Risk is different for different time periods. For example, there
is good evidence that stock returns are uncorrelated from year
to year. Therefore, the standard deviation in yearly stock returns
will __decline__ as the square root of the number of years.
Bond returns are negatively correlated from year to year. Thus
although the bond standard deviation will also decrease with the
number of years, it will not scale directly as the square root
of the number of years. See Table 2 for some data.

a) STOCKS | ||||
---|---|---|---|---|

Holding period (years) | ||||

1 | 5 | 10 | 25 | |

No. of holding periods | 52 | 48 | 43 | 28 |

No. of loss periods | 18 | 7 | 2 | 0 |

No. of periods beating inflation | 33 | 36 | 40 | 28 |

Best annual return | 54% | 24% | 20% | 15% |

Worst annual return | -43% | -12% | -1% | 6% |

b) BONDS | ||||

Holding period (years) | ||||

1 | 5 | 10 | 25 | |

No. of holding periods | 52 | 48 | 43 | 28 |

No. of loss periods | 10 | 2 | 0 | 0 |

No. of periods beating inflation | 33 | 26 | 20 | 11 |

Best annual return | 19% | 10% | 7% | 5% |

Worst annual return | -8% | -2% | 1% | 2% |

c) T-BILLS | ||||

Holding period (years) | ||||

1 | 5 | 10 | 25 | |

No. of holding periods | 52 | 48 | 43 | 28 |

No. of loss periods | 0 | 0 | 0 | 0 |

No. of periods beating inflation | 29 | 26 | 21 | 7 |

Best annual return | 8% | 6% | 6% | 4% |

Worst annual return | 0% | 0% | 0% | 1% |

Another way to look at this is as follows. For the moment, ignore transaction costs and assume you want to purchase and sell the S&P 500 (the 500 biggest corporations in America).

1. If you buy one day and sell the next day, you would have a loss a little less than half the time.

2. If you buy one year and sell one year later, you would have a loss about a third of the time.

3. If you buy one year and sell five years later, you would have a loss only about one-seventh of the time.

4. If you buy one year and sell 25 years later, you would never have a loss. Your worst return in any 25 year period would be better than the best return from any period if you held bonds or T-bills.

Inflation must be included in return calculations over time periods much longer than a year. The usual way of doing so is to subtract the rate of inflation from the return to derive a "real" or "inflation-adjusted "return. (Purists will note that the correct way of accounting for inflation is to divide total return over a given period by the ratio of the Consumer Price Index at the end of the period to the beginning of the period. For small inflation rates, this gives the simple subtraction formula.)

Historical performance over the last 60 years shows that risk-free
investments such as Treasury bills, Certificates of Deposit, Money-Market
Funds, etc. typically __yield the expected current inflation
rate__. That is, *the real rate of return of risk-free investments
is zero!* There are short periods of time, such as the last
few years, where this is not true, but it is a very good approximation
for longer time periods. Thus, in the absence of taxes, you
can preserve your money in risk-free investments, but you cannot
benefit from the power of compound interest since you are not
beating inflation. Since most of us are taxed, in real terms you
will end up __losing money__ with risk-free investments. __The
only way to significantly increase your net worth is to invest
in "risky" investments which offer a higher return than
you can obtain in "risk-free" investments!__

Therefore, one must be conscious of your investment horizon. If you will need your money within 4 years or so, inflation can be ignored in general. You must place your money in relatively safe, lower return investments in order to make sure that the money is there when you need it.

If you are investing for longer periods than about 4 years, you must beat inflation and taxes or else you will end up losing money, even if your money is in "safe" investments. The only way to do this is to place your money in "risky" investments. Fortunately, because in general standard deviations decline with time, "risky" investments often lose almost all their risk over long time intervals!

You have understood this section if you understand the following sentence. For long time periods, "safe" investments lose money and only "risky" investments become safe!

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