A Tale of Anarchy: "The Mathematics of Recovery"

Posted by Carlos Sera on Aug 13, 2015 11:24:00 AM

26870194_sI use the word anarchy to describe the mathematics of investment loss recovery. Anarchy refers to political disorder but you can think of it as portfolio disorder. It is imperative that investors understand the mathematics of recovery. If you don’t you run the risk of outliving your assets. So what is it? The answer is simple. The mathematics of recovery tells us what percentage rate of return we must earn in order to recover our investment after a given percentage investment loss. It’s not as important to those that are still working, saving and investing as it is to those that are retired.

Let me ask a simple question and please answer before you read any further. If you lose 10.00% on an investment what rate of return must you make in order to get your money back? Is it 8.25%, 10.00%, 11.11% or 15.00%? Most people answer 10%. It’s the wrong answer however. If you answered anything other than 11.11% then you need to read and understand this tale.

Let’s look at the following table to understand the investment loss recovery. Once again it is crucial for your investment decision-making when you have a finite amount of money that must last indefinitely. This is important for retirees.

Your Portfolio Drops By

To Get Back To Break-Even Your Portfolio Must Make

















The second thing we learn from the table can be found in column 3. It shows that the more you lose the harder it is to recover. Now imagine that a retiree is taking money out to pay for living expenses when their portfolio drops and you can see that they have to make an even higher rate of return to get back to break-even. This is the reason why our firm tries to structure many retiree portfolios so that losses, even under extreme conditions, are kept under 20%.Lets come up with a formula to understand the mathematics of recovery. It’s very easy so don’t be afraid. In our previous example and from the table we see that if you have for example $100 and you lose 20% you are left with $80. The $100 dollars represents the starting capital and the $80 represents the ending capital. If you divide starting capital of $100 by ending capital of $80 you get 1.25. This means you must make 25% on your $80 to get it back up to your starting capital. Said differently, if you have $100 and you lose 20% of it you now have $80. What rate of return must you make on the $80 that you have left in order to get back to $100? The answer of course is 25%. That’s it. The mathematics of recovery tells us that you must always make a higher percentage rate of return to get back to break-even than the percentage amount you lost. We can see this from the table. We see that column 2 is always larger than column 1.

What can we learn from this bit of mathematical knowledge? We can learn that wealth preservation of a finite amount of capital is critical for the retiree. There is a practical point of no return. You are unlikely to recover your capital in a reasonable period of time once you lose 30% or more of your capital. What does this mean in terms of investment selection? It means that not all rates of return are the same so learn to differentiate. There is a difference between a portfolio that averages an 8% rate of return over a time frame with periods of maximum losses of 40% from a portfolio that also averages an 8% rate of return but does it in a fashion where the losses when they occur are significantly less than 40%. In this case, the second portfolio is less volatile than the first. Read A Volatile Tale to get a better understanding of the types of investments that are better selections for most retirees.


Topics: Retirement Tales


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