# Diversification - No portfolio trading

### Diversification - No portfolio Trading

Another essential aspect of lowering your risk and maximizing your potential of profits is diversifying your portfolio. It is always better not to bet only on a single strategy, but to create a portfolio of strategies (or trades) which are not mutually correlated. In other words, you have to understand how to create a diversified portfolio of uncorrelated strategies! So let’s start with the futures markets portfolio. ##### Portfolio Trading with Futures Markets

The significant advantage of trading futures is that you can trade many uncorrelated markets to create a very well-diversified portfolio of the strategies. We have a positive experience with these markets:

• Stock indices (e-mini S&P 500, E-mini S&P MidCap 400, E-mini Russell 2000, E-mini Dow Jones, NASDAQ)
• Metals (Gold, Copper, Platinum, Palladium, Silver)
• Energies (Crude Oil, Heating Oil, Natural Gas)
• Bonds
• Softs (Coffee)
• Grains (Wheat, Corn, Soybean, Rough Rice)

One of the keys to successful trading and protecting your capital in the first place is to trade an uncorrelated portfolio of robust trading strategies. You already know that. Remember this basic rule: “The more uncorrelated strategies are traded, the higher the probability that your trading results will be successful.”

Correlation means a relationship between two variables: Correlation is something by which we can measure the relationship between two strategies by using their daily returns. This relationship is measured by a correlation coefficient, which can take values from -1 to +1. To calculate the correlation between the two strategies, we use the Correlation Coefficient Figure 42: Graphical representation of correlation coefficient values of -1 to 1

In this Figure 42, you can see the graphical representation of correlation coefficient values of -1 to 1.
When the correlation coefficient value is equal to 1, there is a direct linear relationship between the variables.

When it is equal to 0, there is no relationship between the variables.

When it is equal to -1, there is an indirect linear relationship between the variables. The desired level of correlation between 2 or more strategies is 0.

A well-diversified portfolio’s goal is to have no linear relationship; it means no correlation between their daily returns.

If the correlation coefficient is 1, strategies behave the same way from the return or loss point of view, so there is a linear relationship between them. And from the risk management point of view, it is not good to trade those two strategies together. If the correlation coefficient equals -1, it means that one of your strategies will lose money; the second one will be profitable at the same time. So, one more time: the desired level of the correlation coefficient between two of the strategies should be close to 0. This way, you can lower your risk and maximize the profit potential. However, it is not about to trade only 2 strategies.To prove you a positive effect of diversification, I will present to you five robust trading strategies programmed in TradeStation Easy language. One of the critical measures of providing a real picture of a strategy’s performance and how it behaves in a portfolio of trading strategies is a daily return. We will calculate and use their Daily Returns to measure:

• Average Daily Return divided by Standard Deviation of Daily Return Ratio of each trading strategy. We call this ratio INFORMATION RATIO, which gives us the information about the quality and stability of the given strategy
• We will also measure the mutual correlation between strategies by the use of correlation coefficient

Thanks to daily returns, we can calculate Information Ratio:

##### Information Ratio = Average Daily Return/Standard Deviation of Daily Return

If you don’t know the term Standard Deviation very well, please find the explanation on the internet. By usage of Information Ratio, we can evaluate the strategy from the stability point of view (more stable daily returns, thus better equity curve). The higher the Information Ratio, the better stability of your trading. We want to have our Daily Returns as high as possible. On the other hand, the lower the Standard Deviation, the better for your trading.
Here you can see a comparison of 5 strategies from the Information Ratio point of view (Table 3). Table 3: Information ratio of 5 strategies

As you can see in Table 3, the winner is the Platinum strategy, because its Information Ratio is the highest (0,12). Thus, the Platinum strategy is the most stable one. The lowest Information Ratio belongs to the Euro FX strategy and E-mini Russell 2000. When we combine strategies into one portfolio, you can get the highest Information Ratio (0.18). And voila, we get something that we can call a positive effect of diversification. So, if we trade the portfolio of these strategies in one portfolio (what TradeStation platform perfectly allows), we will significantly increase our overall trading stability. It usually leads to more stable profits and lower risk. Why is it like that? The reason is simple. Table 4: Correlation table

