The Math of Losses

Everyone knows the stock market has its ups and downs, but just what’s involved in recovering from a serious down?  If you lose 10% one year but your portfolio returns 10% the next year, are you even again?

The short answer:  no.  The math of recovering from a loss isn’t quite that symmetrical.  You have to gain more than you lost to recoup all your losses.  To understand why, let’s look at a hypothetical example.  Say you have a $100,000 portfolio.  In Year 1, you suffer a 10% loss and are down $10,000.  That leaves your portfolio worth only $90,000.

In Year 2, the market rebounds and your portfolio rises by 10%.  However, that 10% increase is based on a $90,000 portfolio, not $100,000.  That means a 10% return adds only $9,000 to your portfolio not $10,000, leaving you still down $1,000 from where you started.  You would actually have to earn a return of a little over 11% to get back to your original $100,000.

The bigger the loss, the bigger that rebound needs to be to get you even.  For example, if that $100,000 portfolio had taken a 40% hit, as many did in 2008, you’d need almost a 67% increase to offset that $40,000 loss.  That could take several years even if stocks perform well.

The challenge is compounded by investor psychology.  Adjusting your asset allocation to aim for a higher return is one way to try to recoup losses faster.  However, many investors find it difficult to take on additional risk after having watched their investments take a hit.  And there’s no guarantee that more risk will necessarily produce the desired result—at least not within the desired time frame.

The lopsided nature of recovery from market losses underscores why risk management is such a key component of successful portfolio management.  Being realistic about the level of risk your portfolio involves and how much time you have to come back from potential downturns may help you increase both your emotional and financial resilience.