Wiki Wiki Web

Investment Discount Rate

Short Term Evidence of Asset Returns

Financials assets returns are very volatile, making estimation uncertain over short period.

The GIRY study shows returns above inflation of 6.3% for US and 4.2% for Europe from 1900 to 2016. (GIRY or Global Investment Review Yearbook was conducted by ABN Amro before its demise in 2008, and then by Credit Suisse before its demise in 2022.)

  • USA: real returns of 6.3% for stocks, 2% for bonds, 0.8% for bills
  • World ex-USA: real returns of 4.3% for stocks, 1.5% for bonds
  • Europe only: 4.2% for stocks, 1.1% for bonds

While the reasons for the US outperformance appear clear with 20/20 hindsight, annual volatility experienced in the US was 21% over this period which means that average return over 100 years have a 2.1% standard deviation, which means there is a 15% chance that US got lucky that century and long term returns are the same in US and rest of world.

The real returns of 4% to 6% observed above include capital gains and assume tax-free investors. For much of the fiat era since 1913, World Wars led not only to taxation but also to financial repression at levels that differed depending on location:

  • Russian and Chinese investments were confiscated by the communist government in 1917 and 1946
  • Austro-Hungarian bond and stock holdings were decimated
  • All nations except US, UK and its colonies saw strong inflation that was not compensated by interest rates, a confiscation by inflation
  • The US money market rate compensated investors of inflation, with the caveat that inflation definition was changed for political reason to lower the cost of entitlements, which leads to an unmeasured confiscation of part of the return of the t-bill.

The conclusion is that fiat money investments did not provide a positive return when expressed in gold due to confiscation, financial repression or inflation.

Long Term Evidence of Stock Return

Stock markets existed much earlier than the 20th century, to enable financing maritime trade in the 17th and then to finance industrialization in the 19th. Nominal and real returns are very similar according to GFD except in the 20th century:

  • 1600s 8.17% real
  • 1700s 5.1% real (5.39% nominal)
  • 1800s 6.2% (6.33% nominal)
  • 1900s: 6.29% (9.67% nominal)

We can see the nominal return increasing greatly in the 20th century, with a moderate 3% compound inflation, which was so low only in the country that won both world wars, the US.

Indeed, for much of the preindustrial time, farms and other productive assets would sell at a level where they produce 5% net income. There were some lower yields, such British Gilts, which traded with a yield as low as 2% while lower quality countries would need to pay 5% interest.

To obtain such returns over the long term, one would have to invest in the Netherlands as they waged an independence war against Spain, turn to British investments and then European and later US investments. Such investments would not be possible unless the individual migrates and assimilates in the elite of each successive country.

Longer term evidence for several thousands of years in the Bronze Age cuneiform tablets is the 1 Shekel per month per Mina interest rate, which corresponds to 20% annually.

So, we see returns of 20% for most of mankind's history until the Iron Age, and about 5% in the more recent 4 centuries of the modern European era. We saw Japan going for near 0 and even negative rates, so we turn now to a normative explanation of required yield.

Normative Explanation of Required Yield

Let's assume that an investment of $1$ is possible with a return of $r$ for a duration of $T$ and the discount yield is $y$. The breakeven value for the investment is given by $$ \int_0^T r \exp(-yt)dt = 1 $$ and if the discount rate $y$ is small, we get a first order solution for the breakeven duration $T= 1/r$. If the discount rate $y$ is not small, then the duration required for breakeven is longer. Any productive time beyond accrues the investor an income.

  • The required time to fade for a Bronze Age investor at a yield of one shekel per mina or $20\%$ was 5 years.
  • The required time horizon of a modern investor paid 5% over a gold backed currency is 20 years.
  • The required time horizon for an investor buying a luxury house in Hong Kong with a yield of 0.25% above inflation is 400 years.
  • A bond with negative real yield loses money and does not have a positive investment horizon.

The Hong Kong real estate buyer is not trying to obtain a rental yield from his investment over 400 years, he is paying for the social signaling value of trophy property, and the security of property rights in that city. The bond buyer at negative real yield is either a regulatory captive buyer or someone fooled by the monetary illusion. His action can be reclassified as tax collection rather than investment in the case of JGB with the negative nominal yields and a positive inflation monetary policy target.

House Prices

In practice, we see house prices commanding a 5% to 10% net yield in many countries when no financing is available, the required net yield goes down as mortgage financing becomes available at rates below 5%.

We saw net yields go up to 15% during the mortgage foreclosure crisis in the US after 2010, As house sales were forced on a market where potential buyers could not obtain finance. Once finance became available, the house prices increased and net yields reverted to between 7% and slightly below the mortgage rate depending on the desirability of the location.

There are lifestyle properties with rates below 1% and required investment horizon of more than 100 years.

Stock Markets

Based on distribution to shareholders alone (by dividend and buybacks) and using a 5Y continued growth period followed by 5Y of fade, I compute that the stock market is priced with a yield between 5% during the 1989 crash and the 2009 Great Financial Crisis, and 2.5%, assuming my current tax level and an unchanged distribution policy by the company.

This is much lower than the observed 5% long term return delivered by the SP500, but this 5% performance includes a CAPE multiple expansion from 20 to 30 and a tax-free assumption on dividend that seems heroic for a foreign investor subject to WHT.

A 5% target return on invested capital is not a high hurdle for companies, as they often manage to reach 15%. What happens in such case is that investors with a 5% target will be 3x in stock price for each dollar invested in the company.

I get a 2.5% mkt cap weighted median yield assuming a growth fade from 5Y to 10Y. While the vast majority of stocks do not distribute money to owners and therefore have 0 or negative yield as in case of dilution, the largest market cap stocks have better characteristics including owner yield. The implied yield reached 8% during the GFC in 2009.