Siegel’s paradox

November 13 2013 | Category: Figures and Facts

Siegel’s paradox states that if a fixed fraction of a given amount of money is lost and then the same fraction of the remaining amount is gained, the result is less than the original amount. For example if an investor has £10,000 and loses 10% and then gains 20% he has made £10,800 overall. Another investor has £10,000 and makes 10% with no losses. The results are different.

Investor 1: £10,000 – £1,000 = £9,000 + £1,800 = £10,800

Investor 2: £10,000 + £1,000 = £11,000

So, when constructing an investment portfolio, do you try to achieve the maximum return by ‘playing’ the markets and taking high risks? Or do you try to achieve the maximum return at an acceptable level of risk?

Research tells us that investors are often irrational and do not like volatility. Because of this fear of loss, investors chasing returns may often lose their composure and sell into cash when an investment falls in value – but this erodes returns.

By taking a risk-based approach to investing generally means that any volatility should fall within a tolerable range, therefore removing the irrational instinct to sell out and improving the likelihood of longer term returns.

Take investor A, they invest £50,000 into a well diversified portfolio constructed in a risk-based manner which consistently delivers 4% per year for 18 years. Investor A has turned their original £50,000 into £101,290*.

Investor B has a much less diversified portfolio and therefore suffers from much greater volatility. The portfolio loses 4% in year one and due to this loss they move the portfolio to cash, getting 0% returns in year two. In the third year, investor B reinvests as the market rises and gains 16%. The 3 year return is 12% (-4% + 0% + 16%), which is an average annual return of 4% – coincidentally the same achieved by investor A.

However, coming back to Siegel’s Paradox, because investor B sold out in year 1 they have eroded their returns by some £5,593* less than investor A at the end of 18 years despite having the same average annual return.


The benefits of a risk-targeted approach to investing are therefore very evident. By delivering more consistent returns over the longer term, Siegel’s Paradox shows us that greater returns are delivered.

Of course delivering consistently smooth returns is not simple in the real world and most investors should expect some volatility. At Chilvester we have strategies to suit most investors needs and by constructing well diversified investment portfolios based on asset allocation models we have investment strategies to suit different risk appetites.

*Source: Allianz GI Risk Matters Edition 4

The value of investments are not guaranteed and can go down as well as up.