The surprising Psychological effects and Maths behind Losses in the Stock Market

When investing in the stock market we would rather like to think about the money that we gain than the money that will be lost forever if we don’t act in time. It is an established psychological phenomenon that many investors hold on to losing stocks for way too long until almost nothing is left of the original investment. It is one of the instances that make you wonder if a human being is really a rational utility maximizer as you might have learned in economics class.

Gains necessary to recover from loss:

Loss in % Gain to Break Even
10% 11.11%
20% 25.00%
30% 42.86%
40% 66.67%
50% 100.00%
60% 150.00%
70% 233.33%
80% 400.00%
90% 900.00%
99% 9,900.00%

Let’s say an investor needs money and has the choice between selling a profitable stock investment and one that has lost him some money. So he is presented with a problem. If she or he frames the problem as giving him/ herself pleasure and enjoying the benefits of a perfectly timed investment decision then the investor will hold on to the losing stock and sell the one that made some gains.

The alternative would to sell at a loss and add a failure to the records which only a few people are willing to do. This narrow framing of the of the problem where the investor wants to close each account as a gain is called the disposition effect.

It doesn’t come as a surprise that finance research has shown that investors rather sell a winning stock than a loser. This bias has been given the term disposition effect. (Kahneman, 2011)

Someone rational would think about which stock is least likely to perform well in the future and close that account, regardless if it is a winner or a loser. Losses even give you a tax advantage in most countries while gains will cause you to pay taxes.

However, there is a month when investors become rational again and that is December. Although the tax advantage is available the whole year mental accounting only starts to work in that particular month (Kahneman, 2011). Buying even more of a losing stock is a sunk cost fallacy but we are not getting into this. Only that much shall be said for people who are not familiar with investments. This is similar to a terribly failing government project where the authorities reject common sense and instead of shutting it down pour more money into it.

Let’s get to the mathematical part of making losses in the stock market and this should ring home for everyone that even considers only a small portion of her or his savings for retirement. The reality is that even small losses require much higher gains. As you can see in the table above at a loss of around 30% it becomes harder to get back to the original amount of the investment. the most striking example I find is when you have invested $1,000 and lost 50% and are down to $500 you need to gain 100% again only to get back your original investment. With normal stocks that could take some time or be less likely. Maybe with leveraged products like options and derivatives the recovery would be quicker but would come with a lot more risk.

Please go ahead and play with the slider below it will tell you how many percent you need to gain to fully recover from a loss of x percent.

Total%

I have included this chart below to show you a visual representation what immense gains are necessary to break even again after a loss. I hope to achieve that if you encounter a situation where you hold on to a stock that has lost a huge amount that you will examine yourself and ask yourself whether the behaviour is justified.