A Brief History of Risk and Return
For both risk and return, increasing order is
b, c, a, d
. On average, the higher the risk of an
investment, the higher is its expected return.
Since the price didn’t change, the capital gains yield was zero.
If the total return was four percent,
then the dividend yield must be four percent.
It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
To calculate an arithmetic return, you simply sum the returns and divide by the number of returns.
As such, arithmetic returns do not account for the effects of compounding. Geometric returns do
account for the effects of compounding. As an investor, the more important return of an asset is the
Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
approximate a holding period return. When predicting a holding period return, the arithmetic return
will tend to be too high and the geometric return will tend to be too low. Blume’s formula
statistically adjusts these returns for different holding period expected returns.
T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the
rate of inflation.
Risk premiums are about the same whether or not we account for inflation. The reason is that risk
premiums are the difference between two returns, so inflation essentially nets out.
Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
are smaller than pretax returns.
We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
will probably lose money in real dollars for a taxable investor.
It is important not to lose sight of the fact that the results we have discussed cover over 70 years,
well beyond the investing lifetime for most of us. There have been extended periods during which
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
horizons, and high volatility investments may be very inappropriate in such cases. There are other
reasons, but we will defer discussion of these to later chapters.