April 13, 2020

The following is a post made on a Quantopian forum related to my recent articles on the subject of a portfolio's doubling time (see related files below).

I like the notion of doubling times for a portfolio. It indicates, on average, how much time was required for the portfolio to double in value. It is all a matter of the strategy's CAGR, its compounding rate.

For instance, Mr. Buffett has had an average CAGR of about 20% over the years. From my chart in the **Stock Portfolio Doubling Time** article, this implies a doubling time of about 3.81 years on average.

From that same chart, the higher the average CAGR, the shorter the doubling time, as should be expected.

**Why Should This Be Important**?

Simply because this portfolio management thing requires years to unfold, many years. Mr. Buffett managed to maintain his average CAGR for 50^{+} years, doubling his portfolio every 4 years or so. It does not mean that there were no drawdowns; there were. He has often said he has had drawdowns in excess of 50% four times. His current drawdown is about 30% or so. But, I am not worried, he will rebound again.

The portfolio performance illustrated in my prior post might appear exaggerated to some. But in terms of doubling times, not that much. James Simon's Medallion Fund has been operating at an even higher CAGR level. So, it is not impossible. This can be done.

The November simulation gave a doubling time of about 1.85 years compared to the April results, which averaged at 1.72 (see previous post). Most of the drop in doubling times is due to the huge profit increase in the last few months of the walk-forward. It does say that even a small change in the average doubling time can have quite an impact, especially in the later years of a trading strategy where the bet size was increased considerably. Whatever the trading strategy, in a fixed-fraction scenario, you have to be ready to make those larger bets and take those large positions as the portfolio grows.

It is extremely difficult to reduce the average doubling times over the years. The reason is simple: CAGR decay, the law of diminishing returns. There is a need to compensate for this, and there are tools to do so (I wrote a book on that).

**Trading Is Not The Same As Investing**

Trading is basically about two numbers: the number of trades executed and the average net profit per trade. Both numbers are given in the after-backtest analysis when using the ** round_trips = True** option.

The task in trading is making sure that those two numbers increase with time. But no matter what, you are still subject to the math of the game. In trading, the market can offer a lot, even a lot more than what I presented. There is no secret to the math behind the methods of play.

Many times in these forums I have stressed the importance of the betting system used when faced with uncertainty. We can certainly say that the market lives in this tumultuous ocean of variance and that it is rather difficult to predict which way it is going to go from day to day. But, as a trader, you still have to find ways to make your own doubling time.

If your strategy's doubling time is 14.25 years, equivalent to a 5% CAGR, you are not going that far that fast. And if your initial stake is relatively small, it is even worse since: F(t) = F_{0} ∙ (1 + 0.05)^{t} might not be that big even after 28.5 years on the job F(t) ≈ 4 ∙ F_{0}.

**Doubling Times**

The sequence for the first 10 doubling times is (2^{n}): 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Each 50% drawdown makes you lose a doubling time, and as time progresses, the value of this drawdown increases. For instance, dropping from 4 to 2 does not appear so bad when compared to the drop from 1024 to 512. That drop is 512 times the initial portfolio! Yet, both had a 50% drawdown. One should come to the conclusion that the preservation of capital becomes more and more important as you move along the doubling time sequence.

Mr. Buffett has managed over 14 doubling times so far. His last doubling time was for as much as he ever did in the previous 13 doubling times. It is remarkable. And his 15th doubling time will be as much as he has done over his entire career.

Every percent you add to your portfolio's return will have an impact on this doubling time.

You often see me using equations to explain what I do in my trading strategies. One that might be misunderstood is the payoff matrix, and yet, it is so simple and elegant:

F(t) = F_{0} + Σ (**H** ∙ Δ**P**) = F_{0} + n ∙ x_{avg} = F_{0} ∙ (1 + g_{m} + α – ex)^{t}

with n the number of trades and x_{avg} the average net profit per trade. Increasing both these numbers over the trading interval will result in higher profits, other things being equal. If done over the same time interval, it will increase the CAGR.

**You Are The Strategy Designer**

If your strategy makes 500,000 trades at an average net profit per trade of $10, it will produce the same amount as another trading strategy, making 50,000 trades with an average profit of $100.

You are the one to design that trading strategy using rebalancing or whatever other technique that will dictate how many trades the strategy is bound to make within its portfolio constraints. It becomes which strategy will produce either of the above two scenarios or anything in between or above. The strategy making 500,000 trades might not be the same as the one making 50,000 trades.

For sure, my trading strategies do “fly”. Not all of them, mind you, as should be expected. I do throw some away.

In this case, it should be noted that it took some 17.19 years of compounding to get there, with progressively larger bets executed in order to achieve those results. There is math underneath to support them.

In a sense, in the end, the way I see it, you are the one to choose your portfolio's doubling time. It is all in your payoff matrix strategy design **H**.

**See Related Files**:

**The Financing Of Your Stock Trading Strategy II**

**The Making Of A Stock Trading Strategy**

**Dealing With Stock Portfolio Equations**

**Financing Your Stock Trading Strategy**

April 13, 2020, © Guy R. Fleury. All rights reserved.