The period in which we live is drenched in contradictions; political, economic and financial. The poor old White Queen has been dragged from the pages of Through the Looking Glass to declaim on believing “six impossible things before breakfast” more times than we can count. Most recently on the Today programme this week.

The financial world is also operating in a space previously reserved for the characters brought to life by Charles Dodgson. Earlier this month the value of global bonds paying investors “negative” interest breached $17 trillion. To put that in context, it is over 25% of the outstanding stock of global government debt.

The UK gilt market is not yet in negative territory although at the time of writing 10 year British government debt was yielding 0.654% and thirty year gilts were offering investors 1.12%. That is not a lot of reward for tying your money up for thirty years.

Given that UK inflation is 2%, it’s also a negative real return meaning if you chose to invest in the asset class to maturity you would get less out than you put in. Not the typical definition of an attractive investment.

Negative rates also go to the core of valuation methods used by the financial sector and professional investors. One of the fundamental problems in investment lies in appraising and comparing the value of future income streams. To do that we use a concept known as “discounted cashflow analysis.” In essence, adjusted for risk, the project with the highest discounted (or net) present value, is the one to invest in among a number of competing investments.

However, when discount rates go through the looking-glass and turn negative, it upends a fundamental tenet of investment appraisal. Using simple numbers, at an interest rate of 10%, you would be indifferent to having £1,000 now or £1100 in a year’s time. Conversely, few people would be indifferent to having £1,000 or £900 in a year’s time if interest rates were -10%.

Doing nothing, simply holding cash notes, becomes more profitable than doing something. The financial system is simply not designed to deal with negative rates and paradoxically ultra-low rates could encourage hoarding of cash. Another looking-glass feature of the world we currently inhabit.

What this describes is the “liquidity trap” identified by Paul Krugman and Richard Koo, amongst others, but most famously by Keynes – lowering interest rates is like “pushing on a string.” It also tells you that we are still living with the consequences of the global financial crisis of a decade ago.

Lower discount rates raise present values by virtue of the maths involved. Negative discount rates turbo-charge present value calculations. In the example above, the net present value of that stream of income at a discount rate of minus 10% over ten years (outlandish but just to illustrate the principle) would be £3,735.94.

What does this mean for investors: firstly, interest rates will probably stay a lot lower for a lot longer than anyone thought possible a decade ago; and secondly, some kind of “New Deal” may be necessary to jolt the developed world back to growth.

Finally, the stockmarket doesn’t believe the numbers. Dividend yields on companies have not followed the yields on bonds down. The prospective yield on the FTSE 100, for example, for calendar year 2019 is 4.4% (source: Link Asset Services) although we have to add the very important caveat that company dividends are not guaranteed and can fall.

In the stockmarket, the original looking-glass incident occurred when company dividend yields passed through the yield on gilts. It became characterised as the “reverse yield-gap.” Company dividends were higher than gilt yields because they were recognised and seen to be riskier so investors required a higher return to compensate them for this risk.

The White Queen can at least take some comfort from the fact that the “yield-gap” has again passed through the looking-glass but in the opposite direction.