What Is Volatility?
Volatility is a measure of how much an asset's price fluctuates. It is calculated using the statistical concept of standard deviation - the higher the value, the wider the price swings (and the higher the risk). For example, an asset with 20% annual volatility is likely to fluctuate within a range of roughly 20% above or below its average return.
For an intuitive understanding, books on risk and standard deviation make the meaning of standard deviation and volatility easy to grasp.
In concrete terms, Japanese equities (TOPIX) have an annual volatility of roughly 15 to 20%, developed-market equities around 15 to 18%, and developed-market bonds about 5 to 8%. Equities are more volatile than bonds, and in return they are expected to deliver higher returns over the long term. This is the risk-return tradeoff.
Estimating Potential Losses from Standard Deviation
Assuming a normal distribution, there is roughly a 68% probability that returns will fall within one standard deviation of the mean, and about 95% within two standard deviations. For an asset with an expected return of 5% and a standard deviation of 20%, the one-year return is estimated to land between negative 15% and positive 25% about 68% of the time, and between negative 35% and positive 45% about 95% of the time.
In other words, if you invest 100 man-yen, there is roughly a 2.5% chance it could drop to 65 man-yen within a year. Knowing this worst-case scenario in advance helps you stay calm during market crashes. A rational approach is to work backward from the maximum loss you can tolerate to determine your allocation between equities and bonds.
Reducing Volatility Through Diversification
Combining assets with different price movements lowers the overall portfolio volatility below the simple average of individual asset volatilities. This is the power of diversification. Even if an all-equity portfolio has 20% volatility, adding 40% bonds can bring it down to around 12 to 13%. Returns may dip slightly, but the risk-adjusted return (Sharpe ratio) often improves.
books on quantitative risk analysis for investors teach you concrete methods for quantifying and comparing investment risk.