**3.6 Model 6: maximize the minimal year return**

The model "guarantees" a minimal return year by year. Then, it may generate positive returns each year. Basically, it maximizes the minimum:

```
Set objective: Minimum return of each year (2000–2018)
```
**To:** Maximum

*Quality Control - Intelligent Manufacturing, Robust Design and Charts*

σ

used the following formula:

standard deviation (volatility).

to others:

year:

**To:** Maximum

**To:** Maximum

**To:** Maximum

**3.2 Model 2: maximize rate return**

**Set objective:** Global rate return

**3.3 Model 3: two decades, equals returns**

**Set objective:** Global rate return

**Set objective:** Global rate return

**3.4 Model 4: maximize rate and sharp-ratio**

lowering a little bit the volatility of the portfolio:

lowering a little bit the volatility of the portfolio:

The model equals the return of the two decades (*i i*

**Additional subject to the constrains:** *i i*

**3.5 Model 5: maximize rate and sharp-ratio (version 2)**

to other models, it may generate a more distributed income to investors. Then, in a decade of crises the investor may generate the same return as in a period of expansion. Also, model 3 "guarantees" a minimum return of half of percent each

In this model, the concern is to bring some extra return to the investor. It may generate more income than the model 1 but still with the concern of a stability,

In this model, in a similar way of the previous model (model 4), the concern is to bring some extra return to the investor but still with the concern of a stability,

**Additional subject to the constrains:** Sharp Ratio > 1 (all model)

Finally, the Sharp Ratio (SR) formula:

The, the standard deviation (σ) – the denominator – is a measure of how widely values are dispersed from the average value (the mean), using the "n" method. It is

( )

σ

In this model, the concern is to bring the maximum return to the investor, ignoring the volatility, then we can argue that model 2 presents the higher risk comparing

This is a measure of stability, if SR > 1 it means that returns overcome the

2 *x x n*

<sup>=</sup> *<sup>i</sup> SR* (8)

2000 2010 2011 2018 − − = ). Comparing

2000 2010 2011 2018 − − = ; *ni* > 0,5%

(7)

∑ − <sup>=</sup>

**138**

**Additional subject to the constrains:** Year return > Minimum return of each year

#### **Figure 3.**

*Monthly returns of the 32 assets. Notes: SPX = Standard & Poor's ticker; DJI = Dow Jones Industrials ticker; STOXX = Eurostoxx 600 ticker; HSI = Hang Seng Index; EM = Emerging Markets; RE = Real Estate; B-ST = US Bonds Short Term; B-MT = US Bonds Medium Term; B-LT = US Bonds Long Term; TIP = Treasury Inflation Protected Securities; CorpB = Corporation Bonds; NGas = Natural Gas; EUR/USD = Euro vs. USA Dollars exchange; VIX = Volatility Index (S&P 500).*
