If stock X appreciates 1.5% in one month, the annualized gain for that stock over a twelve month period is (12 x 1.5%) = 18%. Compounded over the 12 month period, the gain is (1.015)^12 -1 = 19.6%.
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A gain on an investment expressed in yearly terms, even though the variable does not directly apply to a year. That is, an annualized gain has been mathematically converted to yearly terms. For example, if the return rate on an investment is 2% after one month, one computes the annualized return by multiplying by 12, resulting in a 24% return rate. An annualized variable is often theoretical; there is no guarantee that the return rate in the example above will be 24% if it is calculated after only a month or two.
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