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The Power Of Compounding

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Novice traders enter the Forex markets with the illusion of becoming independent and wealthy. And they may be right. So why 95% of forex traders fail?

After no trading plan and psychological weaknesses and biases comes Too high position sizing as the main cause for failure.

I guess that the become rich quick mentality, an evident psychological weakness, drives them to trade big at the wrong time. Then Fear and greed make the rest.

Therefore, my first recommendation for a new trader is to doubt about his strength to support the psychological pressure to break his system. That is much better accomplished if he or she risks small amounts. The initial two years of trading should be dedicated to learn and practice the needed discipline to respect the trading rules.

The power of compounding

To help you take out your anxiety for a quick buck profit, Let’s analyse the power of compounding.

Let’s first see, graphically an account of 10,000 € grow at a monthly rate of 0,083%, a nominal annual rate of 1% for 50 years (600 months):

Well, we observe that this state of affairs is only good for the bankers. It takes 50 years to grow 10K into 16,500K. That’s the reason we are willing to risk trading.

Let suppose we get  a risk-free 10% annual return instead, again, with monthly payments of 10%/12:

That is becoming interesting. One, we need to wait patiently for 50 years to become millionaires, and, two, we don’t know how much of that will be erased by inflation.

Let’s suppose we are investing ala Warren Buffett with an annual mean return of 26%, that, also steadily grows on a monthly basis. In this case, the graph is presented in semi-log scale for obvious reasons. The x-scale is in months while the y-scale says how many zeros has the account balance. For instance, 106 means the account has 1 followed by six zeros:

Now, that is another history! We see that in 50 years we will be as filthily rich as Warren Buffett et al. !  We observe, also, that we add one zero to our account roughly once every 100 months. Not Bad. We multiply by ten our stake every two years! And that is achieved with a mean monthly rate of return on our capital of 2.17%, which means we just need to make sure we get a daily return of 0.11%.

The problem is within us:

This one is the same equity curve than the previous one but in a linear scale. We observe that it shows an exponential line, and there resides our psychological problem: The net equity grows relatively slow at the beginning. We need four years to reach six zeros, but in another four years, we will be close to eight. That shows that the power of compounding is a long-distance race, not a sprint.

The other side of growth

Things are not that perfect in trading. We don’t see nice curves up to richness. We should expect not only run-ups but, also drawdowns. Let’s observe the equity curve of a typical system using a nominal risk of 0.5% which takes, for simplicity, one trade per day, or 20 per month. And let’s put a magnifying glass on the first year of its history.

 

 

   Starting Capital:  10,000
Mean ending Capital:  11,817
     Capital % gain:  18.17%
       Max drawdown:  2.64%

This is a real system, achievable, with the basic statistics as follows:
STRATEGY STATISTICS:
              Nr. of Trades: 143.00
                    gainers: 58.74%
              Profit Factor: 1.74
                   mean nxR: 1.22
 Sample Stats Parameters:
           mean(Expectancy): 0.3070
               Standard dev: 1.9994
            VAN K THARP SQN: 1.5353

The monthly mean profit, using a 0.5% risk is 1.5%, which gives an annual growth of 18%. A bit less than what Warren Buffet has been performing. The nice feature is that using a 0.5% risk the max drawdown is 2.64%. Now, let’s see how fare this system, using exactly the same trade percent results when risk rises  because we increase the position size:

2% Risk:

   Starting Capital:  10,000  
Mean ending Capital:  18,910      
     Capital % gain:  89.10%      
       Max drawdown:  10.38%

 

5% risk:

     Starting Capital:  10,000
  Mean ending Capital:  42,615
       Capital % gain:  326.15%
         Max drawdown:  25.39%

 

10% Risk:

     Starting Capital:  10,000
  Mean ending Capital:  118,032
       Capital % gain:  1,080.32%
         Max drawdown:  47.67%

 

20% Risk:

 

     Starting Capital:  10,000
  Mean ending Capital:  308,888
       Capital % gain:  2,988.88%
         Max drawdown:  79.99%

35% Risk:

   Starting Capital:  10,000
Mean ending Capital:  124,613
     Capital % gain:  1,146.13%
       Max drawdown:  96.83%

45% Risk:

 

   Starting Capital:  10,000
Mean ending Capital:  14,725
     Capital % gain:  47.25%
       Max drawdown:  99.53%

 Conclusions:

From the above examples we take that:

  1. Max drawdown is related to position size. The bigger its size, the higher the drawdown.
  2. As position size grows, up to a certain limit, capital gain grows geometrically, but drawdowns grow also, although arithmetically.
  3. Past a certain point, we increase the risk but the gains are reduced. It doesn’t pay to increase the risk.
  4. The ideal position size depends not only on the quality and statistical characteristics of a trading system but also of the type of trader you are. There are traders are willing to accept up to 40% drawdowns. Those traders may risk up to 10% of their trading capital in one single trade. There are less risk-seeker trades that are willing to accept no more than 20%. To those, depending on the system, of course, 5% is their limit.
  5. My advice to new traders is to limit themselves to no more than 0.5% at least during the learning stage, or 1-2 years. During that time they should collect information about their performance and regularly compute the statistical properties of their trading system.

A simple approach to risk

A simple approach to compute the preferred risk per position is to be prepared for a 10-15 consecutive losing streak.

Let’s suppose we want our drawdown to be limited to 20%. If our system statistics show that our percent winners are less than 50%, then we should be protected to at least 15 losers in a row. If our percent winners stats are above 50% and our mean reward-to-risk ratio is above 1, then we may settle for ten losers in a row.

The method to limit the risk is easy. We divide the drawdown amount by the losing streak number.

If we wanted to be protected of a 20 losing streak and our maximum decided drawdown is 20% then, 20%/20 tells us that we cannot risk more than 1% on each trade. In the case of a 15 losing streak, our max risk goes to 1.33%, and it goes to 2 in the case of a 10 figure.

Therefore, If you trade using 0.5% risk on your account, you make sure that your maximum drawdown halves, therefore it’s highly improbable that your drawdown moves above 10% of your current balance.

Below is a possible 30-year history of the sample system using 0.5% risk. Sometimes, the turtle wins to the rabbit, because a too fast rabbit may get hit by a bullet.

 

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