the plan for the future
9 February 2021
Stock markets are at all-time highs while future economic prospects appear poor. That may seem weird and unnatural, perhaps even surreal, but it is The Invisible Hand doing its job. The Invisible Hand was last not seen on the moorlands of Nijverdal, the Netherlands. Interest rates play a major role in a process called discounting. Discounting is determining the present value of future payments.1
If the interest rate is positive then € 1,000 now is worth more than € 1,000 in the future because if you receive the money now, you can put it in a bank account and receive interest and have more money in the future. For instance, if the interest rate is 3% then € 1,000 in the present is worth € 1,030 after a year and not € 1,000.
So how much is a cash flow of € 1,000 in a year worth in the present? That is the reverse calculation and it depends on the interest rate. The formula for the present value of a single future cashflow is:
Present Value = Future Cashflow / (1 + (Interest Rate / 100)) ^ Number of Years
If you have multiple future cash flows then you can add them up. An example can explain it. Assume that the interest rate on government bonds is 3% and you own a 5% government bond that still has two years to go before the principal of € 1,000 will be repaid. You will also receive € 50 in interest after one year and another € 50 in two years' time when the bond is due. If you intend to sell the bond today, you want to know its present value.
There are two cash flows. You will first receive € 50 after one year. The present value of that cash flow is: € 50 / (1 + (3 / 100)) ^ 1 = € 48.54. After two years you will receive an additional € 1,050. The present value of that amount is: € 1,050 / (1 + (3 / 100)) ^ 2 = € 989.73. And so the present value of the bond is € 48.54 + € 989.73 = € 1,038.27.
At higher interest rates the bond will be worth less. If the interest rate is 5%, its present value is (€ 50 / (1 + (5 / 100)) ^ 1) + € 1,050 / (1 + (5 / 100)) ^ 2 = € 47.62 + € 952.38 = € 1000 exactly, which is to be expected. At lower interest rates the bond will be worth more. At an interest rate of 2% the present value is (€ 50 / (1 + (2 / 100)) ^ 1) + € 1,050 / (1 + (2 / 100)) ^ 2 = € 49.02 + € 1,009.23 = € 1,058.25.
It is also possible to calculate the present value at a negative interest rate. If the interest rate is -2%, the present value of the bond is: € 50 / (1 + (-2 / 100)) ^ 1 + € 1,050 / (1 + (-2 / 100)) ^ 2 = € 51.02 + € 1,093.29 = € 1,144.31. It means that the € 1,100 you are going to receive in the future is worth € 1,144.31 in the present. In other words, investors are willing to pay € 1,144.31 now to receive € 1,100 in the future!
At lower interest rates bonds are worth more. Something similar happens to other assets that provide cash flows like stocks and real estate. The present value of future dividends and rents rises when interest rates go lower, even though these payments are less certain than bond coupons. That is a major reason why the prices of stocks and real estate have risen in the face of pale economic prospects.
But why do asset values go to such extremes? The pundits on financial television have difficulty explaining this. And usually they do not bother. But there is an explanation. Imagine a € 1,000 government bond yielding only 0% that pays back the principal over 100 years while the interest rate on government bonds is -3%. The present value of that bond is: € 1,000 / (1 + (3 / 100)) ^ 100 = € 21,029.
It means that investors are willing to pay € 21,029 to get € 1,000 in 100 year's time. So despite zero returns, investors are willing to pay 21 times the amount they will receive. That seems crazy and it is unlikely to happen, but it demonstrates why investors are willing to bid up stock prices despite dim future prospects. Faced with such losses on long-term debts, investors prefer stocks, real estate, gold, and bitcoin. It may seem a recipe for financial disaster but it doesn't have to be.
Until now money is put into circulation with interest so more money has to be returned than the principal. This extra money has to be created producing inflation. With negative interest rates, the opposite happens. Money disappears from circulation, and prices go down. So if you invest in gold or bitcoin, you are likely to lose money too in the long run. Prices of real estate and stocks are likely to go down over time but rents and dividends may cover the losses.
The thing to remember is that € 1,000 in 100 year's time may buy a lot more than it does now. If the rate of deflation is 3% there is no loss of purchasing power if you pay € 21,029 to get € 1,000 in 100 years'time. It appears weird and unnatural but there are reasons to believe that with negative interest rates the economy will be doing fine with fewer crises. And so interest-free money with a holding fee may be the money of the future.
1. Discounting. James Chen (updated 5 December 2020). Investopedia. https://www.investopedia.com/terms/d/discounting.asp