Please, see my first post

for more details regarding the portfolio strategy.

'ACS.MC' 'ELE.MC' 'ENG.MC' 'IDR.MC' 'ITX.MC' 'REE.MC' 'TEF.MC'

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 again of 7 stocks. Indeed, it is the same composition than that of 4 weeks ago. In order to have again equal weights for all the stocks, the turnover respect to previous composition is 4.4% (due to the portfolio growth in the last month). Hence, the transaction costs associated with this rebalancing are low.Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 19% (versus 28% of the Ibex 35).

The weekly 95%-VaR was 4.4% (versus 5.2% of the Ibex 35). See this post for the details about the back-testing.

The last year annualized Sharpe ratio of the low vol strategy was 0.47 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the Ibex 35 was 0.19 over the same period.

Finally, the correlation of the low vol strategy with the Ibex 35 along the last 52 weeks was 93%.

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 Ibex 35 (no costs).

It can be observed that the Ibex 35 attains a bit worse 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 consecutive weeks. On the other hand, each red point represents the mean return and volatility of the Ibex 35 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 20%. The volatility of the Ibex 35 is less stable and near 30%. But what happens with the associated return?

The Ibex 35 does not attain a larger return. In contrast, all 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 Ibex 35. And always again, the corresponding return is better, although this could change a bit over time.

As a summary, the low vol portfolio

*dominates*the market index 100% 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.

## No comments:

## Post a Comment