We have developed an automatic system to
recommend portfolios designed to
deliver significant lower risk than the S&P 500 index and the EuroStoxx
index, while maintaining their returns over the long term. These portfolios are denominated in Dollars and also in Euros, are highly liquid and take only long positions.

# Portfolio Management under Estimation Risk

Practical implementation of low volatility strategies based on quantitative techniques

## Sunday, January 12, 2014

## Monday, February 4, 2013

### US portfolio recommendation (from 4, February 2013)

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 two months, it is desirable to maintain this composition for a
quarter year, and then rebalance with the new composition.

The current long-only portfolio
composition contains 21 stocks and has changed a bit respect to the previous
quarter (three stocks have been purchased and one has been sold). The turnover
is 24% (due to this change and the portfolio growth). On the other hand, the 130:30
portfolio contains 60 stocks and the corresponding turnover is a bit larger: 49%.

Regarding the performance, over the last year (52
weeks), the long-only strategy attained a volatility of 9% (versus 12% of the S&P
500). The volatility of the 130:30 strategy is even better: 8.4%.The weekly 95%-VaR of the long-only portfolio was 1.9% (versus 2.4% 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 1.65 (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 1.17 over the same period.

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

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 (60% and 67% 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.

## Wednesday, November 14, 2012

### US portfolio recommendation (from 12, November 2012)

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 two months, it is desirable to maintain this composition for a
quarter year, and then rebalance with the new composition.

The current long-only portfolio
composition contains 21 stocks and has changed a bit respect to the previous
quarter (three stocks have been purchased and one has been sold). The turnover
is 29% (due to this change and the portfolio growth). On the other hand, the 130:30
portfolio contains 58 stocks and the corresponding turnover is a bit larger: 46%.

Regarding the performance, over the last year (52
weeks), the long-only strategy attained a volatility of 9% (versus 15% of the S&P
500). The volatility of the 130:30 strategy is even better: 8.5%.The weekly 95%-VaR of the long-only portfolio was 1.8% (versus 3.7% 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 1.15 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the 130:30 strategy was 1.6. Finally, the SR of the S&P 500 was 0.69 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 (77% and 83% 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.

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