Time Scaling of Mean and Standard Deviation of Returns
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1. Context
In this short video from FRM Part 1 curriculum, we explore rules of thumb for scaling mean / expected value of returns and volatility / standard deviation when the time period or horizon is changed. Based on simple reasoning using continuously compounded returns with no interim payments and using the i.i.d assumption, we arrive at the rules that mean return scales with time and volatility of returns scales with square root of time. The details of the reading in which this topic appears are given below:
| Area | Valuation and Risk Models |
| Reading | Quantifying Volatility In VaR Models |
| Reference | Linda Allen, Jacob Boudoukh and Anthony Saunders, Chapter 2. Quantifying Volatility in VaR Models In Understanding Market, Credit and Operational Risk: The Value at Risk Approach, (New York: Wiley-Blackwell, 2004). |