Choosing Volatility Measures to Reflect Investors’ Experience
Summary
The document asks how portfolio volatility reports might better match investors’ perception of risk. It starts from the sample standard deviation of monthly returns and notes that the estimate depends on the length of the lookback window. The questioner proposes three years as a compromise between recency and sample size, while recognizing that this choice may be debatable.
The responses describe several alternatives and caveats. One cites a study in which median absolute deviation aligned better with investment professionals’ intuitive volatility judgments, including for normally distributed samples; the evidence came from a small group. Another emphasizes that suitable horizons depend on client risk horizons and that the common thirty-observation heuristic relies on assumptions that may not hold for nonstationary returns. Exponentially weighted estimates or GARCH conditional volatility are suggested as options, while GIPS standards may guide reporting. The discussion offers no universal lookback that captures every investor’s experience, and separates a statistical estimate from individual risk perception.
Key ideas
- Sample volatility estimates change with the chosen return lookback window.
- A cited study found median absolute deviation better matched a small sample of professionals’ intuitive judgments.
- The common thirty-observation heuristic depends on assumptions that may fail for nonstationary returns.
- Exponentially weighted estimates and GARCH conditional volatility are possible alternatives.
- The appropriate risk horizon may differ across investors.
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Full text
# How to measure investors' "experienced" volatility?
# How to measure investors' "experienced" volatility?
In asset allocation, you usually send reports to your clients where you will report the volatility of its portfolio. Assuming you only have monthly returns, you will compute volatility over a considered period of $n$ months with the classic sample volatility estimate:
$$\sigma_s=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}, \quad \bar{x}=\frac{1}{n}\sum_{i=1}^N x_i$$
The result you will get for $\sigma_s$ depends very much on the number of months $n$ you decide to take into account. Hence, I think that this measure can become pretty abstract to unsophisticated investors and they might find it pretty different from the "feeling" the have of the volatility of their portfolio, what I call the "experienced" volatility.
My question is, has there been any research aiming to find out which $n$ is the best to make sure that the measure is closest to the experienced volatility?
I believe this is very much linked to behavioral finance and it might very well depend on the risk-aversion or the sophistication of the investor.
I tried to answer my question by proposing the following:
I assume that investors will be biased by the most recent events in the market; if they have been with you 10 years, they will remember 2008-2012 and would have forgot the quiet and lucrative early years. Hence, I took $n=36$, 3 years, as I thought is was taking a recent enough sample, yet had enough data ($n>30$, intuitively... it might be arguable) to measure a properly the estimate $\sigma_s$.
Does this make sense?
## Answer by snth (score 5)
https://quant.stackexchange.com/a/3410
There is a paper by Goldstein and Taleb (2007) which tries to address this question of what number captures investors intuitive feelings of the volatility of series of returns and whether this coincides with the standard deviation of returns.
What they found was that Median Absolute Deviation does a much better job of capturing this intuition in a small sample of investment professionals, even when the return series were sampled from a normal distribution.
## Answer by Zarbouzou (score 3)
https://quant.stackexchange.com/a/3362
Usually very good questions don't come with straight answers and I think this is the case here. I believe you have two (unfortunatly linked) problems here. One is to get a sense of investors aversion to risk and the other is to get a statistically "receivable" estimate of volatility.
1/ Different investors may be willing to take risk on significantly different time frames. This means that the answer is going to be very dependent on your client. Survey studies could seem to answer this question but will probably hide the problem that investors themselves don't really fully grasp the proper time horizon they are willing to take risk. In any cases you will need to introduce expected payoff to start getting an answer.
2/ As for the statistical estimate, you suggest n>30. It is a fairly common number economists use but is based on strong stationnary hypothesis. This THEORETICAL number (based on the convergence of student to normal) will be very dependent on the model you use to describe your data (obviously driven by your data). Unfortunatly, even returns exhibit non stationnary characterisics. Using weighting procedure (EWMA for example) might help you but will still not be parameter free and hence not fully answer the question.
Good luck with this one.
## Answer by John (score 3)
https://quant.stackexchange.com/a/3398
1) If you want to show an unsophisticated investor with like a real-time estimate of volatility, my main suggestion would be to fit a Garch model to the returns and use those estimates of the conditional volatility. Just provide a chart of it, rather than showing the model and all the details that go into calculating it.
2) If that is too complicated, you might try checking out GIPS performance standards for an industry standard approach to reporting performance.
3) People generally call it realized volatility rather than experienced volatility.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.