The textbook examines the historical risk and return for the three main asset categories (1926-2017).

T-bills: the safest investment on earth. The price paid for this safety is steep: the return is only 3.4%, which is barely above the inflation rate of 2.9% for the period. Further, although many academicians consider T-bills to be "riskless," a quick perusal of the T-bill graph shows considerable variation of return, meaning that you cannot depend on a constant income stream. This risk is properly reflected in the standard deviation of 3.1%. The best that can be said for the performance of T-bills is that they keep pace with inflation in the long run.

Long-term government bonds carry one big risk: interest rates risk. The longer the maturity of the bond the worse the damage. For bearing this risk, investors are rewarded with another 1.5% of long-term return. In the long run, investors can expect a real return (inflation-adjusted) of about 2.6% with a standard deviation of 9.9%.

The rewards of large company stocks are considerable: a real return of greater than 7.3%. This return does not come free, of course. The standard deviation is 19.8%. You can lose more than 40% in a bad year; during the calendar years 1929-32 the inflation-adjusted ("real") value of this investment class decreased by almost two-thirds.

$1 in 1900 would have grown to $1,654 in 2017 if invested in stocks, only $10.20 if invested in bonds, and to $2.60 if invested in T-bills. The message is clear: stocks are to be held for the long term. Don't worry too much about the short-term volatility of the markets; in the long run stocks will almost always have higher returns than bonds.

Stocks have outperformed bonds consistently over long periods of time. However, stocks are much riskier and investors demand compensation for bearing the risk. The question is: is the premium too big?

Other Investment Characteristics

Two assumptions are usually made when investors perform investment analysis using mean and variance.

• Returns are normally distributed.
• Markets are operationally efficient.

Is normality a good approximation of returns? In fact, returns are not quite normally distributed. The biggest departure from normality is that extremely bad returns are more likely than predicted by the normal distribution (fat tails).

There are operational limitations of the market that affect the choice of investments. One such limitation is liquidity, which affects the cost of trading.