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 Post subject: What's the Risk?
 Post Posted: Sun Sep 24, 2017 3:25 pm 
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Some outcomes are more likely than others. Choosing a course based only on the highest mean or lowest standard deviation from historical data provides only a partial glimpse through the clouds of possibilities.

The higher the standard deviation, the more likely the mean is to vary from year to year. We can estimate the range of variation of the mean by using "confidence intervals". This "margin of error" must be included when estimating the chance of having a negative return. The more confident we want to be, the wider the range will be.
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To use a nautical metaphor, the mean is like the sea level, and the StdDev is like the average wave heights. A rougher sea will have higher wave crests. Suppose we measured the instantaneous water height (relative to the land elevation), once every minute for an hour. The StdDev of the data would be a fairly good estimate idea of the wave height. If we repeated measurements for the next hour, we would find that the StdDev was about the same as the first, but that the mean had shifted up or down - depending on the way the tide was heading.

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In a harbor, the chance of the dock being washed over depends on both the mean level (tide and strong wind driven) and the wave height (wind driven). If we want to keep the dock above water, we need to build it above the highest waves, at the highest tide. In some areas, like the coast of Maine, this puts the docks 20+ feet above the water at low tide.
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The chance of having a negative return can be computed using only the ratio of the mean and the standard deviation. That is, the chance of a down is year is equally likely if the mean & Std Dev is 30&15, 20&10, or 10&5. For example, if the Mean/StdDev is 2.0, it is 99% likely that no more than 9.9% of the returns will be negative, and 90% likely that that only 6.1% will be negative. However, we can be certain of a negative return at least 2.3% of the time.

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AGG (F Fund)
iShares Lehman Aggregate Bond (AGG)

S&P 500 (C Fund)
S&P 500 INDEX,RTH (^GSPC)

DWCPF (S Fund)
Dow Jones U.S. Completion Total Stock Market Index (^DWCPF)

EFA (I Fund)
iShares MSCI EAFE Index (EFA)