Measuring Strategy Alpha Decay with Information and Return Tests

# How to compute the alpha decay of a strategy?


# How to compute the alpha decay of a strategy?












How can one compute the alpha decay of a systematic trading strategy?

## Answer by strimp099 (score 11, accepted)

https://quant.stackexchange.com/a/2414

The short answer (which represents one way of surely many ways to do it) is to watch the t-stat of a performance metric such as information coefficient vanish over time. IC is the correlation of predicted expected returns from your alpha strategy to the underlying benchmark.

Look at the expected returns your alpha strategy predicted over the past N time intervals and see how those predicted returns were correlated with the benchmark. This is the IC.

The crux of course is that you need to test if the IC is statistically different from zero or is just random noise. You would do this by computing the t-stat over time and watch it decay as the strategy you managed to build over hundreds of hours of research is unceremoniously drained of edge.

## Answer by Tal Fishman (score 3)

https://quant.stackexchange.com/a/2428

You can come up with many specific answers depending on the application, such as high frequency vs. low frequency, or cross-sectional (e.g. single stock equity relative value) vs. time-series strategies (e.g. trading E-mini S&P 500) (strimp099's suggestion of using information coefficient is a good suggestion for equity relative value). However, a general answer that is likely to at least give you some indication for any strategy is to look at the time series of returns over two adjacent periods and perform a t-test for difference in means. If the later period has a statistically significantly lower mean return, then the alpha has likely decayed. Measuring the precise degree of decay is going to be nearly impossible for anything but a relatively high frequency strategy with a very long time sample.

## Answer by Patrick Burns (score 2)

https://quant.stackexchange.com/a/2476

The blog post http://www.portfolioprobe.com/2011/11/30/alpha-decay-in-portfolios/ tells of one possible method:

Generate two sets of random portfolios. Both sets satisfy your portfolio constraints, and one set is additionally constrained to have high expected returns. You can now look at the distribution of the difference in returns for various time frames.

## Answer by Dhruvil Chodvadiya (score 0)

https://quant.stackexchange.com/a/85366

Alpha decay is not just a drop in returns or Sharpe; it is usually a loss of effective information flow. In many cases the strategy keeps trading and looks statistically fine, while the amount of new information it extracts from the market collapses.

Below is a clean way to think about it mathematically and practically.

- What alpha really means

Let $r_{t+1}$ be the excess return at time $t+1$ and $\mathcal{F}_t$ the information set used by the strategy.

Alpha is the conditional expectation

$$ \alpha_t = \mathbb{E}[r_{t+1} \mid \mathcal{F}_t]. $$

A trading rule produces positions $w_t = g(\mathcal{F}_t)$, and realized PnL is

$$ X_t = w_t \, r_{t+1}. $$

Alpha is therefore not directly observable; it is inferred from time averages of $X_t$.

- The hidden assumption in most alpha measurements

Almost all standard approaches implicitly assume that $X_t$ is stationary and ergodic in observed time $t$. Under this assumption,

$$ \frac{1}{T} \sum_{t=1}^T X_t \to \mathbb{E}[X] $$

as $T$ grows, and metrics like Sharpe ratio, t-statistics, and cross-validation are meaningful.

In practice, this assumption often fails.

- A more realistic model: time-changed alpha

A useful way to model real strategies is as a time-changed process:

$$ X_t = Z_{\tau(t)}. $$

Here,

- $Z_s$ is an ergodic intrinsic alpha process,

- $\tau(t)$ is effective (intrinsic) time.

Intrinsic time does not have to advance linearly. A simple representation is

$$ \tau(t) = \int_0^t \psi(Y_s)\,ds, $$

where $Y_t$ represents latent conditions such as crowding or liquidity, and $\psi(Y_t) \ge 0$ controls the rate at which new information arrives.

- What alpha decay actually is

There are three distinct cases:







The third case is dangerous because standard performance metrics often remain stable.

- Why rolling Sharpe ratios can be misleading

Sharpe and related statistics assume that the variance of the sample mean scales like $1/T$.

Under time change, the correct scaling is $1/\tau(T)$.

If $\tau(T) \ll T$, then variance is underestimated, confidence intervals are wrong, and backtests appear more stable than they should.

- How to measure alpha decay in practice

The effective time $\tau(t)$ is not directly observable, but it can be inferred indirectly.

(a) Effective sample size

Estimate autocorrelations $\rho_k$ of $X_t$ and compute

$$ N_{\mathrm{eff}} \approx \frac{T}{1 + 2\sum_k \rho_k}. $$

If $N_{\mathrm{eff}}$ grows much more slowly than $T$, information flow is decaying.

(b) Information coefficient accumulation

Let $\mathrm{IC}_t = \mathrm{Corr}(\text{signal}_t,\ \text{return}_{t+1})$. If $\sum_t \mathrm{IC}_t^2$ grows sublinearly in time, the strategy is aging.

(c) Failure of empirical convergence

If long-horizon averages of $X_t$ fail to stabilize despite large $T$, effective time is not advancing.

- Key takeaway

Alpha decay is often not a parameter-drift or overfitting problem. It is a time problem: observed time continues to pass, but intrinsic informational time slows or collapses.

Metrics that measure information flow are therefore more reliable than metrics that only measure recent performance.