Estimating EWMA Correlation Decay from Return Data

Summary

The document discusses how to choose the decay factor, lambda, in an exponentially weighted moving average model when estimating correlations. It says familiar RiskMetrics values for daily and monthly observations are not universal recommendations for yearly data, and describes estimating lambda from paired asset returns instead. The suggested approach fits the covariance recursion to observed returns while treating lambda as the unknown parameter, then uses the forecast covariance divided by the product of forecast volatilities to obtain a one-period-ahead correlation.

The response cautions that the original parameter choice was arbitrary and that the suitable value may depend on return volatility and change over time. It also notes that the return window used to estimate volatility is a choice rather than a fixed rule. The document does not provide a worked estimation, a statistical fitting criterion, or empirical comparisons, so it offers a conceptual procedure rather than a validated specification for annual data.

Key ideas

• EWMA lambda can be estimated from paired asset returns rather than selected from a frequency-based convention.
• The covariance forecast is converted to correlation by scaling with the two volatility forecasts.
• The preferred decay factor may vary with return volatility and over time.
• The response gives no worked fit or evidence that its approach is optimal for yearly observations.

Tags

# Estimating correlation using EWMA


# Estimating correlation using EWMA












I am using an EWMA model to evaluate the correlation between yearly time series.

I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data.

Is there a value suggested for yearly data? If not, how can it be estimated?

## Answer by Quantopik (score 4, accepted)

https://quant.stackexchange.com/a/18710

The $\lambda$ value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model:

$\sigma^2_{12,t+1}$ $=$ $\lambda$$*$$\sigma^2_{12,t-1}$$+$$(1-\lambda)$$r_{1,t}$$*$$r_{2,t}$;

given $r_{1,t}$ and $r_{2,t}$ respectively as the returns for the asset 1 and 2 and $\sigma^2_{12,t}$ the volatility at time t.

Solving by $\lambda$ as unique unknown variable, you can find the $\lambda$ estimation.

To compute the correlation forecast, replace $\sigma^2_{12,t+1}$ in:

$\rho_{t+1}$ $=$ $\frac{\sigma^2_{12,t+1}}{\sigma_{1,t+1}* \sigma_{2,t+1}}$;

where $\rho_{t+1}$ is the forecast of the correlation 1 period ahead.

Here the reference of the original paper by JP Morgan; I suggest you to read the paper an estimate $\lambda$ again, since its value depends on the volatility of returns and it changes over time.

The authors used a 20-day returns period to estimate asset volatility and returns and the choice of such time period, again, was arbitrary.

Hope this helps.

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