In Table 4 you can see that a degree of correlation between any two of all these five strategies is around zero, which is the desired value. The highest correlation is between the Platinum and Palladium strategy, just because both metal markets are naturally correlated. Nevertheless, this correlation coefficient 0.172 is still very low, so it is entirely right to trade these two strategies in one portfolio. The lowest correlation coefficient -0.018 is between Euro FX and E-mini Russell strategy. That means there is no linear relationship between the daily returns of these two strategies. Thus, they are appropriate for trading within one portfolio.
Be very careful to trade too correlated strategies in one portfolio. Always be sure that you trade a meaningful diversified portfolio. It can save you a lot of money because it will improve your risk management.
Well, do you use these measures such as correlation coefficient, Information Ratio, etc.? Are you a trader or a gambler? You can answer this to yourself. As you can see, this is not something incomprehensible.
Finally, let me present you Performance Summary of the portfolio of these 5 trading strategies (Figure 43 and Table 5) Figure 43: Portfolio equity curve of five strategies Table 5: Performance Summary Portfolio of 5 strategies

In Figure 44 and Table 6 there’s a Performance Summary of the portfolio of our 3 trading strategies: E-mini Russell 2000, Gold, Platinum: Figure 44: Portfolio equity curve of three strategies Table 6: Performance Summary Portfolio of 3 strategies

Now, imagine that you have a portfolio of 3 or 5 strategies, and you want to start live trading with TradeStation, but you are not sure how much you have to capitalize on your account. You may know that there is one general rule in trading: the higher the capitalization of your trading account, the better. If you started with an initial capital of around \$50,000 in our five strategy portfolio, your Net Profit would be \$904,386 during the ten years. In other words, it means that you could make this significant Average Yearly Return, which would be 172.26% p.a. And you would have to count on a very high Maximum Drawdown – around 40%. Never forget that you always have to include margins from brokerage into your calculations if you trade futures. In our case, it means that you would need to have a minimum \$18,205 in your brokerage account. Be always sure that you clearly understand the principle of margin trading, and you have enough money in your brokerage account. Otherwise, if you had in your account less than \$18,205, you would have to face a margin call, and your broker would immediately exit your positions.
Regarding 3 strategies portfolio, you can see the following: if you started with initial capital around \$20,000, your Net Profit would be \$480,025 during the ten years. It means that you could make this significant Average Yearly Return, which would be 228.58% p.a. You would have to calculate with a very high Maximum Drawdown – around 66.94%. And this is too risky. I would personally accept a Drawdown maximum of about 20% of my brokerage account. Therefore, the better would be to increase your initial capital to lower your drawdowns and lower your Average Return p.a., of course. You may have already realized that your brokerage’s higher initial capitalization account, the better because your approach will be more conservative. You don’t need to worry about margin calls = the main enemy of every single trader.
So, regarding a five strategy portfolio, I would fund my brokerage account with \$100,000. Considering our three strategy portfolio trading, I would use \$50,000 as the minimum amount of initial capital.
Please don’t forget that we get drawdowns from past market data. If you wanted to know your maximum potential Drawdown in live trading, you would have to perform Monte Carlo Analysis.

##### Monte Carlo Analysis

Monte Carlo Analysis aims to quantify the effect of trade order randomization on the trading system’s overall performance (determination of the worst drawdown possible).

When using Monte Carlo analysis in simulated trading, we take into account the order of historical trades. If you change the order of trades, the performance metric like net profit, average trade or profit factor won’t change. But what happens with maximum drawdown when you change the order? For a clear illustration look at this table where you can see an example of trading strategy with 10 trades: Table 7: Specific example of five Monte Carlo simulations applied to a shuffled order of 10 trades

In Table 7, we see that Net Profit, Average Trade and Profit Factor do not change. What changes fundamentally in each situation is, as I mentioned, the Maximum Drawdown. We then perform a Monte Carlo analysis to determine the maximum acceptable risk of our initial capital. It is, therefore, an essential risk management tool. We must decide with a certain probability what the maximum possible drawdown is. Based on our example, we can state that with 20% probability, the maximum potential drawdown will be -400, with 40% then -550, with 60% -750, 80% then -850. With a 100% probability, the worst possible drawdown should be a maximum of -1000. The sample is too small to be considered statistically relevant. Let’s imagine that with the help of Monte Carlo analysis, we simulate that the order of trades of a given trading strategy will change 1000 times, for example. Each such simulation is tested. The results are ranked from the highest value of maximum drawdown to the smallest one.

A multiple of Monte Carlo Maximum Drawdown is often used to determine a live trading account size.

Now let me show you an example from practice: Let’s get back to the strategy EXCELSIOR-RUS2000 on e-mini Russell 2000 (with symbol RTY) (Figure 45) 