I’ll try a quick summary. I’m sure the guys here will correct me if I miss anything.
Mathematically a gilt/bond can’t have a negative yield. This is the calculation of the annual coupon dividend by sell price.
e.g. I pay a coupon of £5 and the selling price is £100. My yield is 5%.
Unless a gilt is flat out paying negative interest (meaning you just get back less at the end) you can’t really have a negative rate.
Given most gilts give a coupon this doesn’t work. The attraction of gilts is cash flow. I want that guaranteed (almost) interest payment.
However, yield to maturity takes into account how long you hold this gilt for and the par value (the amount you get back at the end of the period.)
Keep in mind this only applies if you buy the gilt and then hold it to maturity.
e.g. You pay £100 for this gilt, it lasts two years and pays out £5 a year. Assuming you get back £100 at the end of two years the YTM would be 10%. You put in £100 and after two years walked away with £110.
Now let’s say you get back less than what you paid.
e.g. You paid £100 and you get £5 a year interest payments, and this gilt lasts two years. At the end of two years, I pay you back for £80, rather than the original £100. You get back £80 plus the interest payments worth £10 meaning you paid £100 and got back £90. You have a negative yield to maturity of -10%.
You can get more advance by adding in the rate of inflation, and the “value of money” where the interest payments mean you are losing buying power over time, but that is a different story.
Bottom line is why would anyway buy a negative-yielding product.
Either, you don’t intend to hold onto it until maturity. e.g. interest rates drop and suddenly these interest payments become valuable increasing the value of the gilt (higher value but same payment pushes the yield down, £110 to buy it but it’s still paying £5 a year mean the yield is now 4.55%~.) Or you hold to maturity because you want reliable payments. If you are a pension fund, for instance, you need cash flow. You’d rather lose out with a small negative yield but at least you can pay all your customers in drawdown reliability.
Generally, higher gilt yields mean weaker equity prices (why invest in risky stocks when the government is guaranteeing payments?) and the flip is true as well. Negative yields push more people into riskier investments to try and keep up their own rate of return. If I can’t make £5 a year with gilts I’ll find an investment which can.
Though recently in America we have seen bond and equities prices rise together so I guess people are simply unpredictable.