and**Statistics**techniques to*hedge against the estimation risk*of the associated models. As a result, they attain consistently better risk-adjusted returns than market indexes, as these portfolio recommendations show.
For more details about the implementation of these
strategies, please read the following post: Some
efficient low-volatility
portfolios: the minimum-variance policy.

Although I recommend a portfolio
composition every month, it is desirable to maintain this composition for a
quarter year, and then rebalance with the new composition.

The current long-only portfolio
composition has changed a bit respect to the previous quarter (two stocks are
purchased). The turnover is 15% (due to this change and the portfolio growth).
On the other hand, the turnover of the current 130:30 portfolio is a bit
larger: 26%.

Regarding the performance, over the last year (52
weeks), the long-only strategy attained a volatility of 11% (versus 22% of the S&P
500). The volatility of the 130:30 strategy is even better: 9.5%.The weekly 95%-VaR of the long-only portfolio was 2.2% (versus 4.7% of the S&P 500). The corresponding VaR for the 130:30 portfolio was 1.5%.

The last year annualized Sharpe ratio of the long-only strategy was 0.93 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the 130:30 strategy was 1.90. Finally, the SR of the S&P 500 was 0.35 over the same period.

In the next figure, you can see the compounded return over the last 52 weeks of the three considered portfolios.

Both low-volatility portfolios attain better returns than those of the S&P 500.

But let add information about the risk. The next graph shows the risk-return space for the three considered portfolios.

The red point represents the mean return and volatility of the long-only portfolio over the past 52 weeks. On the other hand, the green point represents the 130:30 portfolio, and finally the blue point represents the S&P 500 index over the same 52 past weeks.

We can see the two low-volatility portfolios have better mean returns than that of the S&P 500, and also their volatilities are better. In this case, we say the low-vol portfolios dominate the index.

I have computed the same risk-return space for every week over the last year, using the same 52-weeks historical method to estimate the mean returns and the volatilities. The long-only and 130:30 portfolios attained a higher return than that of the S&P 500 (100% and 96% of the time, respectively). Moreover, the volatility of both low-vol portfolios was

**always**less than that of the S&P 500.

As a summary, the low-volatility strategies

*dominate*the market index most of the time, showing they attain consistently better risk-adjusted returns.