# RiskMetrics Half-Life and Decay Factor Settings

I have been reading about the RiskMetrics methodology. I read that RiskMetrics recommend a lambda of 0.94 for daily data and 0.97 for monthly data. I would like to convert these numbers to half-lives. I have the formula $$Halflife=\frac{log(0.5)}{log(\lambda)}$$.

I have 3 questions:

1. with the recommended decay factor of 0.94 I get a half life of 11 days for daily data. This strikes me as incredibly short. Is this correct or am I missing something?
2. does this imply for monthly data and a decay factor of 0.97 I should use a half-life of 23 months? This strikes me as quite long.
3. Are the recommended decay factors the same for estimating volatility and correlations or do RiskMetrics recommend different decay factors for each?

# Question 1 and 2:

Preliminary: When working with the EWMA model, it is in our best interest to find a choice of $$\lambda$$ that produces the best predictive accuracy, while adhering to the properties of a covariance matrix (ie. symmetry and positive semi-definite). The best predictive accuracy for the model, is obtained by finding a balance between the arrival of new volatility shocks, $$r_{t-1}^2$$, and the information inherent in past volatility, $$\sigma_{t-1}^2$$.$$^{[1]}$$ The authors in the RiskMetrics paper (1994) do exactly that (see pp. 98 - 100 detailing their estimation of the optimal decay factor across 450+ time-series).

To answer your first two questions: the characteristics of the monthly return-series can differ from the daily counterpart. The recurrence of significant volatility shocks is often greater under daily frequencies, whereas sparsely sampling the return process on a monthly basis, might diminish/eliminate some of these effects. Thus, the daily EWMA model puts more weight on $$r_{t-1}^2$$ to accommodate for the recent volatility shocks, as opposed to the monthly EWMA model, which then favours an increased smoothing of the volatility process (by further increasing $$\lambda$$ to 0.97).

As such, the half-life of 11 days for the daily volatility process implies that it favours newer information and is therefore more responsive to recent shocks. Vice-versa for the monthly process. In general, for $$\lambda \rightarrow 1$$, the less responsive the process becomes.

Yes, it might very well be adequate that the half-life is only 11 days for the daily volatility process, but 23 months for the monthly volatility process. If you're still sceptical, you can estimate $$\lambda$$ yourself on your own data (see bottom of my answer).

$$^{[1]}$$ The recursive equation of the EWMA model is defined as: $$\sigma_t^2 = (1-\lambda) \cdot r_{t-1}^2 + \lambda \cdot \sigma_{t-1}^2.$$

# Question 3: They use the same decay factor for the correlation dynamics

On p. 97 they write:

RiskMetrics applies one optimal decay factor to the entire covariance matrix. That is, we use one decay factor for the daily volatility and correlation matrix and one for the monthly volatility and correlation matrix. This decay factor is determined from individual variance forecasts across 450 time series (this process will be discussed in Section 5.3.2.2).

This makes sense, as you can easily extend the model to a multivariate case. On p. 100 Table 5.9, they further summarize their conclusions for the RiskMetrics volatility- and correlation-forecasts.

If you are still sceptical whether the authors choice of decay factor fits your purpose, you can estimate $$\lambda$$ yourself via Maximum Likelihood Estimation. Just see that the EWMA model is a restricted IGARCH model with $$\omega = 0$$ and $$\lambda$$ being equivalent to the autoregressive parameter, $$\beta$$. In R the decay factor can be estimated in the rugarch package and there's a tutorial on it here.

• Hey @TheUser. Did my answer help with your problem? Do you have some additional questions or something you're confused about? Then feel free to address them in the comments below my answer. Some feedback would be appreciated :-)
– Pleb
Oct 14, 2022 at 7:00