I run these types of analysis professionally and can confirm that they indeed are useful. But please make sure you analyse returns not prices. This is also highlighted by the critique in Slender Means:
To perform PCA, your data have to have a meaningful covariance matrix
(or correlation matrix, but the conditions are equivalent). They analyze
stock prices, which are non-stationary time series variables.
A typical usecase in our analysis is to quantify systemic risk in the market place. The more co-movement in the market, the less of a diversification you really have in your portfolio. This can, for example, be quantified by the amount of variance described by the first principal component. Which is identical to the value of the first eigenvalue.
For financial data, one typically examines a moving window over time. Some form of decay factor that downweights older observations is useful. For daily data, anything from 20-60 days, for weekly data maybe 1-2 years, all depending on your needs.
Note that for global financial markets, with tens- or hundreds of thousands of asset prices changing continuously, one typicall can't run a 100K vs 100K covariance matrix. Instead, typical usecase is to run the analysis per country, per sector or other more meaningful groups. Alternatively break down the return by a set of underlying factors (value, size, quality, credit ....) and do the PCA / Covariance analysis on these.
Some nice articles include Attilio Meucci's discussion on effective number of bets:
, and also Ledoit and Wolf's Honey I shrunk the sample covariance matrix
For a financially oriented introduction to stationarity, why not start with Investopedia. It's not rigorous, but conveys the main ideas.
EDIT: Here is a 3-stock example showing Apple, Google and Dow Jones with daily returns through 2015. The upper triangle shows correlation of return, the lower triangle show correlation of prices.
As can be seen, Apple has a higher price-correlation with Dow (bottom left 0.76) than return correlation (top right 0.66). What can we learn from that? Not much. Google has a negative price correlation with both Apple (-0.28) and Dow (-0.27). Again, not much to learn from that. However, the return correlations tell us that Apple and Google both have a fairly high correlation with the Dow (0.66 and 0.53 respectively). That tell us something about the co-movement (price-change) of assets in a portfolio. That is useful information.
The main point is that although price correlation can be just as easily computed, it is not interesting. Why? Because the price of a stock is not interesting in itself. The price change, however, is very interesting.