A Math Lesson in Investment Losses

All long-term investors have faced this scenario: The portfolio you were counting on for your retirement gets caught in a bear market. As you watch stock values drop, you let your retirement account statements pile up on your desk, unopened.

Looking at the math behind investment losses can provide insight into what it takes to recover from a portfolio loss. In a nutshell a higher percentage gain is necessary to recover from a certain percentage loss. There is a reciprocal relationship between losses and gains. Specifically, their relationship is nonlinear, meaning that as the loss gets bigger, the gain needed to recover increases at a growing rate.

From the chart above, we see that to recover from a 35% loss, a gain of 53.8% is needed to return to the starting balance. Now let’s examine how long it would take the S&P 500 to post a return of that size. The S&P’s largest one-year return was 37.58% in 1995. This tells us that restoring a 35% loss will take longer than one year.

When we analyze historical S&P returns, we can estimate the probability of recovering from a loss within a certain time period. The data below indicates that there’s nearly a 57% probability that a portfolio would recover from a 35% loss in four years. Statistically speaking, a longer recovery period will be required to recover from larger losses and to increase the likelihood of a complete recovery.

Probabilities calculated from historical returns of the S&P 500 Index over the past 40 years. All of these loss recovery estimates are based on the performance of the S&P 500 Index over the past 40 years (1970-2009). They assume no money is withdrawn from the account during the recovery period and that no additional money is invested. Taxes and inflation have not been considered in this analysis. As always, past performance is not a guarantee of future results.
Source: Craig Israelsen, Ph.D.

The good news is that historically, the stock market has always recovered from its losses.

The S&P 500 posted positive returns 31 out of the past 40 years, which is a remarkable batting average for a 100% equity index. During those 31 years, the average gain was 19.2% and during the nine years the index lost ground, the average loss was -15.2%. Given that it takes a 17.6% gain to restore a 15% loss, the S&P’s average annual return of 19.2% is fairly positive evidence of being able to recover from a 15% loss within a year. However, recovery is prolonged when the loss is bigger and/or when a portfolio suffers losses for consecutive years.

This is when discipline and patience, important attributes of wise investors, comes into play. The examples I’ve cited from the S&P 500 only reflect performance of the large-cap U.S. equity market. A wisely-crafted portfolio contains investments that are broadly diversified across asset class, style, industry and region—potentially limiting the severity of losses, even during a down market.

I tell my clients this often: Especially during periods of market volatility, it is important to stick to a long-term investment plan. A long-term outlook based on your personal risk tolerance and investment timeframe is the best way to reach your goals and recover from temporary market downturns.

The thing to remember from this math lesson is that recovering from losses takes time, probably longer than you suspect. What you need to do to weather down markets is to stay invested until your portfolio recovers—with a patient and disciplined approach to investing for your long-term future. This approach is the cornerstone of the work I do with my clients.