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 is very similar to that of previous quarter, except for two stocks bought (out of 20). The turnover is 17% (due to the portfolio growth and the trading of these two companies). On the other hand, the turnover of the current 130:30 portfolio is a bit larger: 32%.

Regarding the performance, over the last year (52 weeks), the long-only strategy attained a volatility of 11.5% (versus 21.5% of the S&P 500). The volatility of the 130:30 strategy is even better: 9.6%.The weekly 95%-VaR of the long-only portfolio was 2.1% (versus 4.7% of the S&P 500). The corresponding VaR for the 130:30 portfolio was 1.9%.

The last year annualized Sharpe ratio of the long-only strategy was 1.11 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the 130:30 strategy was 1.49. Finally, the SR of the S&P 500 was 0.18 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 85% 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.