## The Mathematics Of Losses

Will a 30% advance after a 30% decline in a portfolio, return the account to the same market value?

The answer is no. It will actually take a gain of 42.9% to recover the lost capital.

As an investment loss increases in size, the gain that is required to restore the loss begins to increase at a faster rate. Individual investors have two distinct time horizons that occur over their investment lives:

– An accumulation phase: where the focus is on saving
– A withdrawal phase: where the focus is on spending

We all have a finite time horizon to build wealth that is determined by our own mortality. Even if we are diligent savers, we will likely only have 40 years as an accumulation phase before retiring from the work-force and starting some type of a withdrawal phase.

What happens if you experience a 30% portfolio loss and are then only able to receive 7.4% annual returns?

Loss                1 Year               2 Years            3 Years                   4 Years                     5 Years

30%                 42.9%                19.5%             12.6%                          9.3%                            7.4%

You would need five years of 7.4% annual gains to recover the loss, but those five years also represent 12% of the your wealth accumulation years. Those five years have been removed from your accumulation phase and will never return.

Recovery times for losses matter greatly. In fact, they matter even more when an accumulation phase is ending and a transition to a withdrawal phase is beginning.

What happens if an 8% withdrawal phase begins immediately after a 30% loss?

Loss                1 Year                 2 Years                3 Years                    4 Years                     5 Years

30%                 61.8%                  31.3%                    22.6%                       18.5%                       16.2%

You would now need five year annual gains of 16.2% to recover the lost value and cover the required withdrawals. If your portfolio fails to generate these required annual rates of return, then the capital value of the portfolio will erode further.

You should be concerned not only about the size of investment losses, but also about the amount of time required to recover a loss. The amount of time required to recover can be just as significant to your financial success as the size of the loss.

Ignoring the consequences of financial market uncertainty can be hazardous. Trying to reduce exposure to uncertainty in the midst of financial market turbulence is similar to trying to buy insurance once a house catches fire.

To truly evaluate financial market uncertainty, you must consider both the magnitude and the likelihood of all possible outcomes. This includes not just the good ones, but also the very bad